Calculate the length R...

Question

Calculate the length R of the semimajor axis of a planet whose period is 231 days. 
____ AU

Answer 1

Use Kepler's 3rd law, with the earth as the reference point.

 

The earth's semi-major axis is 1 AU and it's period is 365.25 days.

 

The square of the ratio of this planet's period to the earth's is (231 / 365.25)² = 0.4000.

 

According to Kepler's 3rd law, that's equal to the cube of the ratio of the semi-major axis of this planet to the semi-major axis of the earth.

 

So the ratio of semi-major axes is the cube root of 0.4, which is 0.7368 , so this planet's semi-major axis is 0.7368 AU's.