# How long is a year on planet Y?

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Planet X orbits the star Omega with a “year” that is 200 earth days long. Planet Y circles Omega at four times the distance of planet X. How long is a year on planet Y?

• This is a question on Kepler’s Third Law

http://csep10.phys.utk.edu/astr161/lect/history/ke…

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 = 200 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 = (200 days)² (4Rx)³/Rx³

Evaluating the right hand side results in

Py² = 40,000 days² * 64 Rx³/Rx³. Simplifying and cancelling the Rx³’s:

Py² = 2,560,000 days².

Taking the square root of both sides,

Py = 1600 days. So a year on Planet Y is 1600 earth days.

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