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Chapman, Robert D.; Bondurant, R. Limn, Jr.Comet Halley Returns. A Teacher's Guide,1985-1986.National Aeronautics and Space Administration,Greenbelte, Md. Goddard Space Flight Center.EP-197 .

Jul 8456p..

of Documents, U.Office, Washington, DC 20402.Guides - Classroom Use - Guides

MF01/PC03'Pluk Postage.*Astronomy; *Elementary School Science; ElementarySecondary Education; *Science Activities; ScienceEducation; *Secondary School Science*Comets

S. Government Printing

(For Teachers) (052)

ABSTRACT.

This booklet was designed'ai an aid for elementaryand secondary school teachers. It is divided into two distinct parts.Part I is a brief tutorial which introduces some of the mostimportant concepts about, comets. Areas addressed include: thehistorical importance of Comet Halley; how comets are found andnames; cometary orbits; what Comet Halley will look like; how andwhen this comet can be viewed; the nature of comets; and Comet Halleyin 1910. Part II contains a number of suggested activities builtaround the comet. These include both classrbom exercises andcarefully described field work to observe the comet. Guidance isprovided on where to look for the comet, how to observe it, and howto photograph'it. Virtually every exercise can be done withoutspecial equkpient; all that is ,needed

tosome thought on the part of

the teacher to adapt the activities to the appropriate grade. level. Alist of selected readings is provided at the end of the booklet forthose who desire a more in -depth treatment of the subject. (JN)

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Reproducti*

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VA DEPAimynNT co EDUCATION,NATIONAL INSTITUTE OF EDUCATION

EDUCATIONAL RESOURCES INFORMATIONCENTER (ERIC)

This ocume has been reproduced asrecer ad fro the person or otganizetionorig. mg it

I I Minor changes have been made to Itnprolreproduction quality

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"PERMISSU'N TO REPRODUCE THISMATERI HAS BEEN GRANTED BY

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COVER: Computer enhanced image of Comet Hefty from May 26, 1910. Theimage is the sum of four photographs originally made at the Helwan Observatoryin Egypt. The photographs were digitized, added together and computerenhanced at the Interactive Astronomical Data Analysis Facility of the GoddardSpace Flight Center by Dr. Daniel A. Xlinglesmith, Ill.

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COMETHALLEYRETURNS

A Teachers' Guide1985-1986

For Sale by the Superintendent of Documents,U.S. Government Printing Office,Washington, D.C. 20402

EP-197)1-

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National Aerqnautics andSpace Administration

Educational ProgramsOffice of Public Affairs

Goddard Space Flight CenterGreenbelt, Maryland 0771.

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Robert D. Chapman, Ph.D.Associate Chief,Laboratory for Astronomy and Solar PhysicsGoddard Space Flight CenterGreenbelt, Maryland

and

R. Lynn Bondurint, Jr., Ph.D.Educational Services Officer,Office of External AffaiisLewis Research CenterCleveland, Ohio

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PREFACE

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Comet Halley is on its way to a 1985.86 rendezvous with the earth and thesun. This most famous of all comets is sure to generate an increasing level ofinterest among 'the general .public and particularly among young people as itdraws ever nearer to us, The event offers an unparalleled learning opportunityfor students at all ,levels to gain the skills, understanding and enthusiasmnecessary to study science.

T his booklet has been put together as an aid for teachers in elementary and .

secondary schools. It is divided into two distinct parts. The first part is a brieftutorial which introduces some of the most important concepts about comets,,including their historical significance. In the limited space available, it Om onlyhit the high points. A list of selected readings is provided at the end of the1;soklet for those who desire a more in-depth treatment of the subject. Thesecond part of the booklet contains a number of suggested activities, builtaround the comet. These ,include both classroom exercises and carefullydescribed field work to observe the comet. Guidance is provided on where tolook for the cornet, how to observe it, and how to. photograph it. Virtually'every exercise can be done without special equipment All that is needed issome thought on the,part-01 the teacher to adapt the ictivities to the appro.,.priate g"rade level.

Both authors of the booklet have proven, outstanding abilitiett to communicatescience to laymen. In addition, Chapman is a recognized authority in the fieldof cometary research, having co-authored one of the few professional leveltextbooks on comets. The result of their collaboration is a scientificallyaccurate, and well-planned guide. If you use it well, your students will have aprofitable educational experience with lifelong rewards.

Elva BaileyEducational Programs OfficerGoddard Space Flight CenterJuly 1984

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CONTENTS

PART I. TOE NATURE OF COMETS

THE HISTORICAL IMPORTANCE PF COMET HALLEY

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HOW COMETS ARE FOUND AND NAMED 3

COMETARirORBITS ' 5

WHAT WILL COMET HALLEY LOOK LIKE 9

HOW AND, WHEN WE CAN VIEW COMET HALLEY 10

WHAT IS A COMET? 10

COMETS OF THE PAST 18

COMET HALLEY IN 1910 . 19

PLANS TO OBSERVE COMET HALLEY 19

. . .PART II. EDUCATIONAL ACTIVITIES -, 23

IN THE CLASS1656M 23,

Newspaper Accounts11 23

) ,...- Oral History 24

Time Capsule 24

Comet alley Artistically Speaking 24

Comets and Life Sciences - 24

. Comet Hall of Fame 24

OBSERVING/THE COMET 24

Brightness 25

Length of Comet Halley's Tail in Miles 28

Recording Observations 30

Plotting the Locatiiin of Comet Halley°

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COMET HALLEY'S. ORBIT .4. 33

PLACES TO VISIT THINGS TO DO 36'

COMPUTING AN EPHEMERIS FOR COMET HALLEY 35

SELECTED READINGS 40

INTigX 41

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Part ITHE NATURE OF COMETS

A bright comet is a spectacular object to behold. Ifyou had awakened around 4:00 in the morning inearly March, 1976 and braved the late winter coldyqu would have been rewarded with a beautifulsight: a view. of the naked-eye Comet West. Itwould have been visible in the eastern sky, near thepoint where the sun would rise in a few hours. Thecomet's head would have been near the horizon,and its tail would have been seen streaming upwardtoward the zenith. For those of us who saw thecomet, it will remain a memorable event. For thosewho have never seen one, it is well worth the effortto observe one.

Comet Halley will .be visible to small telescopes,binoculars and even the naked eye in late 1985 andearly 1986. The event is already stirring interestboth. in the scientific community, and in the generalpublic. What is it about this comet that generatesso much interest? How can we observe it when itpaisei near the earth? What will scientists aroundthe world try to find out? These questions andothers will be answered in the following pages, aswe tell the story of the comet. To begin let us takea look at the reasons that Comet Halley is soimportant historically.

THE HISLORICAL IMPORTANCE OFCOMET HALLEY

To tell the whole story of the importance of CometHalley would take a large volume, for we wouldhave to look at the whole history of the develop-ment of our understanding the nature of theplanets and how they move. The early Greeksthought that the plane all revolved around theearth in orbits that a combinations of perfectcircles. In the.first cen A.D., Claudius Ptolemyproposed a complex sys of epicycles that ex-plained almost all of the observed facts about themotions of celestial bodies. This system was usedto predict the motions of the planets for althost 14centuriesa fact that attests to the success of thetheory. However, natural philosophers began totake a new logk at the universe in the Renaissance.Nicolas Obpdhicus (1473-1543) asserted that theplanets all revolved about the sun. Actually,Copernicus' novel idea was based more on aestheticgrounds than on the basis of any scientific results.However, that would change in the late 16th cen-tury, when Tycho Brahe (1546-1601) developednew instruments that permitted him to measurethe positions of celestial objects with unparalleledaccuracy, before the invention of the telescope.Working with Tycho's data, Johannes Kepler(1561-1630) showed that Mars moves. around thesun in an elliptical orbit. He then went one stepfarther and hypothesized that all planets orbit thesun in elliptical orbits.

Two of the most notable scientists of all time wereGalileo Galilei (1664-1642) and Isaac Newton(1642-1727). These two men, more than anyoneelse, in*nted the., modern. science of mechanics.Newton also postulated the existence of universalgravity, which asserted that all bodies in the uni-verse attract one another. 'It is the intense gravityof the massive sun that holds the solar systemtogether.

In parallel with all of these developments in theconcepts of planetary motion were developmentsin our understanding of comets. In the FourthCentury B.C., Aristotle believed that comets were aphenomenon of the, earth's atmosphere. In histreatise Meteorologioa he asserts that comets are"exhalations" in the outer reaches of the atmo-sphere. This view was repeated by such greatphilosophers as Ptolemy. It is interesting to notethat the Roman Stgico philosopher Lucius Seneca(4 B.C. - A.D. 58) held the view that comets arecelestial bodies which travel through space inelongated orbits. Before we Ode Seneca too muchof a pat on the back, we must realize that his ideawas as much of a guess as was that of Aristotle., Itwas Snot until the 16th century that Tycho, withhis very accurate instruments, could make observa-tions which established that comets are celestialobjects. He observed the position of a bright comet'that appeared in 1577 from various sites in Europe.,If the comet were in the earth's atmosphere, thenit would have a measurable parallax (see Figure 1),that is, it would shift against the background of thestars by a measurable amount as he moved hiltequipment about on the surface of the earth,viewing the csmet com different angles. He couldnot detect a mbasura e parallactic shift, so he con-cluded that the come had to be at least severaltimes farther away from ttie earth than the moon:whose parallax he could measure.

In 1665, the Great Plague closed down CambridgeUniversity, and the 23-year old Isaac Newton wasforced into a two-year hiatus in his formal studies.With few responsibilities, Newton had little to doother than contemplate the myiteries of the uni-verse. The results of his contemplations were'formidable. He arrived at a formalized system ofmechanics and a law of gravitation that togetherput the study of motions in the solar system on afirm mathematical footing.

Among his other accomplishments, Newton founta way of calculating the characteristics of theorbital paths of a comet from a eerier of observa-tions of the comet's position in the sky. He didthis, in part, by. assuming initially that the comet'sOrbit was parabolic in shape. A young friend andcontemporary, Edmund Halley, applied the methodto a series of comets that were observed in the

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COMET

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If comet were farther than the moon, the shift due tothe motion of the observer would be smaller, andwould have been difficult to measure in 16th century.

Figure 1. A comparison of the parallax of a comet if it were In the earth's atmosphere and if it were beyond the moon.

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14th through the 17th centuries. , Among the sur-prises that he turned -up was the fact that cometsobserved in 1531, 1607, and 1682 all had verysimilar orbits. He concluded that the three cometswere, in fact, repeated appearances .of one and thesame comet that orbited around the sun once every75 years in an elongated orbit, as shown in Figure2. He predicted that it would return to the. vicinityof the earth and sun in .1758. The comet passedperihelion the closest point in its orbit to thesun-- on March 12,1759, after being recovered by .

an amateur astronomer on December 25, 1758.Unfortunately, Halley died befdre the comet re-turned, and he did not see it again: The returnprovided incontrovertable proof of Newton'stheory, and Halley's orbit calculations. In honorof the great importance of Halley's prediction, thecomet was named after him.

In October 1982, astronomers working with thegreat 5-Meter (200-inch) reflecting telescope onPalomar Mountain in California obtained the firstobservations of Comet Halley as it proceededtoward a 1985-86 rendezvous with the sun and theearth. When these early images were obtained, the

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PLUTO

NEPTUNE

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. SATURN

comet was well over a billion miles from the, sun,farther away than the planet Saturn. It appearedas a, very faint, starlike point of light on the photo-graph (Figure 3); it was too far from the sun tohave formed the features that normally charac-

t/terize a comet. How, then, did. the astronomersrecognize it as a comet? There are two reasons:first, the starlight point of light was seen to moverelative to the stars when two exposures taken Bev-

. eral hours apart were intercornpared; and, scien-tists had calculated where the comet ought to beusing observations made at All the passes sinceEdmund Halley's days, and the comet was found atthe correct position.

