Physics 360/Geology 360*Welcome to Astronomy

We will Meet in S-138 Science Building for the

Semester

Explorations: An Introduction to Astronomy Companion Site, 6/eThomas T. Arny, University of Massachusetts, Amherst - EmeritusStephen E. Schneider, University of Massachusetts, Amherst

ISBN: 0073512176Copyright year: 2010

* This is a cross-listed course

This PowerPoint slide set is closed on 1/20/2010

Grade Determination

• Exams:  Your grade is calculated by taking the three hourly exam scores, the homework score (which will be also treated as an exam and then adding the final exam which counts the same as an hourly exam. 

• You must take the final. 

Homework

• Homework assignments will be made on the McGraw Hill Higher Education Website. (www.mhhe.com/arny) You will complete and submit the assignments on a bi-weekly basis.

• You must first log in (as a student) and register for the first time. There are two sections.

• Section 1 is Geology 360• Section 2 is Physics 360

Login in at: www.mhhe.com/arny

Section 1 is Geology 360 B94-97-47BSection 2 is Physics 360 DEB-D9-B43

We are using the 5e of Arny for Homework and the Aris Homework System

This is last year. Ignore!

You will see this page.

Click on

Click here

Do These

Instructors note. John Q. Smith enrolled in Section 1

Astronomy without a Telescope

Angular Measurements• There are 360 degrees in a full circle and 90 degrees in

a right angle • Each degree is divided into 60 minutes of arc • A quarter viewed face-on from across the length of a

football field is about 1 arc minute across. • Each minute of arc is divided into 60 seconds of arc • The ball in the tip of a ballpoint pen viewed from across

the length of a football field is about 1 arc second across.• The Sun and Moon are both about 0.5 degrees.• Bowl of the Big Dipper is about 30 degrees from the

NCP • Any object ``half-way up'' in the sky is about 45 degrees

above the horizon

I strongly recommend you download the planitarium program HNSKY to your own

personal laptop and use it in this course. It is free, has absolutely no viruses, and is an

excellent educational tool.

http://www.hnsky.org/software.htm#hnsky

HNSKY

http://www.hnsky.org/software.htm#hnsky

In fact, HNSKY can be downloaded in any one of the student computer clusters. The computer does not have to be restarted. After the program is run, you must enter the coordinates of where you wish to view. If you are around here, then using the coordinates listed locally on the main web page for this class (North Terre Haute, IN)

This is the preferred coordinate system (Equatorial Coordinates) to pinpoint objects on the celestial sphere. Unlike the horizontal coordinate system, equatorial coordinates are independent of the observer's location and the time of the observation. This means that only one set of coordinates is required for each object, and that these same coordinates can be used by observers in different locations and at different times.

The equatorial coordinate system is basically the projection of the latitude and longitude coordinate system we use here on Earth, onto the celestial sphere. By direct analogy, lines of latitude become lines of declination (Dec; measured in degrees, arcminutes and arcseconds) and indicate how far north or south of the celestial equator (defined by projecting the Earth's equator onto the celestial sphere) the object lies. Lines of longitude have their equivalent in lines of right ascension (RA), but whereas longitude is measured in degrees, minutes and seconds east the Greenwich meridian, RA is measured in hours, minutes and seconds east from where the celestial equator intersects the ecliptic (the vernal equinox).

Also called topo-centric coordinates

Tip of the Day: (1) How sunrise to sunset is defined. Sunrise is time from just when the top of the sun clears the horizon to sunset when the last bit of sun disappears.

“Apparent Magnitude” was defined by Hipparachus in 150 BC. He devised a magnitude scale based on:

Magnitude Constellation Star

1 (Orion) Betelgeuse

2 Big Dipper various

6 stars just barely seen

However, he underestimated the magnitudes. Therefore, many very bright stars today have negative magnitudes.

Magnitude Difference is based on the idea that the difference between the magnitude of a first magnitude star to a 6th magnitude star is a factor of 100. Thus a 1st mag star is 100 times brighter than a 6th mag star. This represents a range of 5 so that 2.512 = the fifth root of 100. Thus the table hierarchy is the following.

Magnitude Difference of 1 is 2.512:1, 2 is 2.5122:1 or 6.31:1, 3 is 2.5123 = 15.85:1 etc.

(2) Astronomy Magazine Sept. 2002 issue defines the faintest naked eye star at 6.5 apparent magnitude.

Absolute Magnitude is defined as how bright a star would appear if it were of certain apparent magnitude but only 10 parsecs distance. A parsec is 3.26 light year.

Hipparchus or Hipparch (Greek: Ἵππαρχος, Hipparkhos; c. 190 BC – c. 120 BC) was a Greek astronomer, geographer, and mathematician of the Hellenistic period.

At first glance, this system of uniquely positioning an object through two coordinates appears easy to implement and

maintain. However, the equatorial coordinate system is tied to the orientation of the Earth in space, and this changes

over a period of 26,000 years due to the precession of the Earth's axis. We therefore need to append an additional piece of information to our coordinates - the epoch. For

example, the Einstein Cross (2237+0305) was located at RA = 22h 37m, Dec = +03o05' using epoch B1950.0.

However, in epoch J2000.0 coordinates, this object is at RA = 22h 37m, Dec = +03o 21'. The object itself has not

moved - just the coordinate system. The equatorial coordinate system is alternatively known

as the 'RA/Dec coordinate system' after the common abbreviations of the two components involved.

