Physics/Finding the Mass of a Planet
I'm preparing for my Physics exam in first year University Physics next week and am completely stuck on a problem I was hoping to get some help with:
A projectile is launched with an initial speed of 3.0km/s from the surface of a planet(radius 1.5x10^6 m). The projectile reaches a maximum height of 3.0x10^6 m above the surface of the planet. What is the mass of the planet in kg if G=6.67x10^-11 Nm^2/kg^2?
The correct answer according to the back of the book is 1.5x10^23kg.
The only formula I know that deals with the mass of a planet requires that I have the period of orbit which I don't in this case. Thanks a million in advance
v^2 = 2gH and g = GM/r^2 so M = v^2r^2/(2GH) and
M = (3x10^3)^2(1.5x10^6)^2/[2(6.67x10^-11)(3x10^6)] = about 5x10^22 kg
Check my arithmetic since I don't have a calculator handy. Since I have taught physics, I know that the answers in the back aren't always correct.