Kepler's Laws for Planetary Orbits
The
laws for planetary motion about the sun were first discovered by analysis
of measurements of the motion of the planets, as seen from the earth. They
were later derived by Newton using Newton's three laws of mechanics. The
figure shows Kepler's and Newton's version of each law.
In the figure, T is the orbital period of the
planet, a is the semi-major axis (half the length of the longer axis of
the elliptical orbit), M is the mass of the sun, and G is the
gravitational constant from Newton's law for gravity.
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