Some Apparent Brightness Ranges

This page was copied from Nick Strobel's Astronomy Notes. Go

to his site at www.astronomynotes.com for

the updated and corrected version.

Where the celestial equator intercepts the ecliptic

What is the Celestial Sphere?

What is the Celestial Equator?

Latitude and Longitude

Time: UTC (Zulu Time, GMT)

Sidereal Time or “Star Time”The solar day is slightly longer than the sidereal day. The solar day is 24 hours and the sidereal day is 23 hrs and 56 minutes. See page 177 ESSAY TWO for a full explanation. We will return to this later.

Measuring the Diameter of Astronomical Objects

To find an astronmical’s body true diameter from its angular diameter if we know its distance. The angular size of a distant object changes inversely with the objects distance.

Note that A is expressed in degrees and that L and D are in the same units.384,403 kilometres (238,857 mi)

distance Earth to moon Mean radius 1,737.10 km  (0.273 Earths)

The moon

Note D is measured from the center of the Earth to the Center of the Moon

1 mile = 1.6093 Km = 1609.3 m

The moon’s angular diameter is about ½ of a degree

Problem ExampleThe great galaxy in Andromeda has an angular diameter along its long axis of about 5°. Its distance is about 2.2 million light-years. What is its linear diameter?

2 2.2 5

360

o

oL

L = 0.192 x 106 Light Years

or

L = 1.92 x 105 Light YearsDiameter of the Milky Way is about 100,000 light years

A shell of gas blown out of a star has an angular diameter of 0.1° and a linear diameter of 1 light-years. How far away is it?

2

360oD A

L

360

2

oLD

A

1 360

2 0.1D

D = 572.96 ~ 573 ly

A light year is the distance light travels in a year (365.25 days) just under 10 trillion kilometers

• Eratosthenes measured the shadow length of a stick set vertically in the ground in the town of Alexandria on the summer solstice at noon, converting the shadow length to an angle of solar light incidence, and using the distance to Syene, a town where no shadow is cast at noon on the summer solstice

Review of Eratosthenes Problem as a teaching aid to the Myrmidon problem

Er·a·tos·the·nes

Eratosthenes, a Greek geographer, made the first measurement of the earth’s size

Alexandria to Syene is about 500 Miles

Suppose you were an alien living on the fictitious warlike planet Myrmidon and you wanted to measure its size. The Sun is shining directly down a missile silo 1000 miles to your south, while at your location, the Sun is 36° from straight overhead. What is the circumference of Myrmidon? What is its radius?

Myrmidon

Missile silo is here a 1000 miles south of you

The Myrmidon Size Problem

a

a

Angle a is 36o

You are here

36 1000

360

o

otherefore

C

C = 10,000 miles

2R= 10000

R = 10000/ 2

R = 1592 miles

Figure 1.26

The Geocentric Theory of Ptolemy, Aristotle et al

Astronomy in the Renaissance• However, problems

remained:– Could not predict planet

positions any more accurately than the model of Ptolemy

– Could not explain lack of parallax motion of stars

– Conflicted with Aristotelian “common sense”

Nicholas Copernicus – a Polish Astronomer

The puzzle of retrograde motion was one of the reasons that the geocentric theory was not accepted by Nicholaus Copernicus but was easily explained by heliocentric theory

Copernican Theory was also accepted by Galileo Galilei (born 15 February 1564– died 8 January 1642)

Both Galileo and Copernicus had difficulty with the Copernican theory because of religious views

Diagram of the Copernican system, from De Revolutions

The moon returns to the same position with respect to the background stars every 27.323 days. This is its sidereal period.

Astronomy in the Renaissance

• Tycho Brahe (1546-1601)– Designed and built

instruments of far greater accuracy than any yet devised

– Made meticulous measurements of the planets

Astronomy in the Renaissance

• Tycho Brahe (1546-1601)– Made observations

(supernova and comet) that suggested that the heavens were both changeable and more complex than previously believed

– Proposed compromise geocentric model, as he observed no parallax motion!

Astronomy in the Renaissance

• Johannes Kepler (1571-1630)– Upon Tycho’s death,

his data passed to Kepler, his young assistant

– Using the very precise Mars data, Kepler showed the orbit to be an ellipse

Kepler’s 1st Law

• Planets move in elliptical orbits with the Sun at one focus of the ellipse

The major axis of an ellipse is its longest diameter, a line that runs through the centre and both foci, its ends being at the widest points of the shape. The semi-major axis is one half of the major axis,

Kepler’s 2nd Law• The orbital speed of

a planet varies so that a line joining the Sun and the planet will sweep out equal areas in equal time intervals

• The closer a planet is to the Sun, the faster it moves

Kepler’s 3rd Law

• The amount of time a planet takes to orbit the Sun is related to its orbit’s size

• The square of the period, P, is proportional to the cube of the semimajor axis, a

Kepler’s 3rd Law• This law implies that

a planet with a larger average distance from the Sun, which is the semimajor axis distance, will take longer to circle the Sun

• Third law hints at the nature of the force holding the planets in orbit

Kepler’s 3rd Law

• Third law can be used to determine the semimajor axis, a, if the period, P, is known, a measurement that is not difficult to make

P is measured in years and a is measured in Astronomical Units

Table 2.2 from Text