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Physics - Formulas - Kepler and Newton - Orbits

In 1609, Johannes Kepler (assistant to Tycho Brahe) published his three laws of orbital motion:
  1. The orbit of a planet about the Sun is an ellipse with the Sun at one Focus.
  2. A line joining a planet and the Sun sweeps out equal areas in equal time.
  3. The square of the sidereal period of a planet is directly proportional to the cube of the semi-major axis of the orbit.

While laws 1 and 2 are statements, law 3 is presented as an equation:

A semi-major axis is the full width of an ellipse. Law 3 states that if a planet has a sidereal orbit of 11.87 years (like Jupiter in the previous page), the diameter of the orbit is:

Kepler was not the only one interested in orbits. Sir Isaac Newton, using his fundamental work of gravity and forces modified the Kepler equation to take into account the gravity effects of the orbiting bodies:

This equation actually gives us a bit more power. By applying Newton's Law of Gravitation, we can determine how mass influences rotation, as well as determine mass if we know the orbital diameter. To understand this a bit better, think about the standard forces and centripetal motions when dealing with an orbit that is circular (not elliptical like a planets orbit):

Unfortunately I am not a mathematics wizard so I cannot explain the concepts behind these (and other) equations, but my understanding of these problems came about by just looking at the equations (without their corresponding values) and imaging how each variable interacts with each other. Either way, hopefully this section (and the other sections) are helpful.

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