How long is a year on planet Y?

1 Answer

• 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.