Kepler - can be simplified down to period#1 = period#2 ×...

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Kepler's Third Law Kepler's third law of planetary motion says that the average distance of a planet from the Sun cubed is directly proportional to the orbital period squared. Newton found that his gravity force law could explain Kepler's laws. Since Newton's law of gravity applies to any object with mass, Kepler's laws can be used for any object orbiting another object. Let's look at satellites orbiting a planet. If you have two satellites (#1 and #2) orbiting a planet, Kepler's third law says: (period #1/period #2) 2 = (distance #1/distance #2) 3 , where the distance is the average distance of the satellite from the planet---the orbit's semimajor axis. The satellites must be orbiting the same planet in order to use Kepler's third law! Kepler found this law worked for the planets because they all orbit the same star (the Sun). If you have measured the orbital period of one satellite around a planet, you can then easily find how long it would take any other satellite to orbit the planet in any size oribt. Kepler's third law
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Unformatted text preview: can be simplified down to period #1 = period #2 × Sqrt [(distance #1/distance #2) 3 ] OR period #1 = period #2 × (distance #1/distance #2) 3/2 . Those of you with a scientific calculator (one that does powers, trig functions, scientific notation, etc.) will want to use the formula on the last line (remember that 3/2 = 1.5). Those with a calculator that just has a square root button will want to use the formula on the second-to-last line. If the satellite is orbiting the Sun, then the relation can be greatly simplified with an appropriate choice of units: the unit of years for the orbit period and the distance unit of astronomical units. In this case, the reference ``satellite'' is the Earth and Kepler's third law becomes period = distance 3/2 . Let's use this to find out how long it takes to explore the solar system....
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