HOW COMETS ARE FOUND AND NAMED

Many comets have been discovered by amateurastronomers who spend hours sweeping the skywith wide field,low magnification' telescopes called"comet seekers." Typically, the observer sees afaint, fuzzy object among the stars in some region

, of the sky, where catalogs 'say there should not bea fuzzy object. There are many types of objects

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Fi',ure 2. The orbit of Comet Halley. The circles represent, from theInsideout, the orbits of earth, Mars, Jupiter, Saturn, Uranus, Neptune, and Pluto.The outer three planets orbits' are added for reference. These planets wereunknown at the time Halley ascertained the parameters of the ortoit of CometHigley. Note that in this picture the planets orbit in a counterclockwisedirection, while the comet orbits in a clockwise direction. The vie*. is fromabove the north pole of the earth.

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Figure 3. Rediscovery photograph of Comet Halley made in October 1982 using the great 200-inch reflector onPalomar Mountain, California. (Courtesy of G. Edward Danielson of Ca/tech.)

that appear fuzzy to a small telescope: galaxies,star clusters and glowing interstellar gas clouds alldo. The clue as to whether an observed ftizzy.object is a comet or not is its motion. A cometwill be observed to move its p9sition over thecourse of several hours, while any of the otherobjects mentioned do not appear to move relativeto the stirs.

When a person discovers a comet he or she is re-warded by having the comet named after him orher. Occasionally, two or even more observers findthe same comet nearly simultaneously, in whichcase up to three independent Observers will hivetheir names attached to the comet. For example,Comet Ikeya-Seki, which became visible to thenaked eye in 1965, was discovered by two Japaneseamateurs, K. Ikeya and T. Seki. Kaoru Ikeya dis-covered his first comet in 1963 when he was only19 years old, using a home-made telescope. Hisdiscovery, which culminated 16 months of search-ing, brought him much deserved fame for hisenergy and persistence. He has now discoveredmany more comets.

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Not all comets have been found by amateurs, ofcourse, although comet seeking is one field wherethe layman can assist and even compete with theprofessional. The most successful comet seeker ofall times, Jean Louis Pons (1761-1831) started hiscareer in astronomy as the caretaker at the Mar-seilles Observatory in 1789. In his active lifetime,he discovered over. thirty-seven comets and workedhis way up in the astronomy profession until hewas appointed director of the Marna Observatory.

One of the most incredible stories of the discoveryof a comet is the following. An astronomer at theLick Obiervatory. D. Perrin, discovered a cometin 1896. On subsequent nights he continued tomake routine observations of the object. At onepoint, he received a telegram from the Kiel Observa-tory also reporting the position of the comet. How-ever, unknown to him, there had been an error in thetransmission of the telegram resulting in an incor-rect position being listed. The incorrect position wasonly two degrees from the correct one, so Perrinedid not notice the difference. When he looked atthe wrong position, there was a second new eomet.

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Comet seeking is an area where women have dis-tinguished themselves. Carolina Herschel discov-ered or co-discovered eight comets between 1786and 1797, earning her a world wide reputation.In the U.S., Maria Mitchell discovered her firstcomet, Comet Mitchell, in 1847: She went onto become a professor of astronomy at VasserCollege. Mitchell is considered to be the firstAmerican women astronomer.

The method of naming comets after the discovererleads to some tongue twisters. Names such asComet Honda-Mrkos-Pajdusakova take a while tospell out. The Astronomers A. Schwassmann andA. A. Wachmaun together have discovered severalcomets, so we must speak of Comet Schwassraann-Wachhiann I, Com Schwassmann-Wachmann IIand so forth. In 1 73, L. Kohoutek discoveredtwo comets within eight day period. The first,and fainter Comet KOhoutek passed perihelion (itsclosest point to the inin) a few months after dis-,covery and faded rapidly from view. However, thesecond one became quite bright and stirred a lot ofinterest at the time. Pigure 4 is one picture Madeof the second Kohoutek durihg 1974. Both cometswere called Comet Kohoutek, a fact that cduldlead to some confusion.

To avoid this type of confusion, comets are num-bered as well as named. There are two numberingsystems. First of all, when a comet is found, it isdesignated according to\the order of discovery. Thefirst comet discovered in 1983 is termed 1,983a,the second 1983b, and so on. Comet IRAS-Araki-Alcock was the fourth comet discovered in 1983,so it is called comet 1983d. (Incidentally, thislatter comet was first noticed in data gathered byNASA's Infrared Astronomy Satellite (IRAS), ao itwas named in honor of the satellite, ,a notable ex-ception to the rule of naming comets after humandiscoverers.) On the scheme based on year andorderof discovery, the two Comets Kohoutek werecomet 1973e and 1973f. The second comet-numbering system is based on the order in whichcomets reach the perihelion points in their orbits.The first comet to pass perihelion in 1983 istermed comet 1983 I, the second comet 1983 II,etc. On this system, Comet Schwassmann-Wachmann I is also called comet 1925 II andComet Honda-Mrkos-Pajdusakova is also calledcomet 1945 III. .

COMETARY ORBITS

The orbit of a comet is a conic section, that is, anellipse, a parabola, or a hyperbola. If the orbit isan ellipse, the comet will return periodically to thevicinity of the sun. A comet in a hyperbolic orbit,on the other hand, is not bound to the" solar sys-tem. Such a comet will zip by the sun and headoff into interstellar space never again to return.

An ellipse is a closed figure obtained' by inter-secting it circular cohe with a plane. As shown inFigUre 5, when the intersecting plane is perpen-dicular to the axis of the cone one obtains thelimiting case of a circle. When the plane is tippedat an angle to the axis, one obtains an ellipse. Thegreater the intersecting plane is tipped, the morethe ellipse is elongated, until a point is. reached

. where the curve resulting from the intersection isno longer a closed curvq. Wheh the plane is parallelto a generatrix (a straight line through the apex ofthe cone and on the suktace of the cones for exam-ple, a pole in a tepee is V,generatrix) of the cone,the figure is a parabola. If the plane is made par-allel to the axis of the cone, then the conic section

'generated is a hyperbola.

The size and shape of the comet's orbit and theorientation of the orbit in space are specified bysix quantities known as the orbital elements of thecomet. Once the orbital elements are ascertained,a table of the future positions called an ephemeriscan be computed. An initial calculation of theorbital elements can be carried out once threeaccurate measurements of the comet's positionhate been made. Usually, only a small arc of the,orbit is included between the three initial posi-tionsrand the calculation of the elements of the.whole orbit can be inaccurate. An ephemeris cal-culated from the initial orbital elements is usuallyonly a rough approximation to the expected com-etary motion. However, as more position observa-tions become available, the orbital elements can besuccessively refined, and more accurate ephemer-ides can be calculated. For the initial calculationof the elements of the orbit of a comet, astron-omers often follow Halley's lead and assume thatthe comet moves.in a parabolic orbit. In fact, in alarge fraction of the cases the refined orbit turnsout to be very close to a parabola.

One does not have to unders ,d about orbital ele-ments to understand comets. however, let's take acloseillOk at thiconcept fpr those of you'who areinterested. There is more Than one valid set of or-bital elements, but we will choose et particular setfor discussion, First, it takes three angles, i, S2, and

, to describe the orientation of the orbit in space.These angles are illustrated in Figure 6. Next, wemust describe the size and shape of the orbit. Tra-ditionally, the shape is given by the eccentricity, e,of the orbit. A circle has an eccentricity of 0.0,and a parabola has an eccentricity of 1.0. -Ellipseshave eccentricities between 0.0 and 1.0. The orbit'ssize is given by the parameteil q, which is the ditance from the sun to the comet at perihelion. T ef;e elements i, SZ , w , e, and q fully describecometary orbit. Finally, we must specify wherethe comet is in the orbit. This is usually done bygiving the time when the comet passes perihelion.The time of perihelion passage, T, is the sixthorbital element.

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Figure 6. Graphical illustration of the angular elements of an orbit. The symbol marks thedirection to the vernal equinox. The elements are explained in the text.

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Coinet Halley is a short period comet. Like theplanets, it moves, in an elliptical orbit. However,there the resemblance to 'planetary orbits ends.While the orbits of the planets are nearly circular,the orbit of Comet Halley is an elongated ellipse.The solar system, as defined by the region of spacewhere tie planets move, is a flat system. With theexception of Pluto, rr. of the planets' orbits istilted by more that. 4%0 degrees from the planeof the earth's orbit. in addition to the flatness ofthe solar system, there is also a common direction'to almost all motions in the system. For instance,all the planets revolve around in a counterclock-wise direction as seen from far above the earth'snorth tole. In addition, all the planets exceptVenus and Uranus rotate in the same direction thatthey revolve, and of the 32 planetary satellitesknown, before the last flyby of Saturn, 21 revolveabout their parent planet in the counterclockwise,or direct sense.

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the long period ,comets. The in li-1 r t

In contrast to e flat, regularly moving system Ofplanets, the stem of comets is a hodgepodge;particularlynations of it orbits to the ecliptic can be y-

- thing froritt-4 to 90° and their orbital motion anbe direct Or retrograde. Comet Halley, for , in-stance, moves in a retrograde sense in an orbit tiiutis tipped by:18°o the earth's orb:

,

The long /period comets are those courts whoseA t

orbital revolution periods exceed 200 Years. Theyare the majority of comets; only about 20% pf allcomets with well observed .orbits (or about 100comets) fall into the short period group. In fact,all comets that have welestablished periods areshort period comets. The ,xact size of a very ellip-tical orbit, and therefore the period of revolutionof the comet, is difficult to ascertain even from aseries of good observations.

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The group of s short period comets has a meanperiod of revolution of seven years. The orbitalplanes of these comets ....nd to be near the plane ofthe ecliptic, and the comets motions tend to bedirect. Comet Halley is somewhat exceptional,with its retrograde motion. Its period is among thelongest of the short period comets as well. Theshortest period comet known is Encke's cometwith a period of 3.3 years.

One of the most uncertain facts about any comet is:c the 'magnitude that it will have when it is at its

r. brightest. The factors determining tne brightnessare: (1) \the distance from the sun to the comet,which tells how much light reaches the comet;(2) the size of the comet, which determines howmuch light it produces; and (3) the distance fromthe comet Aso the earth, which tells how' much ofthe, reflected light we receive. Of these three fac-tors, the second is the most uncertain.

WHAT WILL COMET HALLEY LOOK LIKE

When a typical comet is first ob;erved, it is a fuzzy,nearly round object i the sky. In May of 1983,,

astronomers found comet 1RAS-Araki-Alcock

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(Figure 7) using data obtained by the InfraredAstronomy Satellite, as we mentioned earlier.When it was first seen, it was a nondescript fuzzyobject. In mid May, the comet reached naked eyebrightness, when it appeared to be a nondescript,bright fuzzy object. The fuzzy spot of light iscalled the coma. As the comet approaches the sun,the coma will grow in size and brightness. Typicalcoma diameters range between 19,000 and 190,000kilometers (12,000 and 120,000 miles). WhenCom4 Halley was recovered in late 1982 (seeFigure 3), it was so far from the sun that its comahad not yet formed. All that we see then is thenucleus of the cow t. Even in the brightest comets,the, nucleus remains a starlike point `of light. Whencomets are near the sun the nuclei are difficult orimpossible to see inside the bright coma. Cometarynuclei are estimated to be a few kilometers indiameter. From its brightness, for instance, we.estimate the nucSus of Comet Halley is about 5kilometers in diameter. The nucleus and comamake up the head of the comet.

The most spectacular characteristic of a comet isits tail, which develops as it nears the sun. Acomet could have a tail as long as 160 inion kilo-meters (100 million miles), although typical lengths.

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Fiore 7. Comet IRA3Areki-Aleock photographed on May 12,1983. (Joint Observatory for Cometary Research photograph.)

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are more ,like a few million kilometers. A comet'stail. always 'points away from the sun. ComeIRAS-Arsild-Alcock was unusual in that it did ndevelop a conspicuous tail. Most comets do develotails. Comet Halley developed a tail each time ithas been observed in the past, and there is no rea-son to believe that it will not develop one this time.Figure 8 is a well known photograph of CometHalley made during 1910.

HOW AND WHEN CAN WE VIEWCOMET HALLEY

p.

