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→The Law of Equal Areas
This can be shown to be true using the law of conservation of angular momentum.
This can be shown to be true using the law of conservation of angular momentum.
[[Image:Gravitation%20for%20wiki_html_m4a5ede30.png]] <br>
If “v” is the velocity of the planet, in time “dt” the planet moves a distance vdt and sweeps out an area equal to the area of a triangle of base “r” and altitude vdt sinα.
If “v” is the velocity of the planet, in time “dt” the planet moves a distance vdt and sweeps out an area equal to the area of a triangle of base “r” and altitude vdt sinα.
Because the angular momentum is conserved, the rate of change of area covered is constant. This means that the planets move with different velocities depending upon their position in the orbits.<br><br>
Because the angular momentum is conserved, the rate of change of area covered is constant. This means that the planets move with different velocities depending upon their position in the orbits.<br><br>
=== The Law of Periods ===
=== The Law of Periods ===