Calculating Change in Potential Energy of Moon 4.0 cm Closer to Earth

[m.rahim]

earth?

Homework Statement

Mass of moon - 7.3 x 10^22 kg
Mass of Earth - 6.0 x 10^24
distance between moon and Earth - 356400 km
change in distance 4 cm

Homework Equations

The Attempt at a Solution

I just need to check if my answer is correct, I get some thing to the power 28, using the equation GMm/r

Is my answer reasonable?

 

[flatmaster]

You should get something to the 28 for the potential energy at 356400 km. Now move it 4cm and find a new potential. You will need to keep a lot of digits because most will subtract out when you find the difference between the two potentials.

 

[m.rahim]

You should get something to the 28 for the potential energy at 356400 km. Now move it 4cm and find a new potential. You will need to keep a lot of digits because most will subtract out when you find the difference between the two potentials.

I get something to the power 28 when I use the formula:
for r in meters,
-GMm/r - ( - GMm/(r+4x10^-2)

so is the value I got wrong then?

 

[m.rahim]

By the way do I need to find the potential (i.e. GM/r) or the potential energy (GM m(moon) )/r ?

 

[flatmaster]

-GMm/r

This itself should be about 10^28 if you do an order of magnitude estimate

- GMm/(r+4x10^-2)

This also be around 10^28 and be very close to the previous value.

It should be so close because r changed by only about 0.00001% This means that there should be a large number of digits that subtract out between the two numbers.

Your initial post said potential energy, so I think that's what you need. You wouldn't need the moon's mass to find potential.