How is Gravitational Potential Calculated on the Moon's Surface?

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The gravitational potential at the Moon's surface is calculated using the formula Vg = -GM/r, resulting in a value of -3.0 x 10^6 J/kg. The work required to remove a 1.5 x 10^3 kg spacecraft from the Moon's surface is determined to be -4.5 x 10^9 Joules. To find the minimum speed needed for escape from the Moon's gravitational field, the kinetic energy must equal the work calculated. This escape velocity is essential for a body to break free from the Moon's gravity. The discussion highlights the application of gravitational formulas to solve these problems effectively.
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[SOLVED] Gravitation Problem

Homework Statement


The moon has a mass of 7.7times10^22kg and radius 1.7times10^6m. Calculate:
a) The gravitational potential at its surface.
b) The work needed to completely remove a 1.5times10^3kg spacecraft from its surface into outer space.
c) What is the minimum speed which a body must have to escape from the moons gravitational field?

Homework Equations


Vg=-GM/r
Ep=GMm/r
Ek=.5m(vsquared)
Vg is the gravitational potential
Ep is potential energy


The Attempt at a Solution


a) Vg=GM/r
G=6.67times10^-11
M=7.7times10^22kg
r=1.7times10^6m
Plug in the numbers and I get -3.0times10^6
b)Ep=Gmm/r
M=7.7times10^22Kg
m=1.5times10^3Kg
r=1.7times10^6
Plug in numbers and get -4.5times10^9 Joules
c)In need help on this one.
 
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Pho3nix said:
c)In need help on this one.

Equate the KE to the work done in (b). That gives you the minimum v, which is called the escape velocity, which is the minimum speed that has to be given to the body remove it to infinite distance.
 
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