We need to stress at the outsetsthat the 1985-86return of Comet Halley will not be as spedtacularas the returns of 1835 or 1910. However, it will bea naked. eye object during some title 'periods in1985 and 1986. Many of you may remember thatComet Kohoutek was supposed to be an unusuallybright comer fn late 1973 and early 1974. Yet,many people did not see it. Why? The experienceof some of the comet observers I know is instruc-tive. One of my colleagues travelled to a tell sit-uated comet observatory (The Joini Observatoryfor Cometary Research) in southern New Mexico,on a high mountain near Socorro. During.iltnuary1974, he saw the comet as a bright naked eyeobject almost every night. By contrast, I remainedin the Washington, D.C. area, and never really sawit well. The difference was the environment.' InNew Mexico, there was no indAtrial air pollutionand no large cities with their bright lights to drownout the-subtle. light of the comet. In the North-

...ekstern U,S.t by contrast, it is 'hard to find a;siteaway from air pollution and city lights. Youshould remember this as you plan to see ConietHalley. A trip to the moinitains (and I don'tmeanall the way to the Southwest) will pay off in yourability to seethe comet..

There are two Iiine periods when Cometwill the most easily observed by sonone in theU.S. The first period encompasses th t week inNovember and the first week in Devember 1985,when the comet will be fairly bright though itwill probably be obseriable only with ,binoeThe comet will then pass through perihelion, andbe invisible behind the sun until about March 1986.It is then predicted to be its very brightest in lateMarch and early April of 1986. In late March, thecomet will be observable in the morning sky,toward the'southwestern horizon. If yqu are at thelatitude of New York City, you can see it about10° above the horizon. The farther youth you are,the higher it will be in the sky at that time. Fromsouthern Florida or Texas, the comet will bealmost 30° above the horizon. The best views willbe from the southern hemisphere. If you couldvisit South America, for instance you would havean exceptional view. The comet will then swingfarther north, and will be visible in the evening skyfor observers at the latitude of New York City as

10

.much? as 30° above the horizon:. However, at thistime it will once again require I, binoculars to beseen. Figures 9 throtigh n summarize the discus-sion in pictorial form.

, .WHAT IS A COMET?ok

In- the early 1950's, De F. LWhipple of theHarvard College Observatory presented a picture ofcomets that, with some minor modifications, ispeCepted today. Whipple propoied that the nucleus

/is in effect a dirty iceberg, a large mass of frozenwater, methane, ammonia, carbon' dioxide, andother constituents, in which is embedded meteor-like, solid particles of various sizes.. When thenucleus is heated by the radiation ofthe sun, itsices\ sublime that is, go from the solid state tothe gaseous state and as a-result/the nucleus issurrounded by a cloud of gas and the dust particles,that were relearned. This cloud is the coma. Figure42 illustrates the parts of a typical comet that wewill describe fiere.

When one turns a 'spectrograph on the eoma of acomet, the spectrum is found to contain lines orbands which indicate the presence of simple con-stituents such as H,OH, 0, CN, Cg, Cs, CO *, NH,NH2, CH, N2* H20+ as well at other constituents.When , comets are observed at radio wavelengths,evidence of molecules such as methyl cyanide(CH3CN) and hydrogen cyanide (HCN) may befound. With only a very few exceptions, these con-stituents will not exist as such when frozen in thenucleus. Instead,' they must arise' from chemicalchanges to the frozen molecules that are foundthere. We refer to the molecules frozen in the nu-cleus as "parent" molecules, and the observed con-stituents as "daughter" molecules. Astronomersbelieve the parent molecules to include ofetinarywater (H20), ammonia (NH3), methane (CH4), aswell as C2, N2, and CO2.

When the parent molecules are exposed after sub-liming from the nucleus, the ultraviolet photonsfrom the sun . can break them apart (photo-dissociate them) into the daughter molecules. Theprocess takes place so quickly that we do not havetime to see the parent molecules. The solar windparticles also have an effect on the constituents.The complete story is far from fully understood.We hope a detailed study of Comet Halley willshed additional light on these problems. In 1973,we issued a booklet like this one for CometKohoutek, and we ended this section by saying:"we hope It stndy of Comet Kohoutek will shedfurther light .hese problems." It did. We firstobserved H2O* in Kohoutek, giving us additionalevidence for the presence gf water in the nucleus.But Kohoutek did not solve the problem, andComet Halley will not solve the problem com-pletely either. Employment is assured for futuregenerations of comet scientists..

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Figura 9. Comet Halley as observedin 1986 by an observer located at 40° north latitude. The comet positions are given for the beginning ofmortwilight or at the end of evening twilight. Approximate visual magnitudes are given in parentheses following dates.

(From Cornet Halley Handbook, Courtesy D. K. Yeomans.)

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AZIMUTH, DEGREES

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Figure 10. Comet Halley as observed in 1988 by an observer located at 30° north latitude. The comet positions are given for the beginning of morningtwilight or the end of evening twilight. Approximate visual magnitudes are given in parentheses following dates.

From Comet Halley Handbook, Courtesy D. K. Yeomans.)

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Figure 11. Comet Halley as observed in 1986 by an observer located at 20° north latitude, The comet positions are given for the beginning otmorning twilight or the end of evening twilight. Approximate visual magnitudes are giverein parentheses following dates,

(From Comet Halley Handbook, Courtesy D. K. Yeomans.)

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Figure 12. Artist's conception of a typical comet.

According to scientific theory, alight beam is com-posed of a stream of particles called photons. Abeam of photons bouncing (reflected) off one sideof a small dust particle exerts a force on it, and ifthe dust particle. is small enough the photons canpush it along. The intense sunlight falling onminute clustiparticles in the coma of a comet, whenthe comet is near the sun, pushes the dust particlesout of the coma, producing the comet's tail whichpoints away from the sun (Figure 13). If you lookat Figure 14 you will notice two ttti!F One tail isgently curving and appears smooth. This tail is thedust tail, caused lal the mechanical action of thesolar radiation. The other tail is more nearlystraight and has a turbulent appearance like

cigarette smoke in a breeze. That tail is composedof ionized molecules blown out of the coma by thesolar wind, a stream of ionized atomic particlesconstantly blowing away from the sun. A color-picture of a comet shows the dust tail to be, yellow.ish, which is the color of sunlight ,reflected fromthe small particles. The gas tail is blue, on theother hand, causes by characteristiC emissionsof the ionized molecules present (predominantlyCO+ ).

As the comet approaches the sun, the coma is ob-served to grow.-Clearly, this growth occurs, becauseof increased sublimation of the ices of the nucleus.However, *a point is reached when .the coma mayactually shrink as the comet approaches evencloier to the sun. This shrinkage may occur whena point is reached when gas and dust are., blowninto the tail faster than it sublimes from Arhenucleus.

If an expert had been asked before 1969 to de-scribe a comet, he would have tokt you about, thenucleus, coma and tail. However, in 1969 and1970 an unexpected discovery was made when theOrbiting Astronomical .0kae, reatory, 0A0-2, wasturned on Cometr,,Tago-Sato-Kosaka .and Cornet'Bennett. Each was found to be surrounded by atenuous but giant cloud of hydrogen gas. The ob-

iservations of comet Bennett were subsequentlyverified.bylthe Orbg,geophysical Observatory.The hydrogen. cloud around . Comet TagQ -SatoKosaka was as big .46 the sun, Mid the .loud aroundComet Bennett was even_ largel. It is believed_ thatthe hydrogen cloud arises when ultraviolet photonsfrom the sun.break up water molecules sublimedfrom the-nucleus, producing hydrogen and free OHradicals.

What happens to the material blown out of thecomet's nucleus? Each dust particle circles the sunin an orbit similar to the parent comet's orbit.Eventually the entire path of the comet is outlinedwith dust.. 'Occasionally, the earth passes notmerely through the plane of the comet's orbit, butacross the very path of the comet. Then the dustparticles make their presence known as a showei ofmeteors (shdoting stars). The particles are burnedup in the earth's atmosphere due to the heat gen-erated by friction between the air and the particleswhich may speed through the atmosphere as fast as45 km/sec. For instance, the earth crosses the orbitof Comet Halley in May and again in October, eachyear, and each time a meteor shower is observed.The Eta Aquaril shower occurs in May and theOrionid shower' in October. At the 1910 returnthe earth was to pass through the tail of CornetHalley. Some panic was generated by the an-nouncement because of the noxious gasses in thetail. However, only the usual meteor showerresulted.

In some cases, the debris is bunched up in a clumpwhich moves around the comet's orbit. In these

25 15

tj

Figure 13. As a comet passes around the sun its tall swings around andalways points away from the sun.

cases when the earth crosses the orbit only a fewmeteors are observed while at other times a spec-tacular meteor show is observed. 1111866 the earthcrossed the orbit of Comet 1866 I, and a meteorshower (the Leonid shower) with a rate of 100,000meteors per hour was observed. As it turns out,the earth had also passed through the comet'sorbit and met a dense shower in 1833, but inyears between 1833 and 1866 no spectacular

16

shower was observed. The period of the comet inquestion is 33 years. In this case the debris ishighly bunched up.

Since cometary nuclei slowly sublime while thecomet is in the vicinity of the sun, it is clear that acomet must have a finite lifetime. Some estimatessay that a comet cannot survive more than a fewhundred close approaches to the sun.

2

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f

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Figure 14. Comet West on March 9.1976. Note the gently curving, smooth dust tall uppermost in the picture and the straight b turbulent looking plasma tall(Joint Observatory for Cometary Research photoriph.)

2728

We have arrived at a mystery. If a comet can lastonly a few hundred passes around the sun, thenComet Halley should live a few times 7500 years.Even a comet like Comet Kohoutek with a periodestimated to be around 100,000 years will disinte-grate in something like 10 million years. Both ofthese times is short compared to the 4 billion yearage of the solar system. One would think, if thistheory is correct, that. there would be no cometsleft in the system today. Why do we see comets atall? Particularly, why do we see short periodcrets like Halley? . ..

One possible answer to these questions was pro-vided by the modern Dutch astronomer Jan Oortin 1950. He suggests that there existaa giant cloudof literally billions of comets completely sur-rounding the solar system at a distance from thesun at least as great as 150,000 times theearth'sdistance. This distance is a large fraction of theaverage distance beiween the sun and other nearbystars. Every few million years, C. Ae of the nearbystars, in their random notions through space willpass close enough( to the sun to perturb a numberof comets in the cloud. Some of these will beIornout of the solar system, and will fly off into spacenever to be seen again. However, some will be sent,in toward the inner solar system. These cometswill become long period comets, with periods of afew million years. A number of these comets willpass near the massive planet Jupiter on eir tripsthrough the inner solar system. The ombinedeffect of Jupiter over several passes can to slowthe comet's motion, in which case it can graduallybecome a short period comet, forever remaining inthe inner reaches of the system.

One fascinating aspect of Oort's theory is thethought that the comet cloud may actually befrozen chunks of the nebula out of which ;the sunand planets were formed, in which case cometsconsist of the primordial material of the solar sys-tem. What better reason that this do we have forthe careful scrutiny of any comet? The hypo-thetical cloud of comets is now referred to as theOort cloud in honor of Dr. Oort.

C1METS OF THE PAST

Many comets that have been observed over the lastfew centuries have exhibited unexpected behaviorin various ways, and others have been spectacularbecause of their great size or brilliance. Lets lookat some of the unusual comers of the past, sincetheir behavior may tell us something of whaetoexpect from Comet Halley and other bright cometsthat may appear in the near future.

Among the most unusual occurrences in the annalsof cometary study is the behavior exhibited byComet Biela. This comet, which had an orbital rev-olution periodrof 6.75 years, was observed for sev-eral passes in the late 18th and 19th centuries,

18

during which time it appeared to be a fairly ordi-nary comet. A few days after the comet was pickedup on its return in 1846, it actually split into twodistin t omets. For several months the two piecesfollow e another in almost the same orbit,but wi one trailing the other by 250,000 km(160,000 miles) or so. Each piece had an observ-able nucleus, a coma and a tail; in short, each was acomplete comet. However, they underwent re-markable changes in brightness, with first one thenthe other being the most brilliant. In 1852, thecomets returned on schedule, but now were about2,400,000 km (1,500,000 miles) apart. The year1866 was to be a particularly favorable one forviewing the comets, and astronomers awaited their,return with great anticipatiorr. But, alas, they havenever been seen again. .

