Physics universal gravitation

Question

How long would our year be if our Sun were two thirds its present mass and the radius of the Earth’s orbit were seven times its present value? Answer in units of y.

Answer 1

The relation between the orbit period T, the mass of the sun M_s and the radius of the earth orbit r is:

, therefore if the new mass M_s' is 2/3 of M_s and the new radius r' is 7 times of r, the new period T' will have:

so we have .