Kepler's Laws of Planetary Motion 1st Law 2nd Law 3rd Law Johannes Kepler was a mathematician who was hired by Tycho Brahe to study observations that Brahe had been making for years without a telescope. In 1609, Kepler defined 3 laws of planetary motion from Brahe's data. Tycho possesses the best observations, ... only he lacks the architect who would put all this to use according to his own design. - Johannes Kepler Kepler's 1st Law The orbits of all planets are elliptical with the Sun being at one focus. Kepler's 2nd Law An imaginary line from the Sun to a planet will sweep out equal areas in equal times. If the T 1 = T 2 then A = A and vice versa. Kepler's 3rd Law Took several more years to work out, but the creation looked like this: The force responsible for delivering the required centripetal force is gravity. Kepler's 3rd Law Took several more years to work out, but the creation looked like this: R F G The force responsible for delivering the required centripetal force is gravity. F c = F G Kepler's 3rd Law Took several more years to work out, but the creation looked like this: R F G The force responsible for delivering the required centripetal force is gravity. F c = F G m satellite v 2 R Kepler's 3rd Law Took several more years to work out, but the creation looked like this: R F G The force responsible for delivering the required centripetal force is gravity. F c = F G m satellite v 2 R G m satellite center R 2 = Kepler's 3rd Law Took several more years to work out, but the creation looked like this: R F G The force responsible for delivering the required centripetal force is gravity. K sun would be the same value for any object orbiting the sun. (ie Earth, Mars, Saturn) K earth would be a different value than K sun but would be true for any object orbiting the earth. (ie the moon, space shuttle, satellite) Kepler's 3rd Law R R 3 T 2 = K Once K is determined, you can choose a period of revolution and let that determine how high the satellite must be placed or vice versa. Kepler's 3rd Law R R 3 T 2 = K K can be determined by plugging in known satellite data Kepler's 3rd Law R R 3 T 2 = K K can be determined by plugging in known satellite data For K earth use the moon Kepler's 3rd Law R R 3 T 2 = K K can be determined by plugging in known satellite data For K earth use the moon T = 28 days mean R = 3.8 x 10 m Kepler's 3rd Law R R 3 T 2 = K K can be determined by plugging in known satellite data For K sun use the earth Kepler's 3rd Law R R 3 T 2 = K K can be determined by plugging in known satellite data For K sun use the earth T = 365.25 days Kepler's 3rd Law R R 3 T 2 = K K can be determined by plugging in known satellite data For K sun use the earth T = 365.25 days mean R = 9.3 x 10 7 miles Kepler's 3rd Law R