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.

Question

(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?
(b) If the probe is to achieve a maximum distance of 8.0x10^6 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero?

For Further Reading

* Physics/Math - drwls, Wednesday, March 7, 2007 at 5:55am

Use the rel;ationship
KE + Potential energy) = constant.

The potential energy at distance R from the center is
-GMm/R
M is the planet's mass and m is the probes.
That means (1/2) mV^2 - GMm/R = constant
Use that fact to compute the unknown kinetic energy in each problem

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this is what i did..

V = sqrt(2GM/R)
V = sqrt(2(6.67e-11)(1.0e23)/(3.0e6))
V = 2108.7
[..would i use earth's gravity for this question? .. if not.. what should i use for G?]

then..

(1/2) mV^2 - GMm/R = constant
(.5(10)(2108.7)^2 - ((6.67e-11)(1.0e23)(10)/(4.0e6))
111165392.3 - 16675000 = 94490392.3 = 9.4e7

.. what am i doing wrong?

and how would i go about with the 2nd question?

please help!! thanks! :)