Those of us sitting on the edges of our chairsawaiting the return of Comet Halley should takecognizance of Comet Ensor which was discoveredin 1906, and Comet Westphal which was discov-ered in 1913. Both comets were predicted to bespectacular when they passed perihelion, based ontheir orbits and on early. observations. However,both comets grew very rr idly as they approachedthe sun and as they grew .,tiey became increasinglydiffuse and faint, until they completely faded fromview'. By the time the comets should have passedperihelion they were nowhere to be seen. Nodoubt, in each of the cases we have described, wewere seeing the end of the lives of the comets. Inthe case of Comet Biela, it had probably sublimedunevenly, leaving a distorted nucleus that couldnot hold together, After all, a snowball doesn'thave muclimechanical strength.

In June 1058 the Florentine astronomer G. B.Donati &Covered a comet which appeared as afaint pot of light. In was not until late August ofthat year that the comet showed a 4211, and then itwas only as long as the dianieter of the full moon.During September the comet increased remarkablyin brightness as it approached the sun, and reachedgreatest brilliance in early ! October. The cometthen had a tail which stretched one-fourth of thesway across the sky, was very bright and easily vis-lible to the unaided eye. After the comet passedperihelion, it moved very far south in the sky andcould only be followed by southern hemisphereobservers. It remained visible to large southerntelescopes until March 1859.

Comets that are bright enough to be seen in broaddaylight are few and far between. Estimatei of thenumber range around four or five each. century.The great comets of 1843 and 1882 were both day-light comets. If one would screen out f '6 fullglare with a hand, one could easily hay, m thesecpmets. Interestingly, both comets fall into a classknown as "sun grazing" comets. The comet of1843 passed only 120,000 km.(80,000 miles) abovethe surface of the sun and the, comet of, 1882passed 'about 480,000 km (300,000 miles) above

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the solar surface. These distances seem like a comefortable margin until we remember that the sun is1,400,000 km (864,000 miles) in diameter, so infact the distances are small compared to the size ofthe sun. The comet of 1882 was torn apart by thehuge gravitational field of the sun; it was seen asfour chunks after perihelion pass. The brightestsun grazing comet of the 20th century was CometIkeya-Seki observed in 1965.

Comet Howard-Koomens-Michels did the sungrazers one better. It plowed into the sun onAugust 30, 1979. The comet was discovered byan instrument flown on an Air Force satellite tostudy the sole corona. The conictt was seen onseveral frames approaching very close to the sun,then it disappeared. At the moment of its dis-appearance, a portion of the corona increasedmeasurably in brightness. One supposes that asthe comet completely sublimed in the sub's ultra-hot atmosphere, the material briefly increased thedensity and therefore the brightness of the corona.

COMET HALLEY IN 1910

Comet Halley was redise ered on its way towardits 19 passage near the sun' on September 11,1909, ughly six months before it passed peri-helion. Contrast this with the upcoming pass,when it as rediscovered 40 Months before pal-.helion. This remarkable difference is due to thetremendous strides in technology in the 75 or soyears between passes. One hopes that the discov-eries during the rest of the 1985-86 pass are asmuch an improvement over 1910 as the discov-eries to date. To give some idea of what we expectto see in 1985 and 1986, we will take a brief lookat what happened in 1910. May 1910 was themost impressive time for Comet Halley. Then itwas at its closest to the earth, and actually passedbetween the earth and the sun. On May 18, thetail of the comet was 120° long, its greatest lengthin 1910. Barnard described the comet during thisperiod as quite bright to the naked eye, with a

.bluish white color. .

On May 18, the comet passed direct between theearth and the sun. At the time of t actual transitof the solar disk, it was daylight in urope, and de-tailed observations were made a e MoscowObservatory. The observations were completelynegative. There was no sign of the comet as itpassed across the sun. Given the geometry of thepass, the nucleus would have been seen in silhou-ette against the sun if it had been as large as100 km. As we said earlier, we now think that thenude% is a mere 5 km in diameter. The very ten-uous coma caused no observable effect.

An interesting aspect of the passage of the cometbetween the sun and earth is the fpassed over or near the earth. Thegen, CN, is a deadly poison, and th

t that the tailolecule cyano-re were those

that predicted the end of the world as the gasmixed into our atmosphere. The newspapers werefilled with stories related to the impending passageof the comet. One entrepreneur down in Texassold so-called comet pills to some of the unsuspec-ting locals. The pills, which turned out to be aharmless mixture of sugar and quinine, were sup-posed to ward off the evil effects of the cometarygasses. Business was brisk, and the fraudulent pillpeddlers made a good piece of change, before theywere caught: 1When the event actually happened,there was no noticeable effect, other than themeteor shower, mentioned earlier.

ReCently, ah interesting type of cometary eventhas been explained; a sn-called disconnection eventor DE in which a con one tail and growsanother. The event sees. Aleur wilt., a cometcrosses a region in span ere the interplanetarymagnetic field rapidly nges direction, and aprocess kno as reco. .ion causes the tail tobreak off. A disconne, event was observed tooccur in Comet Kohoutek in 1974, and then simi-lar events were sought in other comets. A numberof DEs have been found, including five in CometHalley in 1910. Figure 15 shows one of the events.The unusual appendage to the comet's tail ob-served half way down the tail is actually the oldtail that has been disconnected from the comet.

PLANS TO OBSERVE COMET HALLEY

Thete is a major worldwide effort underway to ob-serve Comet Halley. Three different missions willencounter the comet in March 1986. The EuropeanSpace Agency is mounting a mission called eat()in honor of the great Italian painter_ who produceda masterful frerco bf Comet Halley after its 1300return. One of the chief objectives of the GiOttomission is close-up imaging of the nucleus of thecomet. .Images of the type the mission plannersenvision will go a long way toward proving or'dis-proving Whipple's dirty iceberg model of thenucleus. Giotto will also study the gas and dust inthe vicinity of the comet, and will measure its mag-netic field. The Giotto spacecraft will pass within1000 kilometers of the comet's nucleus in March1986. The Soviet Union and Japan are each plan-ning missions to the comet. The Soviet's space-craft, built around their spacecraft that .flew toVenus, will fly to within 10,000 km of the comet'snucleus. They call their mission VEGA. TheJapanese Planet A Mission will pass within 100,000kilometers of the nucleus, also in March 1986.

The United States is planning several efforts. TheASTRO mission consists of a group of instrumentsdesigned to carry mit-astronomical observations inthe ultraviolet reg an of the spectrum from theShuttle bay. NASA has decided to add a pair ofsmall, wide fiel cameras to the payload to obtainimages of the entire comet. The Astro payloadwill be sent into orbit for about a week when

32 19

20

r

Figure 15. Comet Halley (top to bottom) on Jurfe 8.66,1910 from Wisconsin,on June 6.77, 1910 from Hawaii, and on June 7.29, 1910 from Lebanon.

(Yerkes Observatory photograph.)

33

Comet Halley is closest to the earth, giving us ourfirst detailed ultraviolet studies of the comet tocompliment the studies done by the spacecraftmentioned above.

In additiori to the Astro Mission, NASA is plan-ning the International Halley Watch (IIIW). TheIHW will organize a series of ground-based ob-serving networks to study .the comet. The basicidea of the networks is as follows. Studies ofComet Halley in 1910 and studies of othercomets as well showed that there are thingshappening in the comet that cannot be fully ob-served from one site. A complete disconnectionevent, for instance, takes about 24 hours. Onenight is too short to completely follow a DE, butso much happens during the 'daylight hours be-tween two nights that it is hard to correlate whatone seer on one night with what was seen the nightbefore. The only answer is to observe the cometfor 24 hours. This can be done by setting up a net-work of cooperating observatories all, around the

world. As the sun rises at observatories in theSouthwestern U.S., for instance, it is still dark inHawaii. Thus Hawaiian observers can continue ob-serving the comet for a number of hours. Whenthe sun rises in Hawaii, it is night once again inEurope, and so forth. In the network to take largescale photographs of the comet to study suchthings as DEs, there are about 90 observatoriesspreact around the world (Figure 16). Since thereare so many observatories, it is also very likely thatat West one of them will have clear skies when it isdark. The bottom line is, at least one observatory,in the network will be able to observe the comet atany time. The wide-field imaging .network is onlyone of several networks. Others will carry outspectroscopy, infrared and radio observations, pho-tometry, and so forth. The data gathered by thesenetworks will be essential to the understanding ofthe data collected by the spacecraft that will studythe comet. We will see some very exciting observa-tions come from these activities. I can't wait to seethe close-up images of the nucleus.

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3421

SELECTED READINGS

Brandt, John C.: Comets: Readings from Scientific Amer FranciWo: W. H. Freeman and Com-pany, 1981. This book is a compendium of articles about comets from Scientific American. It is appro.priate for a well read high school student or above.

Brandt; John C. and Chapman, Robert D.: Introduction to Comets. New York: Cambridge UniversityPress, 1981. This is a professional level book about Comets aimed at advanced undergraduate students,profbssional astronomers, and advanced amateur astronners.

Brown, Peter L.: Comets, Meteorites and Men. New York: Tap linger, 1974.

Calder, Nigel: The Comet is Coming: e Feverish Legacy of Mr. Halley. New York: Viking Press, 1981.4 i, 4..

Chapman, Robert D., and Brandt, John C.: The Comet Book. Boston: Jones and Bartlett Publishers,1984. This book, to be published in late 1984, is a popular level book that should be accessible by a widerange of readers. Ik

Muirden, James: The Amateur Astronomers Handbook. New York: Harper ana Row, 1983.

Norton, Arthur P.: Norton's Star Atlas. Cambridge, Mass.: Sky Publishing Corp., 1978.

Roth, G. D., ed.: Astronomy Handbook. 1%1v York: Springer!Verlag, 1975.

Wilkening, Laurel L. ed.: Comets. Tucson, AZ: U. of Arizona Press, 1982.. This book is compen-dium of technical articles on comets written by the experts in the field and skillfully edited by Wilkening.

Yeomans, Donald K.: The Comet Halley' Handbook: An Observers Guide. Second Edition. Pasadena, CA:NASA Jet Propulsion Laboratory, 1983. This guide contains a wealth of information for the potentialserious observer of the comet. Of special'note is the extensive ephemeris for Comet Halley.

22

35

Part IIEDUCATIONAL ACTIVITIES

The first part of this book described the nature ofcomets, with particular emphasis on Comet Halley.The appearance of Comet Halley in the sky willoffer a unique learning experience for students atall levels. In this part of the book, we will .suggosta number of activities that you can use to takemaximum advantage of the opportunity. The sug-gested activities cover a wide range of skills inscience and mathematics. Same of the. activitiesare quite appropriate for primary grades, andothers require the skills learned in the secondarygrades. Clearly, you the teacher will have to de-cide which of the activities is appropriate for yourstudents. In 'some cases, it will be possible for youto adapt an exercise to your specific needs. Thematerial is meant to serve as a guide and as a helpto you. Be creative in its use.

Some of the activities can be done in the class-room. These activities are includes to provide anunderstanding of the historical importance of thecomet, and to enhance the student's understandingof these wonderful celestial objects. However, it isessential that the students be encouraged to getoutdoors to observe .the comet first hand, when itis visible. Several activities are included that willintroduce the skills and knowledge required tolocate and observe Comet Halley. Comet Halley isan ideal; subject for bulletin board displays inschools, by the way.

IN THE CLASSROOM

During the span of almost 2100 years during whichComet Halley has been observed to return from thedepths of space to pass by the sun, we have come along way in our understanding of comets fromancient times when comets were considered to bevapors burning in the upper atmosphere, to mod-ern times with our capability to send space mis-sions right up to the comet. The study of CometHal* has given astronomers valuable insights inthe past, and will continue to provide unique infor-mation about the nature of comets.

Every return of Comet Halley to the vicinity ofearth has been recorded since 239 B.C., with oneexception. We know of no records of the cometfrom the 163 B.C. return. Each time the cometpasses the earth it finds the planet in a slightly dif-ferent state; after all, great changes can take placein our civilized society in just 76 years. Just thinkabout the tremendous technological changes thathave taken place since Comet Halley's last visit in1910. Comet Halley would find differences in thesize of the population, advances in medicine andscience, and additions to the great creations ofmusic, art and literature. Table 1 lists the years

in which the comet has been observed during itspass near earth.

Table 1List of Years when Comet Halley was Observed from Earth

B.C.

