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Laws of Planetary Motion

The figure below illustrates two orbits with the same semi-major axis, focus and orbital period: one a circle with an eccentricity of 0.0; the other an ellipse with an eccentricity of 0.8.

Prior to this in 1602, Kepler found from trying to calculate the position of the Earth in its orbit that as it sweeps out an area defined by the Sun and the orbital path of the Earth that:

Kepler published these two laws in 1609 in his book Astronomia Nova.

For a circle the motion is uniform as shown above, but in order for an object along an elliptical orbit to sweep out the area at a uniform rate, the object moves quickly when the radius vector is

This law he published in 1619 in his Harmonices Mundi . It was this law, not an apple, that lead Newton to his law of gravitation. Kepler can truly be called the founder of celestial mechanics.