keplers laws
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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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