239 86 11

A.D. ...

66 141 218 295 374

451 530 607 684 760

837 912 t 1066 1145 1222

1301 1378 1456 1531 16071682 1759 1835 1910 1986

As an activity, have your students be chroniclers oftime1Either individually or as a group exercise,have the students imagine that they are reportersonboard Comet Halley. They should report thenews of planet earth as viewed from the comet forone particular passage. The categories that can beincluded in the news account depends on the agegroup of the students. Some examples of the typeof information that students might includelare: thepopulation of earth; explorations being made at thetime; major modes of transportation; the geographyof the known part of the planet; art, music and lit-erature of the time period; scientific discoveries;wars and political issues; feelings about the comet;and other major issues of the time.

The students might report their news through thenewspaper format, radio shows, or where equip-ment is available, over closed circuit television.When everything is complete, you might have acommunity open house to view ancr hear about thehistory of the earth as viewed from Comet Halley.

Newspaper Accounts

The newspapers of May 191.0 contained a greatdeal of information about Comet Halley becausethat month the earth was supposed to fly throughthe comet's tail. Banner headlines at the time in-cluded such comments as this one from the May18,1910 New York Times.

CHICAGO IS TERRIFIED

Women are Stopping up Doors.andWindows to Keep Out Cyanogen

Have your students do a library search of hometownnewspapers to find out local reaction to Comet,Halley. It would be easiest to limit the search toMay 1910, when a lot of comet activity occurred.

3623

Oral History

There are still people alive today who saw CometHalley during 1910. Have your students do oralhistory interviews with individuals who saw it. Anannouncement over the local radio or televisionstations or a request in the local newspaper willhelp the students locate possible resource personsto interview.

Have your students record their interviews on atape recorder. It is 'important to prepare for theinterview. Beforehand, make sure the studentshave their questions written out. Such questions asthe following might be included: How old wereyou when you saw Comet Halley? Where were youliving at the time? What are some of the things youremember about Comet Halley? Was there a lot ofexcitement associated with the return of CometHalley? What were some of the reactions to it?Itow did people learn about Comet Halley sincethere was no radio or television to tell them aboutit? Were you afraid?

Time Capsule

After doing the exercises suggested to provide ahistorical perspective about Comet Halley, thestudents will be aware that changes occur veryrapidly on earth. To get ready for the nextpassage,have your students prepare a time capsule. Thetime capsule might contain student predictions ofhappenings on earth during Comet Halley's nextreturn in 2062. You might even plan to bury thetime capsule on February 9, 1986, the date whenthe comet is at its perihelion point. The time cap-sule could then be opened on the perihelion date in2062.. Students could be guided to predict suchthings as: average life spans; the population oftheir city; science advances at the time; what wewill be doing in space; and major concerns of thecitizens of their city, the U.S., and the world in2062.'

As an alternative to the time capsule, your studentscould publish their predictions in the local news-paper so that some futire student doing a litera-ture search in 2062 will discover this information.

Co e Artistically Speaking

In 1910 c eras were used for the first time tophotograph omet Halley. Before 1910, artistsrendered Comet Halley on several different occa-sions. For instance, it was depicted on the famousBayeux Tapestry that highlighted the victory ofWilliam the Conqueror in 1066 at the battle ofHastings. _Art historians believe that Comet Halleyserved as the model for the Star if Bethlehem inGiotto's "The Adoration of the Magi." This spec-tacular work of art is one of the works in thefresco cycle executed by Giotto di Bondone in theScrovegni Chapel, in Padua. There have been

24

numerous poems and works of literature thatmention Comet Halley.

Your students could follow in the path of the greatmasters of the past and compose works of art in-spired by the comet. Have your students write apoem or compose a song about Comet Halley.Have them make a painting or drawing of the cometas they observe it. They could design a T-shirtwith the comet on it, or sculpt a pager machemodel of it. Perhaps you could even sponsor an artshow to display various Comet Halley piecescreated by your students.

Comets and Life Sciences

There are some articles in the literature today thatspeculate on the role of comets in spreading lifethroughout the universe. Some scientists have sug-gested that a rudimentary form of life might formin the nucleus of a comet, which would then col-lide with a planet planting the seeds for the forma-tion of life. There have even been suggestions thata comet collided with the earth and led to the ex-tinction of the dinosaurs. In this case, the collisionwould have produced a giant cloud of dust whichwould have blocked sunlight and cooled the earth,affecting the dinosaur's food supply. These ideasprovide excellent research topics for your students.Have them survey the literature on the topic anddecide for themselves if there might be any basisfor the speculation. Have your students speculateon what would happen if a comet as large as CometHalley were to collide with earth today,. Such acollision is highly unlikely, but not impossible.What is the likelihood that such a collision wouldaffect populated areas of the planet?

Comet Hall of Fame

Over the past 21(70 years, there have been a num-ber of individuals who have contributed signifi-cantly to our understanding of comets. Have yourstudents do a "Comet Hall of Fame." When pos-sible, students should include a picture of that per-son as well as a biographical sketch and a descrip-tion of the contribution to comet science for eachcontributor. Some of the "Hall of Famers" mightinclude: Aristotle., Isaac Newton, Johannes Kepler,Edmund Halley, Tycho Brahe, John Winthrop,Friedrich Wilhelm I3essel, Jan Oort, Fred Whipple,and E. E. Barnard.

OBSERVING TIE COMET

As discussed earlier Comet Halley will not benearly as spectacular in 1985-86 as it was in1910. However, with patience and care the cometcan be observed. It will be at its brightest iiroun4December 1985 and again in April 1986. It willnot be easily visible from large cities particularly inthe Northeastern U.S. If you live in that area of

9

/ 37

the country, you will have to get out into thecountry away from city lights and air pollution.But the effort will be worth every bit of the effort.Figure 17 is a star chart showing the path amongthe stars. This chart, along with Figures 9, 10, and11 should be sufficient to permit you to locate thecomet in the sky.

Brightness

Everyone has noticed how some stars appearbrighter than others. The brightnesses of stars aredescribed by their apparent magnitudes. The mag-nitude scale used in astronomy has developed overthe years into a well defined, but somewhat arbi-trary scale. The brithtest stars in the sky are moreor less first magnitude, and the faintes( stars visibleto someone with good eyesight and ideal observingconditions (no clouds, city lights, or air pollution)is sixth magnitude. The brighter a star, the lowerthe numerical value of its magnitude. The brighteststarssin the constellations Orion, Bootes, and Lyra(Rigel, Arcturus, and Vega) are extremely bright._These stars are zero magnitude objects. They arethe first stars to be seen in the evening sunset andthe last to be seen in the morning twilight. Firstmagnitude stars are also very bright. The brighteststars in Scorpius, Cygnus, and Virgo (Antares,Deneb, and Spica) are a few examples: The secondmagnitude stars such as Polaris, the pole star, aremoderately bright and 'an be easily identified.Third magnitude stars are still fainter. On a mistynight these are usually the faintest stars that onecan see. The fourth magnitude stars are visible ona ..moonlit or hazy night. Fifth and sixth magni-tude stars are visible only under the most ideal con-ditions. If you are used to the kindsof skies yousee around cities, iyou can be confused by a veryclear sky. If you were to go to a high mountain-top in the Southwest on a superclear night thereseem to be so many stars in the sky that it takes aminute or so to find the constellations. Figure 18is a sketch of the little Dipper, with the magni-tudes of the stars indicated. Since the stars aremagnitudes 2, 3, 4, and 5, it makes a good refer-ence in the...sky. You can also get a feeling for theviewing conditions on a given night by checkingthe Little Dipper. If you can see all the starsclearly, it is a fairly good night.

The following formulas will let your students pre-dict the total magnitude of Comet Halley. Here wemust be careful with our understanding of whatmagnitude means. The comet is not a point objectlike a star, but is spread out over a larger area. Thetotal magnitude is the brightness the comet wouldhave if the light were concentrated into a starlikeimage. You can imagine that if we were to spreadout the light of a star over a comet sized are itwould seem fainter. A comet that is third maghi-tude will be harder to see than a thirdstar, for instance. The formulas were determinedfrom the behavior, of Comet Halley at its previouspasses; that is, they are empirical formulas. The

same formula will not work for both pre-perihelionand post-perihelion magnitudes,

Pre-Perihelion:

Total Apparent Magnitude

= 5.47 + 5.0 x log(A) + 11.1 x log(R)

Post-Perihelion:

Total Apparent Magnitude

= 4.94 + 5.0 x log(A) + 7.68 X log(R)

In these formulas the symbol A stands for the dis-tance from the earth to the cornet, which we callthe geocentric distance, and the symbol R standsfor the distance from the sun to the comet, whichwe call the heliocentric distahce. The magnitudedepends on both distances for a simple reason.The distance from the sun determines how muchlight reaches the comet, and the distance from theearth to the comet determines how much of thelight reflected by the comet reaches us. Hidden inthe constants are assumptions about the reflectiv-ity of the comet. Included in the 5.0 multiplyingthe logarithm of A and the constant multiplyingthe logarithm of R is the fact that the brightness ofan object decreases with the inverse square of itsdistance.

In Table 2 we list the geocentric and heliocentricdistances of Comet Halley at selected times. Thefollowing example for October 15, 1985, whenA = 1.59 and R. = 2.16 shows how students can cal-culate total magnitudes for the comet.

Total Apparent Magnitude

= 5A7 + 5.0 x log(1.59) + 11.1 x log(2.16)

= 5.47 + 5.0 x 0.201 + 11.1 x 0.344

= 5.47 + 1.005 + 3.707

= 10.2

The formulas are not sufficiently precise to.permitus to calculate magnitudes to more than one figureafter the decimal point. Have your students calcu-late some magnitudes from the data in Table 2. Wehave given magnitudes as checks for your students,or for you to use if this exercise is too advancedfor your students.

From January through April, Comet Halley willhave an apparent magnitude in the range 4 to 5.So beware of the fact that it will require ideal con-ditions to observe the comet. Have the studentscompare the apparent magnitude of Comet Halleywith the stars in the Little Dipper. How can wecompensate for the fact that the stars are points oflight and the comet is an extended object? Oneway is to observe the stars with binoculars thathave been purposely racked out of focus to giveextended star images.

38 25

.50'

40

20

10

0

-10

20'

-10

-10

-50

TT 1

T L1RUS0

or) CI ANDROMEDA 0

0

0.ARIES111, PEGASUS

PL EIAOES

\ %Nov

6"

ekt'. r

1 i 1 1---- i I. i 1 1 i®, ,

'NO.-CYGNUS

r4b/ N

> \_____..1110C°R1AIILAIS 1,180.07;\

.01.YRA

HERCULES\ I

1 \ \/ \ N. \

IA 1 XNe

1 .., \af

0

-,,OPHIUCHUS

----__.

