## SAT Physics Subject Test

## Chapter 6 Curved and Rotational Motion

### KEPLER”S LAWS

Many motions in the real world are not exactly circular, one of the most important examples being planetary orbits. Three laws, known as Kepler”s Laws, describe the motion of planets around the Sun.

**The Skinny on Kepler”s Laws**

**First Law**: The orbit of each planet is an ellipse and the sun is at one focus.

**Second Law**: An imaginary line from the sun to a moving planet sweeps out equal areas in equal intervals of time.

**Third Law**: The ratio of the square of a planet”s period of revolution (the time for one complete orbit) to the cube of its average distance from the sun is a constant that is the same for all planets.

**Kepler”s First Law**

Every planet moves in an elliptical orbit, with the sun at one **focus**. Just as a circle has a center—that special point inside the circle from which every point on the circle is the same distance—an ellipse has two **foci** (plural of focus): A pair of special points inside the ellipse such that the sum of the distance of every point on the ellipse to the two foci is always the same.

**Kepler”s Second Law**

As a planet moves in its orbit, a line drawn from the sun to the planet sweeps out equal areas in equal time intervals.

Therefore, the planet moves faster when it is nearer the sun than when it is farther away.

**Kepler”s Third Law**

If *T* is the period (the time it takes the planet to make one orbit around the sun) and *a* is the length of the semimajor axis of a planet”s orbit, then the ratio *T*^{2}/*a*^{3} is the same for all the planets.