What could Kepler's second law be used to measure?

Answer 1

Kepler's second law says that the line joining a planet to the Sun sweeps out equal areas in equal time.

Kepler noticed that when a planet's orbit takes it slightly further from the Sun, it moves more slowly. He deduced from calculations made from observations that when the distance increases by 1%, the angular speed decreases by 1%, so the distance times the angular speed, which is the area swept out per second, stays constant. He found this is true all the time for all the planets, a very important discovery in the history of science.

The planet's mass times the distance times the angular speed is the angular momentum, and this stays constant. So angular momentum is 'conserved' as the planet goes round, speeding up and slowing down in its orbit.

Therefore the second law is now known as a statement of an important physical principle called the Conservation of Angular Momentum. In this way Kepler's second law contributed to scientific progress after his death.

Angular speed is measured in radians per second, and the angular momentum is mass times distance times angular speed. For a single particle it is equal to the linear momentum of the particle (mass times speed), while for a rigid body it is the angular speed times the moment of inertia.