\I. PISCES

O

39

111UATDReLa..---... N /\ VSEsw

N / \\L11RA.II N./

MOWN! SCALE6 IN0 Ind

MA

41,

CAPRICORM.\.,

4

A Lto d./

1 1 1 I I 1 1 I 1

5^ 4" 3" 2" 1" Oh 23" 22" 21" 20" to' le" 17"

NYORA

Apt. 10

I I I I i I I10" 10" 14" 13" 12" II" 10"

Figure 17. Prkth of Comet Halley between November 1985 and May 1986.

copy 101,10 Pm 5

«oo'

40

440'

+M

+100

-too

-30*

.0*

-eft

Table 2Selected Ephemeris of Comet Halley

DATER.A. DEC ,, A R

MAOH M o I A.U. A.U. o 0

,trco

r.4

6 38 89 1

10 111 112 1

666666

103745484120

+13+13+13+12+12+11

534927501454

7.997.316.816.075.294.67

7.066.536.346.095.815.56

21.937.558,286.1

118.0151.7

3.15.47.89.48.74.8

tococc1.4

1 12 13 14 15 1

55445

4716585300

+12+12+13+14+16

0341395512

4.334.354.554.794.89

5.284.774.734.424.12

16.015.7

162.3126.2

94.362.835.5

3.29.2

12.111.68.2

ii2co0,-I

6 17 18 19 1

10 1

55566

1533541113

+17+18+18+19+20

2215532100

4.784.443.812.982.04

3.793.473.102.732.34

15.314.713.812.711.1

10.515.340.366.194.6

2.84.5

12.219.825.2

loco

0'-'

10 1511 11 1

11 1511 2011 25

65432

0324001114

+20+21+22+20+18

3850025020

1.591.070.740.660.62

2.161.921.721.651.57

10.28.87.47.06.6

110.8136.8170.1172.8154.5

25.620.75.74.3

15.7

tocoa',-1

12 112 512 in12 1512 2012 25

10

23232222

072848185436

+13+10+06+03+01-00

513451492624

0.630.670.730.820.921.02

1.481.421.351.271.191.11

6.46.36.26.26.16.0

131.7117.6102.1

j 68.8i, 77.5

67.6

29.737.945.750.853.754.7

cocoa,,-I

1 11 152 12 62 15

2221212120

1748180953

-02-05-08-09-11

2313273461

1.161.501.561.561.50

1.010.800.620.590.60

a''''

.,

5.85.14.1

; 3.94.1

55.333.710.26.5

14.7

53.443.016.510.924.8

to0,-I

3 13 53 103 153 20

2020202019

282111GO44

-16-17-19-22-25

1242523051

1.271.181.060.940.81

0.720.770.840.920.99

4.44.44.54.54.5

34.740.748.456.665.8

51.356.661.664.866.1

3 254 14 54 84 10

1918171615

2224221624

-30-38*-44

( -47-47

1545140632

0.690.530.460.430.42

1.071.181.241.291.32

4.34.14.03.94.0

76.596.0

110.6123.1131.5

85.057.549.140.734.8

cococa-

4 124 144 164 184 20

1413131212

3244033106

-46-43-40-36-33

2453284300

0.420.430.450.480.52

1.351.381.411.441.47

4.04.24.44.64.8

139.2145.2148.7149.3147.7

29.124.621.720.921.4

toQ,co,-I

4 255 15 156 17 1

1110101010

2456312634

-25-18-10-06-05

062,1324510

0.640.801.241.802.74

1.541.631.842.082.47

5.46.17.48.7

10.2

139.3128.5108.790.564.5

25.128.931.429.321.7

to°°cc.-I

8 19 1

10 111 112 1

1011111111

5211273942

-06-08-10-12-15

0300215406

3.574.174.524.624.50

:.

2.863.203.573.914,22

11.212.012.512.813.0

39.918.216.740.067.4

13,15.64.69.4

12.5

c.-coCl5,-

1 12 13 14 15 1

111110109

3105340549

-16-16-13-10-06

3007480353

4.274.104.164.575.21

4.534.835.105.385.65

13.113.313.513.814.3

99.4133.9158.1141.2110.8

12.48.54.26.79.6

NOTE: R.A. and DEC are the right ascension and declination of Comet Halley, using the equinox of the date. A is thedistance from Comet Halley to the earth, the geocentric distance. R Is the distance from Comet Halley to the sun, theheliocentric distance. MAO 'is the total magnitude. 6 lithe aniribetween the sun and the comet as seen from earth, andiris the atiiTt eWeen the sun and the earth as seen from the comet.

27

Al

35

2 4

5 (Variable)

*4

2

Figure 18. The Little Dipper showing the magnitudesof the stars.

With a wide angle telescope or a pair of binoculars,students will be able to see Comet Halley before itbecomes visible to the unaided eye. Figure 19 is agraph of the limiting magnitude for various objec-tive apertures (the diameter of the main lens of thetelescope or binoculars), given in inches. A 7 X 50pair of binoculars has an objective of 50 mm 26.4mm/inch or 2 inches (rounded to the nearest whole

t

I t1

i

1

r-------'fi

8

28

7 9 10 11

MAGNITUIN12 13

8

7

6

5

4

3

2

014

Figure 19. A graph of the limiting magnitude versusobjective size in inches for telescopes or binoculars.

number). Under ideal conditions, a pair of 7 X 50binoculars should let us observe Comet Halleywhen it has a magnitude of 10.8.

4

Length of Comet Halley's Tail in Miles

Measuring angles in the sky is not very difficult.There are several good angle reference points inthe sky. For instance, the Moon is about one-halfdegree in diameter. The pointer stars in the BigDipper are 5° apart, while the stars on the top ofthe bowl of the Dipper are 10° apart (tre Figure20). A paper clip held at arms length can be usedlike calipers to measure angles in the sky as shownin Figure 21. A cross staff can also be constructedto measure the length of the comet's tail (or otherlarge angles on the sky) in degrees, with moderateprecision. To construct a cross staff, carry out thefollowing steps. /

.1. Select a straight length of 1" by 1" lumber,at least 36" long.

2. Decide on one of the 1" sides to be the top,then mark off 1" increments along each sideof the stick. Starting at either end, numberthe marks 1", 2", 3", and so on.

3. Drive two nails into the top of the stick, oneat each end to serve as sights.

4. Select a seco9d piece of 1" by 1" lumber, atleast 21" intiength to be the cross piece.Carefully find and mark its center. Thenmark 1" increments on the sides, beginningat the center. Number these increments 1",2", and so on, beginning at the center andworking outward toward each end.

5. live a nail at the 2" mark, the 5" mark,and the 10" mark at each side of the center.

6. Construct a slide mechanism for the crosspiece. The simplest way is to drive a nail onthe bottom of the cross piece 1-1/2" fromthe center on each side of the center. Bendthe nails toward the center to serve as a slide.

Figure 22 shows a cross staff built to these specifi-cations. Notice that it has a slightly better slidemechanism made from two blocks of 1" by 1"lumber. The cross staff is easy to upe. Hold it justas the young lady is doing in the figure, and alignthe sight nails on the long piece with one end of

. the comet. Then slide the cross piece backward orforward until one of the nails (the 2", the 5", orthe 10") on the cross piece is aligned with theother end of the comet. Read two numbers fromthe cross staff: the distance of the cross piece fromyour eye, and the distance from the center cis thecross piece of the nail that you used for the otherend of the comet. Table 3 can be used to convertthese measurements to degrees.

42

Figure 20. The Big Dipper showing angle sceles.

00

ti

Figu!21. Using a paper clip held at arms length to compare known angular extentsin the sky with unknown extents.

s ,JY

'. I

t

L_

Aim the cross staff at the head and tail of the comet to determine the angular measurement of Cornet Halley.Figure t2. Using a well made cross staff to Measure angles, The construction of the cross staff is

reasonably clear in the photograph.

43 29

Table 3Conversions for Cross Staff Measurements

Length(inches

Width

2 inches 5 inches 10 inches

Angle in Degrees

2 45.0 68.2 78.7

3 33.7 59.0 73.35 21.8 45.0 63.4

8 14.0 32.0 61.3

12 9.6 22.6 39.8

15 7.6 18.4 33.7

18 6.3 15.5 29.1

21 5.4 13.4 26.6

24 4.8 11.8 22.6

27 4.2 10.5 20.3

30 3.8 9.5 18.4

33 3.5 8.6 16.9

36 3.2 7.9 1G.5

Once the observed length of the tail is measured indegrees, its length in kilometers, miles or astronom-ical units can be calculated. Remember that oneastronomical unit is 150,000,000 kilometers or93,000,000 miles.

Length of tail= geocentric distance x

sin (observed length in degrees)

Suppose that on January 15, 1986, your studentsobserve Comet Halley to have a 45° tail. Look upthe geocentric distance in Table 2, and find the sineof the tail length in a convenient trig table. Then'

Length =1.50 x sin(5°)= 1.50 x 0.087 = 0.13 astronomical unit.

The to of the comet does not lie exactly in theplane of the sky. It may also have extent towardor away from you. Have your students discuss thelength you calculate in light of this fact. To com-pensate for the projection effect, you can dividethe length, calculated above by

sin(sunrcomet-earth angle in degrees -observed comet tail length in degrees)

where the sun comet-earth angle is the angle [5 inTable 2.

Recording Observations0

It is very portant for the students to record theirobsery ons. A suggested Comet Halley observa-tion orm is included. Careful recording of theirob ations will permit students to compare oneob .rvation with another.

Q

30

The students should be encouraged to make draw-ings of the comet as acctirately as possible. Thenucleus (if one is visible), coma, and tail of thecomet should be recorded for each observation.The other data required on the form should also berecorded. When possible, students should compareunaided eye views of the comet with those madethrough a telescope or binoculars. Have the stu-dents list advantages of viewing the comet with thetelescope or binoculars. Have them determinesome of the advantages of viewing the comet with-out use of a telescope or binoculars.

Students should be encouraged to phOtographComet Halley when they have the appropriateequipment. The camera with standard lens mustbe mounted on a tripod and fast color or black andwhite film must be used: The students should ex-periment with different exposure times. Theymight try a sequence of shots like 5, 20, 40, and80 seconds. Longer exposures will smear thecomet due to the earth's rotation.

If your school has a block driven telescope, it mightbe used as a base for the camera. The camerashould be fastitriled (tape will be fine) to the for-ward part of he telescope. With a clock driventelescopelonger exposures can be made. If a blackand -white photograph is being made during a timewhen the moon is out or during twilight, a redfilter might be used. Increase your exposure timesby a factor of four to compensate for the filter.Try several exposures of different lengths. Use thephotographs to determine the magnitude of CometHalley from the stars. The magnitude of stars canbe determined from various observer handbooks.

40

Plotting the Location of Comet Halley

A familiarity with the use of a star chart andknowledge of how to plot the locations of CometHalley are needed to successfully "keep track" ofHalley. A star chart is included to assist you in thisactivity. See center of booklet and Figure 17.

Notice on the star chart that the constellations arenamed. Constellations are "pictures" in the skyand are used to identify the different sky regions.The different sized dots represent the differentmagnitudes of the stars. (Refer to the magnitudekey on the star chart.) Also, notice the line thatruns through the center of the star chart in an east-swest direction. This line is celestial equator. Thecelestial equator is nothing more than the earth'sequator projected onto the plane of the sky.

To find a location on earth, one uses longitude andfatitude; however, different terms are used in refer-ence to analogous coordinates in the sky. In thesky, right ascension (RA) is the coordinator equiva-lent to longitude and declination i equIvalent tolatitude. Notice on the star chart that at the bot-tom are a series of numbers 6, 5, . . . , 0, 23, . . . 9.Each number is the right ascension of that area of

44

Name

Date

COMET HALLEY OBSERVATION FORM

Time of Observation

ObserVer Location

Weather Conditions ,,

Moon Phase

Comet Halley's Location in Sky:,

Degrees Above Horizon Constellation Region

S4tch Area of Sky

,--

*

e,

45 31

PHYSICAL APPEARANCE OF COMET FORM

UNAIDED EYE VIEW TELESCOPE/BINOCULAR VIEW.

Length of tail in degrees

Size of Objective

Magnification

Length of tail in degrees

Color of Comet Color of Comet

Estimated Magnitude Estimated Magnitude i

Description of Nucleus,Coma, Tail

Description of Nucleus,Coma, Tail

. .

Drawings (Comet shape,direction, length of tail)

.

Drawings (Comet shape,direction, length of tail)

32 46

the sky. Right ascension is measured eastwardfrom the Vernal Equinox along the celestial equa-tor, In hours. Every degree moved eastward fromthe Vernal Equinox equals an addition of fourminutes of right ascension. Therefore, 15° east ofthe Vernal Equinox is equal to one hour of RA;30°/ east equals two hours of RA, eta.

On a star chart one uses a "+" sin to represent lo-cations north of the celestial et, uator and a "-":.sign for locations south of the celestial equa r.An object with the declination of +15°north of the celestial equator, while -15° ouldplace the object 15° south of the celestial equ r.Table 2 lists selected RA and declination locati sfor Comet Halley from 1981-1987. A more incsive list can be found in an ephemeris, such as thatin the Comet Halley Handbook (see Bibliography).As an activity, have the students plot the positionsfor Comet Halley on a starehart. Generally, theplanets and the moon move from west to eastamong the stars. This is not sip for Comet Halley.Halley moves from east to west.

5°

To plot Halley's positions, the students are to put apoint at the intersection of the RA and declinationlocations for each of the dates given. Notice thatHalley/ motion among the stars is not a smoothline frOm east to west. Halley's apparent motionappears to loop occasionally. This isa result of theearth passing Comet Halley during our orbitaround the sun for that particular gear. Again, ageneral astronomy textbook will provide a moredetailed explanation of retrograde motion.

