2. History
The study of planetary motion owes much to two of the greatest minds of our time: Johannes Kepler and Sir Isaac Newton. Kepler, a German mathemetician in the 16th and 17th centuries, used raw observational data to derive these three fundamental laws of planetary motion:
The planets follow elliptical orbits, with the sun at one focus. At all points in its orbit, a planet sweeps out equal areas in equal amounts of time. This means that the planets must travel faster when they are close to the sun than when they are distant from it. The ratio of the cube of a planet's mean distance from the sun to the square of its orbital period is a constant, the same for all planets.
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Newton contributed his three laws of motion:
A body in motion will remain in motion at a constant velocity in the absence of a force. If a body is acted upon by a force it will experience an acceleration in accordance with
Force = Mass x Acceleration.
For every force that exists there exists another force with equal magnitude in the opposite direction.
as well as his law of gravitation
where F is the attractive force between the objects, G is the gravitational constant
(6.67 x 10-11), M and m are the masses of the two objects, and r is the distance between the objects.Newton was also the originator of what came to be called "The Two Body Problem". Briefly stated, this question asks "Given at any time the positions and velocities of two massive particles moving under thier mutual gravitational force, the masses also being known, [can we] calculate thier position and velocities for any other time?" (Roy, 1988)
