Question #f608f

1 Answer
Mark C.
Nov 5, 2017

OK, some algebra required but not too hard. Incidentally, I think the ratio should read #r^3/T^2# not #T^3# but on that basis, we can proceed.

Explanation:

We know that #r^3/T^2# is constant for the system.

So for any body orbiting in this system #r^3/T^2 = 3.5xx10^-18# and for planet y: #r^3/T^2= (3xx10^10)/T^2# putting these two equal to each other and rearranging for T squared gives:

#T^2 = (3xx10^10)/(3.5xx10^-18)#

So #T = 9.25xx10^13# s

Voilà! (Wasn’t Kepler wonderful?)

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