Kepler’s Laws of Planetary Motion
Kepler was assigned the task by Tycho Brahe to analyze the observations that Tycho had made of Mars. Of all the planets, the predicted position of Mars had the largest errors and therefore posed the greatest problem. Tycho’s data were the best available before the invention of the telescope and the accuracy was good enough for Kepler to show that Mars’ orbit would precisely fit an ellipse.
In 1605 he announced The First Law:
Planets move in ellipses with the Sun at one focus.
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.
Circular and Elliptical Orbits Having the Same Period and Focus
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:
The radius vector describes equal areas in equal times. (The Second Law)
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 short and the object moves slowly when the radius vector is long.
On May 15, 1618 he discovered The Third Law:
The squares of the periodic times are to each other as the cubes of the mean distances.
This law he published in 1619 in his Harmonices Mundi . It was this law, not an apple, that led Newton to his law of gravitation. Kepler can truly be called the founder of celestial mechanics.
