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Unformatted text preview: Astronomy Picture of the Day The Victoria Crater, seen by the Mars Opportunity Rover Announcements • No ofFce hours tomorrow Kepler’s laws • Kepler’s frst law: The planets orbit the sun on elliptical paths, with the sun at one Focus oF the ellipse Sun Planet Note: this diagram is very exaggerated: the actual orbits oF the planets in our solar system are very nearly circular (small ellipticity) Kepler’s second law Planet moves faster when it’s closer to the sun Planet moves slower when it’s farther from the sun • Planets move on their elliptical orbits in such a way that a line joining the sun and the planet will sweep through equal areas in equal times Kepler’s third law • The period of a planet’s orbit is the amount of time it takes to orbit the sun once • Kepler’s 3rd law: the square of the period of a planet’s orbit is proportional to the cube of the semimajor axis of the ellipse Here, P = orbital period R = semimajor axis of orbit k = a constant, which is the same for all planets in our solar system P 2 = kR 3 Using Kepler’s third law • We can use a particularly simple system of units: the Earth’s orbital period is 1 year, and its orbital radius is 1 AU • For other planets in our solar system, we can use Kepler’s 3rd law in this form: P 2 planet P 2 Earth = R 3 planet R 3 Earth Kepler’s third law • Saturn’s period of revolution about the sun is 29.4 years....
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 Fall '02
 staff
 Kepler's laws of planetary motion, Celestial mechanics, Orbital Motion

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