Question

Planet X orbits the star Omega with a "year" that is 250 earth days long. Planet Y circles Omega at four times the distance of Planet X. How long is a year on Planet Y?

Answer 1

Let Px be the period of revolution (that is, a 'year') of Planet X,

Rx be the distance of Planet X,

Py be the period of revolution of Planet Y and

Ry be the distance of Planet Y.

Kepler's Third Law tells us

Py²/Px² = Ry³/Rx³

Or, Py² = Px²Ry³/Rx³

You're given that Px = 250 days.

You also know the distance of planey Y is 4 times the distance of planet X, so Ry = 4Rx. Substituting this information in gives

Py² = (250 days)² (4Rx)³/Rx³

Evaluating the right hand side results in

Py² = 62500 days² * 64 Rx³/Rx³. Simplifying and cancelling the Rx³'s:

Py² = 4,000,000 days².

Taking the square root of both sides,

Py = 2000 days.

So a year on Planet Y is 2000 earth days.