Mechanical Energy Homework: Zero Planet w/ 10kg Probe Launch

[norcal]

Homework Statement

Zero, a hypothetical planet, has a mass of 1.0x10^23 kg, a radius of 3.0x10^6 m, and no atmosphere. A 10 kg space probe is to be launched vertically from its surface.
(a) If the probe is launched with an initial kinetic energy of 5.0x10^7 J, what will be its kinetic energy when it is 4.0x10^6 m from the center of Zero?

Homework Equations

(1/2)mv^2 - (GMm/R)=(1/2)mv^2 - (GMm)/(10R)

The Attempt at a Solution

5.0e7 - [(6.67e-11)(1e23)(10)]/(3e6)= KE - [(6.67e-11)(1e23)(10)]/(10(4e6)]

I don't think that I am using the right values for R though. Am I?

 

[Mentz114]

(1/2)mv^2 - (GMm/R) = (1/2)mv^2 - (GMm)/(10R)

I can't see where the 10R comes from. Should be R as on the LHS.

 

[norcal]

ok, well do I have the correct values of R set up in the equation or do I need to take the difference of the distance of the satellite to the center or anything?

 

[Mentz114]

I think all your distances are measured from the centre of Zero.