# SAT II Physics : Orbits

## Example Questions

### Example Question #1 : Orbits

Suppose a planet has a mean distance from the sun four times that of Earth's. How many Earth years would it take this planet to orbit the sun?

Explanation:

Kepler's third law gives the relationship between the period of a planet's orbit (year) and the radius of its orbit (distance form the sun):

The square of the period is proportional to the cube of the radius. We can set the product of these values equal to a constant, since they are proportional.

In our question, we know that the distance is increased by a factor of four and the period for Earth is 1 year.

Solve for the period of the new planet.

The period for the new planet is one-eighth the period of Earth, meaning that in one Earth year this planet will complete only one-eighth its orbit. It will take eight Earth years to equal one complete orbit for this planet.