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When and how was it first discovered that Kepler's Third Law applies not just to the motions of planets around the Sun but to satellites around a planet?
Kepler's laws help describe the motion of planets around their star. The third law determines the relationship between the mass of the star and the period of rotation for the planets. This is often called the law of harmonies.
Many scientists looked into Kepler's laws to find more uses for them than simply describing the motion of the planets. Isaac Newton, for example, looked at the third law and derived conclusions about universal gravitation from them. Newton was also the scientist who conceived of satellites moving at such a speed that they were constantly falling towards earth, and constantly missing it. His theories on gravity were effective on proving Kepler's own laws. He determined that these would be effective in describing the orbit of the Moon around Earth as well.
