KEPLER:KEPLER: the laws of planetary motion

Monica LeeA.P. Physics – Period 4Mrs. Burns

KEPLER’S FIRSTLAW

KEPLER’S SECOND

LAW

KEPLER’STHIRDLAW

INTERESTINGAPPLETS

Johannes Kepler

Born on December 27, 1571 in Germany

Studied the planetary motion of Mars Used observational data of Brahe

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Tyco Brahe

Danish astronomer who hired Kepler as his assistant

Came up with accurate observations of Mars with his naked eyes

Assigned Kepler to develop a theory of planetary motion using his observations

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Instruments

Tyco Brahe only compass and sextant No telescope – naked eye

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Kepler’s FIRST Law

“The orbit of each planet is an ellipse and the Sun is at one focus”

Kepler proved Copernicus wrong – planets didn’t move in circles

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Ellipse

Elongated & flattened circle Characterized by eccentricity and

length of major axisEccentricity – degree of flatnessMajor axis – longer axis

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KEPLER’S FIRSTLAW

Focus

Focus – one of two special points on the major axis of an ellipse

Foci – plural of focusA+B is always

the same on any point on the ellipse

KEPLER’S FIRSTLAW

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Eccentricity

Eccentricity is the degree of flatnessEccentricity (e) = 0 is circleEarth e = 0.017 e = c/a

c = center to focus a = half of major axis/

semi-major axis

KEPLER’S FIRSTLAW

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Aphelion & Perihelion

Aphelion is the point on the orbit farthest from the sun

Perihelion is the point on the orbit closest to the sun

KEPLER’S FIRSTLAW

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Kepler’s SECOND Law

“The line joining the planet to the sun sweeps out equal areas in equal intervals of time”

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In Another Words…

The area from one time to another time is equal to another area with the same time interval

All of the areas (in yellow and peach) have equal intervals of time

KEPLER’S SECOND

LAW

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Acceleration of Planets

Planet moves faster when closer to the sun Force acting on the planet increases as

distance decreases and planet accelerates in its orbit

Planet moves slowerwhen farther from the sun

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KEPLER’S SECOND

LAW

Kepler’s THIRD Law

“The square of the period of any planet is proportional to the cube of the semi-major of its axis”

Also referred to as the Harmonic Law

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T² a³

T = orbital period in years a = semi-major axis in

astronomical unit (AU)Can calculate how long it takes

(period) for planets to orbit if semi-major axis is known

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KEPLER’STHIRDLAW

Astronomical Unit

Astronomical unit – AU AU is the mean distance between

Earth and the Sun1 AU ≈ 1.5 x 108 km ≈ 9.3 x 107 miles

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KEPLER’STHIRDLAW

Examples of 3rd Law

Calculating the orbital period of 1AU T² = a³ T² = (1)³ = 1 T = 1 year

Calculating the orbital period of 4AU T² = a³ T² = (4)³ = 64 T = 8 years

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KEPLER’STHIRDLAW

Orbital Data

The orbital data of various planets

Planeteccentricity

(e)T (yr) a (AU) T2 a3

M ercury 0.206 0.24 0.39 0.06 0.06

Venus 0.007 0.62 0.72 0.39 0.37

Earth 0.017 1 1 1 1

M ars 0.093 1.88 1.52 3.53 3.51

J upiter 0.048 11.9 5.2 142 141

Saturn 0.056 29.5 9.54 870 868

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CometsAlthough Kepler’s

laws were intended to describe the motion of planets around the sun, the laws also apply to comets

Comets are good examples because they have very elliptical orbits

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Kepler’s Three Laws

Orbit of each planet is an ellipse & Sun is at one focus

Equal areas in equal intervals of time

T² = a³

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Contributions

Kepler’s second law (equal area) helped Newton come up with his Law of Universal Gravitation

Motions of satellite and spacecraft in orbit near planets

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Interesting Applets

http://www.fed.cuhk.edu.hk/sci_lab/ntnujava/Kepler/Kepler.html

http://csep10.phys.utk.edu/astr162/lect/binaries/visual/kepleroldframe.html

http://www.ioncmaste.ca/homepage/resources/web_resources/CSA_Astro9/files/multimedia/unit4/keplers_laws/keplers_laws.html

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Works Cited

Drennon, Bill. “Kepler’s laws.” Central Valley Christian High School. 14 March 1997. 23 May 2008. http://home.cvc.org/science/kepler.htm

Fendt, Walter. “Kepler’s First Law.” Java Applets on Physics. 18 January 2003. 23 May 2008. http://www.walter-fendt.de/ph14e/keplerlaw1.htm

Fendt, Walter. “Kepler’s Second Law.” Java Applets on Physics. 18 January 2003. 25 May 2008. http://www.walter-fendt.de/ph14e/keplerlaw2.htm

"Johannes Kepler." World of Earth Science. Online. Thomson Gale, 2006. Reproduced in Biography Resource Center. Farmington Hills, Mich.: Gale, 2008. http://galenet.galegroup.com/servlet/BioRC

“Johannes Kepler: The Laws of Planetary Motion.” University of Tennessee. 25 May 2008. http://csep10.phys.utk.edu/astr161/lect/history/kepler.html

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Works Cited II

“Kepler’s Laws.” Orbitessera. 26 May 2008 http://www.mindspring.com/~n2wwd/html/kepler_s_laws.html

"Kepler's laws of planetary motion." Encyclopædia Britannica. 2008. Encyclopædia Britannica Online. 25  May  2008. http://www.britannica.com/eb/article-9045134.

Nave, R. “Kepler’s Laws.” HyperPhysics. 25 May 2008. http://hyperphysics.phy-astr.gsu.edu/hbase/kepler.html

Soper, Davison. “Kepler’s First Law.” University of Oregon. 2002. 23 May 2008. http://zebu.uoregon.edu/~soper/Orbits/kepler1.html

Weisstein, Eric. “Kepler’s Third Law.” Eric Weisstein’s World of Physics. 2007. 26 May 2008. http://scienceworld.wolfram.com/physics/KeplersThirdLaw.html

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