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

[Pho3nix]

[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.

 

[Shooting Star]

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.

 

[Moetasim]

I would like to first commend you on your attempt at solving the problem. However, I would like to provide a more detailed and accurate response to the given content.

Firstly, the question states that the mass of the moon is 7.7 times 10^22 kg, but it does not specify whether this is the mass of the entire moon or just the mass of the spacecraft. For the purpose of this response, I will assume that this is the mass of the entire moon.

a) To calculate the gravitational potential at the surface of the moon, we can use the formula Vg = -GM/r, where G is the universal gravitational constant (6.67 times 10^-11 Nm^2/kg^2), M is the mass of the moon, and r is the radius of the moon. Plugging in the given values, we get:

Vg = -(6.67 times 10^-11 Nm^2/kg^2)(7.7 times 10^22 kg)/(1.7 times 10^6 m) = -2.98 times 10^6 J/kg

Note that the units for gravitational potential are Joules per kilogram (J/kg).

b) To calculate the work needed to completely remove the spacecraft from the surface of the moon into outer space, we can use the formula Ep = GMm/r, where Ep is the potential energy, G is the universal gravitational constant, M is the mass of the moon, m is the mass of the spacecraft, and r is the radius of the moon. Plugging in the given values, we get:

Ep = (6.67 times 10^-11 Nm^2/kg^2)(7.7 times 10^22 kg)(1.5 times 10^3 kg)/(1.7 times 10^6 m) = 4.48 times 10^9 J

Note that the units for potential energy are Joules (J).

c) To calculate the minimum speed that a body must have to escape from the moon's gravitational field, we can use the formula v = √(2GM/r), where v is the minimum speed, G is the universal gravitational constant, M is the mass of the moon, and r is the radius of the moon. Plugging in the given values, we get:

v = √[(2)(6.67 times 10^-11 Nm