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phys: kepler

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eggy 2020-11-23 12:02:51 -05:00
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@ -617,6 +617,9 @@ $$\vec{F}_G=\Sigma\vec{F}_c$$
So the orbital speed of a satellite must be independent of its own mass, such that: So the orbital speed of a satellite must be independent of its own mass, such that:
$$v=\sqrt{\frac{GM}{r}}$$ $$v=\sqrt{\frac{GM}{r}}$$
Additiionally, Kepler's third law, derived from centripetal force and the universal law of gravitation, states that the square of the period of an orbit is proportioanl to the cube of the radius.
$$T^2 \propto r^3$$
A **geosynchronous** orbit is one that returns to its original position relative to the orbitee after one rotation of the orbitee. A **geosynchronous** orbit is one that returns to its original position relative to the orbitee after one rotation of the orbitee.
A **geostationary** orbit is a geosynchronous orbit that always remains in the same position relative to the orbitee. A **geostationary** orbit is a geosynchronous orbit that always remains in the same position relative to the orbitee.