Once the plotting exercise is completed, studentscan use their star charts to assist them in locatingComet Halley either with an optical instrument orthe naked eye. The star chart will be especiallyhelpful from November 1985 through May 1986.

Comet Halley's Orbit

Earlier we discussed the elements of the orbit of acomet. To supplement this information, have yourstudents construct a model of Comet Halley's orbit.Figure 23 gives an overview of the angular elementsof Comet Halley's orbit, near the earth's orbit.

1. Construct the earth's orbit. On a piece ofposter board roughly 24" x 24" draw a circlewith a diameter of 6 inches. In this case 3"equats one astronomical unit. The sun is lo-cated at the center of the circle. Then drawanother circle with a diameter of 12 inchesto provide a'2 A.U. scale, and a circle withan 18" diameter to provide a 3 A.U. scale.Next divide the earth's orbit into 12 equalparts. Each part is to represent the earth'slocation for one month of the year. Labelthe earth's orbit as indicated in Figure 24.This is the view you would have if you werelocated above the earth's orbit and werelooking down on it. In the figure the Roman

numerals refer to huurs of right ascension.Review the plotting exercise if necessary.

2. Draw a line from 58° through the center ofthe circle to 238° . At the 58° point in theearth's orbit, Comet Halley will pass fromsouth to north across the earth's orbitalplane. It will later pass from north to thesouth of the earth's orbital plane at the 238°point.

3. A slit needs to be made in the earth's orbitso that you can" insert Comet Halley's orbitlater. Comet Halley's orbit is positionedsuch that it extends 1:85 A.U. from the sunon the 58° side of the earth's orbit and 0.85A.U. on the 238. side. On our scale this cor-responds to a distance of five and one-halfinches and two and one-half inches. Using asingle edged razor blade, make a slit in theearth's orbit according to the instructions.

4. Comet Halley's orbit is elliptical in shape.Refer to the drawings in Figure 25. Notethe terms on the drawing: semimajor axis,semiminor axis, semilatus rectum, aphelion,and perihelion. Also, note the equationsgiven to solve for the 'different part ofComet Halley's orbit, if you would like toassign this as an exercise.

For Comet Halley, .the length of the semiminor axisis equal to a distance of 17.945 A.U. The eccen-tricity is equal to 0.9672671. Ifave the studentssolve the different equations to gilt a better under-standing of Comet Halley's orbit, if they are a theappropriate level of mathematics.

Let a = semimajor axis = 17.945 A.U.

Let e = eccentricity = 0.967281

Then:

Perihelion Distance = a(1-e)

= 17.945 x (1.0-0.967281)

= 17.945 x 0.032719 = 0.587 A.U.

Aphelion Distance = a(l+e).

= 17.945 x (1.0+0.967281)

= 17.945 x 1.967281 = 35.3029 A.U.

Length of Semiminor axis = a(1-4 )1/2

= 17.945 x (1.0 - 0.9672812)1/2

= 17.945 x (0.06436746)1/2

17.945 x 0.2537

= 4.552 A.U.

33

47

LOCATION OFVERNAL EQUINOX--

PERIHELION

.:

9

COMET 9.6LLEY'S ORBITo-EARTH'S ORBIT

Figure 23. Angular elements of Comet Halley's orbit. The quantities are as follows: A is the longitude ofthe ascending node, with a value 58.15°. B is the inclination of the orbit to earth's orbital plane, with avalue 162.24 . C is the -4gument of perihelion and D is the perihelion point.

yz

34

XDZ

210°

1800

4141 2 01 7 I°

90° VT1,4411 iXX * 111 EL

300° W 0°

330° 30°

,XX11

Mar 270

0° IL

Figure 24. A view of the earth's orbit seen from above. The rightascension is marked both in hours (Roman numerals) and in degrees.The three circles represent the earth's orbit (1 A.U.) as well as a 2 A.U.and 3 A.U. scale. The heavy line marks the cut to insert the model ofComet Halley's orbit.

48

DISTANCE FROM SUNTO COMET HALLEY

PERIHELION DISTANCE all -e)

COMET,HALLEY

LENGTH OF SEMIMINOR AXIS = all - e2)%

PERIHELION a-

SEMILATUS RECTUM

LENGTH OF SEMILATUSRECTUM = e2)

APHELION

1

Figure 25. The geometry of Comet Halley's orbit. All relevant terms are defined on the figure.

Length of Semilatus Rectum = a(1-e2)

= 17.945 x (1.0 - 0.9672782)

= 17.945 x 0.064367 = 1.155 A.U.

Have your students onvert their answers to milesor kilometers.

5. Draw Comet Halley's orbit to scale. Notethat the distance of the semilatus rectum is1.115 A.U. (you can have your studentil cal-culate this number, too). The total distanceacross the orbit atthe sun is twice this dis-tance or 2.230 A.U. Since we are using ascale of 3" equals one A.U., the latus rectumis 2.230 x 3 = 6.69 inches. To make matterseasier, you can round this off to 6 and 3/4inches. Similar , calculate the periheliondistance in inch . In round numbers, it willbe 1 and 3/4 inc es. Draw an elliptical arc

*representing a portion of the orbit as shownin Figure 26a. We will not draw the entire' orbit; it would be excessively large on ourscale.

6. Cut out the orbit and slide it through the slitfrom the underside of the earth's orbit. UseFigures 26b and 26c to properly orient thecomet's orbit.

Places to Visit - Things To Do

Field trips to a planetarium or an observatory are amust during your study of Comet Halley. Resourcepersons from the community should be contactedto visit your classroom. Your local astronoiy club

is a good resource to help you with your comet ac-tivities. Pe -haps such a club could host a star party.

Work with your school librarian now to begin togather boc ks and articles for the study of comets.Watch for radio or television programs that couldbe of interest and value to your students. Youmight want to publicize your aLtivities on themedia.

Computing an Ephemeris for Comet Halley

A table of positions of the comet at various timesis called an ephemeris. If your school has a com-puter that operates in .the BASIC language, yourstudents can calculate an ephemeris for CometHalley using the program starting on page 37,written by R. Chapman. It is not as sophisticatedas programs written by astronomers who calculatethe position of the comet to an accuracy of sec-onds of arc, but it will allow you to calculate itsposition to better than a few minutes of arc. Italso prints* out the position of the sun and thecomet's magnituee. The X, Y, and Z coordinatesof the sun and Comet are rectangular coordinatesin a right handed system where the x-axis pointstoward the vernal equinox, and the xy-plane is theplane of the earth's equator. The right ascension,declination X, Y, and Z are referred to the vernalequinox at 1950. R is the heliocentric distance ofthe comet, and delta is its geocentric distance. Theprogram also calculates the altitude and azimuth ofthe comet for a given time. These numbers aregood for your latitude, and the time that youinput. These numbers will help you locate thecomet. An altitude larger than 90° means thecomet is below the horizon. The details of the

4936

DECEMAER 23, 1985

NOVEMBER 9, 1985

(a)

FEBRUARY 9, 1986

MARCH 10, 1986

MARCH 30, 1986

/./

(b)

162°

(c)

Figure 26. (a) Measurements for a portion of Comet Halley's orbit; (b) Location of Comet Halley on five dates, to be usedin the model; (c) Tilt of Comet Halley's orbit to the earth's orbit.

3650

program are beyond the scope of this booklet, andmight be a good library project for yourstudents.The program has been annotated with REMstatements to help see what is going on. Theauthor of the program wrote it and tested it on an

Apple IIe computer using BASIC, but it shouldwork on other systems. We do not endorse anyparticular personal computer; we are merelyproviding a warning that the program has not beenchecked out of a variety of systems.

Even though Comet Halley will fade out of sight in the visiblesky soon after April 1986, not to reappear for another 76years, the young people that you have worked with will carrywith them memories of Comet Halley all through their lives.In addition, they will gain the skills, understanding, andenthusiasm to look at the skies for their entire lives. Who canpredict the total life-long impact of such a meeting withComet Halley?

PROGRAM10 REM *** INPUT NUMERICAL CONSTANTS ***20 REM *** OB = OBLIQUITY30 PI 3.14159265:0B 0.48914:RD 57.2957795sTPI 2.0 * PI40 REM *** INPUT ORBITAL ELEMENTS ANGLES IN RADIANS***50 REM EECCCENTRICITY; 010NODE LONGITUDE; 02PERIHELION LONGITUDE60 REM ININCLINATION; A=SEMI MAJOR AXIS; PPERIOD IN YEARS70 REM PDJULIAN DAY OF PERIHELION; PHADDITIONAL DAY FRAC. AT PERI.80 E 0 0.9672768,01 1.81482798102 1.9521174390 IN = 2.83160961:A = 17.941104:P 75.993100 pp 2446478.5IPH 0.45174110 GOSUB 6000120 N I TP / P / 365.25: REM MEAN MOTION121 HOME s VTAB 8: PRINT "THIS PROGRAM CALCULATES INFORMATION"122 PRINT "OF INTEREST FOR COMET HALLEY FOR ANY" -

123 PRINT "LOCATION ON EARTH. THE OPERATION"124 PRINT "IS SELF EXPLANATORY.", PRINT125 PRINT "SOME DEFINITIONS: ": PRINT "X,Y,Z ARE COORDINATES IN EQUATOR'AL"126 PRINT "SYSTEM IN A.U. R IS DISTANCE FROM SUN.".127 PRINT "DELTA IS DISTANCE FROM EARTH."s PRINT128 PRINT "INPUT YOUR LATITUDE IN DECIMAL DEGREES": INPUT " NEGATIVE IF.

IN SOUTHERN HEMISPHERE ";LA129 LA LA / RD130 INPUT "DATE OF INTEREST? (MM,DD,YYYY) " ;MM,DD,YYsS = 1: GOSUB 5000140 INPUT "TIME OF INTEREST? (HH,MM) ";HH,M1150 JH 0I;(HH + M1 / 60) /24160 M ((JD PD) + (JH PH)) * N165 OMB 7500: REM FIND POSITION OF SUN170 KY 10 8180 GOSUB 7000: REM SOLVE KEPLER'S EQUATION190 SOWS 80001 REM FIND X,Y,Z OF COMET193 REM SCSUNCOMET DISTANCEess sc SCR (XC * XC + YC * YC + ZC * ZC)210 X XC + XSsY YC + YSsZ = IC + ZS220 REM CALCULATE EC-EARTH COMET DISTANCE230 REM ACRIGHT ASCENSION OF COMET; DC0DECLINATION OF COMET240 EC SQR (X *X+Y*Y+Z* Z)243 IF KY 1 THEN 250248 DM 0.003772 * EC * NsM M DMsKY = is GOTO 180250 SA Z / ECsCA MIR (1.0 SA * SA)s GOSUB 8500260 DC A3sSA Y / (EC * CA):CA = X / (EC * CA), GOSUB 8500270 AC A3280 REM THANGULAR SEPARATION SUNCOMET290 CA SIN (DC) * SIN (OS) + COS (AS AC) * COS (DC) * COS (DS)

51 37

300 SA mm SOR (1.0 CA * CA). GOBUB 8500319 TM mm A3320 SOSUB 9000e REM FWD SIDEREAL TIME330 HA m ST AC. REM A:04HOUR ANGLE332 IF HA ( 0 THEN HA mm HA + TP.$40 X.s COS (DC) * SIN (HA)359 Y SIN (DC) * COS (LA) COS (DC) * COS (HA) * SIN (LA)360 Z SIN (DC) * SIN (LA) + COS (DC) * COS (HA) * COB (LA)370 SA ZiCA SOR (1.0 SA * SA)1 BOGUS 8500380 EL mm AMA X / CAMP Y / CA1'008U8 8509385 IF EL ) 4.72 THEN EL EL TP390 AZ gm A3400. IF JD ) 2446470.5 THEN 430410 MT 5.47 + (5.0.* LOG (EC) + 11.1 * LOG (SC)) / 2.3026420 GOTO 440.439 MT mg 4.94 + (5.0 * 'LOG (EC) + 7.68 * LOG (SC)) / 2.3026'440 MN 14.1. + (5.0 * LOG (EC) + 5.0 * LOG (SC)) / 2.30262000 HOME I PRINT " POSITION OF COMET HALLEY ": PRINT2919 PRINT "DATE: "OM;"/";DD;"/";YY;" JULIAN DAY " ;JD: PRINT2020 RA mm 3.81971863: REM CONVERT RADIANS TO HOURS2022 ST mm ST 41, RA:H INT (ST)0612 INT t60 * (ST H))2024 PRINT "LOCAL TIME: SOLAR ";HH;" ."01;" SIDEREAL= " ;H ;" "022026 PRINT2028 PRINT "COORDINATES OF THE SUN:2029 XS - INT (10000 * XS) / 10000sY8 mm INT (10000 * YS) / 10000sZ8 INT

