An imaginary planet has a diameter twice that of our earth. The planet has one moon with an orbital radius of 5.0x10^7 km and orbital period of 10 earth days.
Determine the strength of the gravitational field at the surface of the planet.
Radius of earth = 6.38 x 10^6m
Orbital radius of moon = 5x10^10m
orbital period = 8.64 x 10^5 s
r^3/T^2 = GM/4pi^2
g = GM/r^2
i think that's all..?...
The Attempt at a Solution
GM = (4pi^2(5x10^10)^3)/(8.64x10^5)^2
= 6.61 x 10^21
g = 6.61x10^21/(12.76x10^6)^2
this number is massive!!! I must be doing something wrong. any help?