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?
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.