CAPE Physics Unit 1 · 2002 · Paper 2 · Question 5(a)(ii)

In another galaxy, planet P has a circular orbit with the same radius as Earth's orbit. The masses of the suns in the two galaxies are S_E and S_P. Planet P completes its orbit in half the time it takes Earth.

Show that the period of the planet, P, is given by T = 2π * sqrt(r^3 / GM_P), where M_P is the mass of the planet and r the radius of the orbit.