I'm writing an essay, and the third paragraph must be about the topic above.. I can't seem to find the answer in my notes, only equations without explanations. If you could help in any way, it'd be greatly appreciated. Thanks!
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Isaac Newton showed that Kepler's laws are a natural result of gravity. Actually, Newton's version is a little big different.
1. Both the sun and the planet orbit around the center of mass.
2. The period of the orbit depends on the sum of the masses, not just the mass of the sun.
Lets look at a particular case.
Kepler wrote that the period squared is proportional to the orbit size cubed. That is, P^2 / a^3 = some constant. (At least, it's constant for stuff in the solar system that orbits around the sun.)
Newton figured out that the ratio P^2 / a^3 = 2 pi / GM, where G is the gravitational constant, and M is the combined mass. Since the sun is over 1000 times the mass of any of the planets, M is practically the same as the mass of the sun.
1. Both the sun and the planet orbit around the center of mass.
2. The period of the orbit depends on the sum of the masses, not just the mass of the sun.
Lets look at a particular case.
Kepler wrote that the period squared is proportional to the orbit size cubed. That is, P^2 / a^3 = some constant. (At least, it's constant for stuff in the solar system that orbits around the sun.)
Newton figured out that the ratio P^2 / a^3 = 2 pi / GM, where G is the gravitational constant, and M is the combined mass. Since the sun is over 1000 times the mass of any of the planets, M is practically the same as the mass of the sun.
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Proofs of Kepler's laws from Newtons laws are a standard exercise in vector calculus and basic kinematics functions set-up in 2-dimensions.
http://en.wikipedia.org/wiki/Kepler's_la…
If you have no idea of what any of those words mean, you aren't ready to answer this question.
http://en.wikipedia.org/wiki/Kepler's_la…
If you have no idea of what any of those words mean, you aren't ready to answer this question.