Gravitational Potential Energy of astronaut

[Erwin Schrodinger]

A 120kg astronaut stands on the surface of an asteroid of radius 600m. The astrunaut leaves the surface with 15J of kinetic energy and reaches a maximum height of 300m above the surface. What is the mass of the asteroid? (Answer: 3.4*10¹²kg)

At the maximum height, all of the kinetic energy becomes potential gravitational energy.

E_K = E_pg
15 = Gmm'/r
15 = 6.67*10^-11*120*m'/(300+600)
1.7*10¹²kg = m'

I think there's an error in the calculation somewhere because my answer is exactly half the correct answer but I can't figure out what I'm doing wrong.

 

[kleinwolf]

I don't know but at first sight, you don't take into account the pot. energy at the surface-...does this make sense, like : Kinetic+potenial=converved=15-Gmm'/600=0-Gmm'/900 ??

 

[dx]

Remember, you want the change in potential energy, not the potential energy itself.