(10000 * Z8) / 100002030 PRINT " 1mm ";XS;" Y "044F, Zim2040 AS mm AS * RA:H INT (AS):M2 gm INT (69 * (AS H))2050 DS mm DS * RDel) mm INT (DS):M3 INT (fte * (DS D)): IF D ( im 90 THEN

29702060 D D 359:M3 mm 60 M32070 PRINT " R.A.- " ;H ;" " ;M2 ;" " ;D ;" "032075 PRINT edPRINT "COORDINATES OF THE COMET.2078 XC ft INT.(10000 * XC) / 10900:YC mm INT (10000 * YC) / 10000:ZC - INT

(10000 * ZC) / 100002980 PRINT " X= " ;XC ;" Ymm " ;VC ;" ";ZC2090 AO AC * RAIH mm INT (AC):M2 mm INT (60 * (AC H))2100 DC mm DC * RDiD mm /NT.-(DC):M3 INT (60 * (DC D)). IF D ( mm 90 THEN

2120

2120 PR NT "2110 D 359.013 mm 60 M3

R.A. ms " ;H ;" " ;M2 ;" DEC- " ;D ;" " ;M32130 PR T Rom "; INT ( 100 * SC + 0.5) / 100;2140 PRINT " DELTA- "; INT (100 * EC + 0.5) / lea2145 TH mi INT (190 * TH * RD + 0.5) / 1002150 PRINT " SUNCOMET ANGLE ";TH2160 HA gm HA * RAIIX gm 9: IF HA ) 12 THEN X mm 1:HA mm 24 HA2170 H INT (HA).012 mm INT (60 * (HA H) )

2180 PRINT " HOUR ANGLE " ;H ;" " ;M2;2190 IF X 0 THEN PRINT " WEST"2800 IF X 1 THEN PRINT " EAST"me AZ mm AZ * RDeD mm INT (AZ):M3 - INT (69 * (AZ D))2229 PRINT " AZIMUTH- " ;D ;" " ;M3223$ EL mo EL * RD.D mm INT (EL):M3 mm INT (60 * (EL D))2240 PRINT " ELEVATION " ;D ;" " ;M3

ene MT mm INT (10 * MT) / 100N mm INT (10 * MN) / 102260 PRINT : PRINT se NUCLEAR MAGNITUDE- " ;MN2270 PRINT," TOTAL MAGNITUDE- " ;MT2280 PRINT4990 PRINT "DO YOU WANT ANOTHER DATE? (Y/N): ": GET C$4992 IF C$ mm "Y" THEN 1304993 HOME : vTps 12e PRINT " SIGNING OFF"4999 END5999 REM **CALCULATES JULIAN DAY**5010 IF MM ( mm 2 THEN X mo 1

38 52

5020 IF MM ) 8 THEN X 0 95030 IF S 9 THEN C = 25040 IF S = 1 THEN C = INT ((YY - X) / 100)5050 Al - INT ( INT (365.25 * (YY - X)) -5060 8 0 INT (367 * ((MM - 2) / 12 + X))5070 IF 8 ( 0.THEN = 8 + 1

C)

3080 JD 1721088.5 + DD + Al +B5090 RETURN6000 REM6095 REM *** SETS UP VECTORS TO CONVERT FROM ORBITAL ***6010 REM *** TO ECLIPTIC COORDINATES ***6015 REMsees PX - COS (02) * COS (01) - SIN (02) * SIN (01) * COG (IN)6030 PV - COS (02) * SIN (01) + SIN (02) * COS (01) * COB (IN)6040 PZ SIN (02) it SIN (IN)6050 GX - - SIN (02) * COS (01) COS (02) * SIN (01) * COB (IN)6060 GY = - SIN (02) * SIN (01) COS (02) * COS (01) * COS (IN)607068907880701079207930705079607070708070997100711071e.713075807510752975307550756075787580758575867590

OZ - COS (02) * SIN (IN)RETURNREM *************************REM * ITERATIVE SOLUTION OF *REM * KEPLER'S EQUATION *REM ******4******************

TPt = 2.0 * PIX 0 M / TPIM 0 (X - INT (X)) * TPIEA 0 MES = EA -.(EA - M E * SIN (EA)) / (1.0 E * COS (EA) )IF ASS (ES - EA) / ES ( 1E - 8 THEN 7130

EA 0 ESOOTO 7090RETURNREM POSITION OF THE SUNREM 91 -MEAN ANOMALY; OP-PERIHELION LONG; Li -SUN'S LONGITUDE

DI (JD - 2415020) + JHX1 - (358.4758 + 0.9836 * DI) / 360.91 = (X1 - INT (X1)) * 360 / RDOP - (281.2208 + 4.7E - 5 * D1) / RDLI = 01 + 0.03344 * SIN (611) + 3.49E - 4 * SIN (2 * Gl) + OPX1 = Ll / TPIREM CALCULATE FINAL LI AND PRECESSREM THEN SUN AND COMET ARE REFERRED TO SAME EPOCH

LI (X1 - INT (X1)) * TPI + 2.437E - 4 * (2433282.5 - JD) / 365.25

7f.Vb REM BE -SUN -EARTH DISTANCEIXS,YS,IS=RECT. COORD. OF SUN7600 SE - 0.99972 / (1.0 + 0.01675 * COS (LI - OP))7610 X8 0 SE * COS (LI)76e0 YS - SE * SIN (Li) * COS (OS)7630 ZS - SE * SIN (Li) * SIN (08)7648 REM --- AS -RIGHT ASCENSION OF SUN --7643 REM --- DS- DECLINATION OF SUN - --7650 SA se ZS / SEICA - SQR (1.0 - SA * SA): (3OSUB 85007960 DS 0 03e8A - YS / (SE.* CA)NCA - X8 / (SE * CA)* GOSUB 85007670 AS 0 A37880 RETURN8000 REM CALCULATES COORDINATES IN8010 REM ECLIPTIC SYSTEM

xl as A * ( COS (EA) - E)8W30 YI 0 A * 80R (1 - E * E) * SIN (EA)8048 X 0 X1 * PX + Yl.* GX8050 Y X1 * PY + Y1 * GY8060 Z 0 X1 * PI + Y1 * OZ8063 REM ***ROTATE TO EQUATORIAL SYSfiEM8070 XC 0 XsYC - Y * COS (DB) Z * SIN (OB)sZC = Y *

(08)

53SIN (MB) + Z * COB

39

aim RETURN8500 REM8585 REM TWO ARGUMENT ARCTAN8510 REM CAmCOS(A);SAmSIN(A); RETURNS A IN PROPER QUADRANT8515 REM8520 IF ASS (CA) ( lE 8 THEN 8540u8530 A3 - ATN (SA / CA): GOTO 85608540 IF SA ) 0 THEN A3 sa 0.5 * PI8550 IF SA (0 THEN A3 - 1.5 * PI8560 IF CA (8 THEN 85908570 IF CA ) 0 AND SA ( 0 THEN 86008580 SOTO 86108590 A3 m A3 + PI: GOTO 86108600 A3 m A3 + 2.0 * PI.8610 RETURN9000 REM CALCULATE SIDEREAL TIME9010 T1 - (JD 2415020) / 36525s REM CENTURIES SINCE 19009020 XI m (18.64606 + 2400.0513.* TI) / 24 + 0.5 + JH9030 ST - (X1 INT (X1)) * TPA REM SIDEREAL TIME IN RADIANS9040 RETURN10000 12 m ((1986 + YY) / 2 1900) / 10010010 X3 as 3.07234 + (0.00186 * Te):Y3 m 20.0468 (0.0085 T2):Z3 m Y3 /

1510020 13 - (JD PD) / 365.3510030 X4 m 7.2722E S * T3 * (X3 + (Z3 * SIN (AC) * TAN (DC)))10049 X5 m 4.8481E 6 * T3 * Y3 * COS (AC)10050 AC m AC +X4tDC - DC + X510060 RETURN

54

40

amateur astronomers, 3ammonia, 10aphelion, 33, 35Aristotle, 1, 24Astro Mission, 19, 21BASIC program, 37-40Bayeux Tapestry, 24Chapman, R., 36comet,

brightness, 9, 18collision with, 24coma, 9, 10, 16

diameter, 9composition, 10discovery, 3-4hall of fame, 24heal, 9hyarogen cloud, 15lifetime, 16, 18naming, 3nucleus, 9, 10, 15, 16, 21

nature, 10orbit, 1, 6-9parts, 9tail, 9, 16, 23

dust, 15, 16length, 9orientation, 10, 16plasma, 16, 16

Comet Bennett, 15Comet Biela, 18Comet Donati, 18Comet Ensor, 18Comet Halley, 1, 11, 10, 20, 29

appearance, 9-10art, 24brightness, 25, 29classroom activities, 23-24ephemeris, 27, 36-40historical importance, 1-3lifetime, 18newspaper accounts, 23observations, 30, 31, 32orbit, 3, 33-36path, 26photography, 30plans to observe, 19-21position, 12, 13, 14, 26, 27, 30recovery, 4returns, 23tail, 30

encounter with, 23viewing, 10, 24-40

Comet Honda-Mrkos-Pajdusakova,Comet Howard-koomens-Michels, 19Comet Ikeya-Seki, 4, 19Comet Kohoutek, 5, 6, 10, 18, 19Comet IRAS-Araki, Alcock, 6, 9, 10Comet Schwassmann-Wachmann 1, 5Comet Schwassmann-Wachmann II, 6Comet Tago.Sato-Kosaka, 16Comet West, 1, 16Comet Westphal, 18comets,

daylight, 10, 18longperiod, 8, 18short-period, 8, 9. 18sun-grazing, 18, 19sun-hitting, 19

cornet seeker, 3conic section, 5, 7

circle, 7ellipse, 5, 7hyperbola, 5, 7parabola, 1, 5,

INDEX

55

constellation, 25, 28, 30Copernicus, N., 1

cross staff, 28-30cyanogen, 19, 23declination, 27, 30, 35dinosaur, 24direct motion, 8disconnection event, 19, 21eccentricity, 5ephemeris, 5, 27, 35 -40field trips, 35Galileo, 1generatrix, 5, 7geocentric distance, 25, 27, 36Giotto, 19, 24Giotto Mission, 19gravity, 1, 19Halley, E., 1, 5, 24heliocentric distance, 25, 27, 35Herschel, C. 5horizon, 13, 14, 15, 35hydrogen cyanide, 10, 19, 23Ikeya, K., 4inclination, 5, 8International Halley Watch, 21interstellar space, 5Kepler, J., 1latitude, 35magnitude, 25, 26, 27, 28, 30, 32

limiting, 28meteor, 15meteor shower, 15, 16methane, 10methyl cyanide, 10Mitchell, M., 5molecules,

daughter, 10parent, 10

Newton, I., 1, 3Oort, J., 18Oort cloud, 18oral history, 24orbit 1, 5, 8

elliptical, 1, 5parabolic, 1, 6hyperbolic, 5

orbital elements, 5; 8, 34parallax, 1, 2perihelion, 3, 5, 10, 24, 33, 35I1errine, C., 4perturbation, 18photon, 15Pons, J., 4Ptolemy, C., 1radical, 16retrograde motion, 8, 9right ascension, 27, 30, 34, 35Seki, T., 4semimajor axis, 33, 35semiminor axis, 33, 35semilatus rectum, 33, 35Seneca, L., 1solar wind, 15sublimation, 10, 16, 18time capsule, 24Tycho Brahe, 1vernal equinox, 3, 8, 33, 34, 36water, 10Whipple, F., 10. 24

41