Earth and Moon (Acceleration of Gravity)

[physics817]

Homework Statement

The moon has a mass M = 7.36e+022 kg and an average radius R = 1740 km.
for part a)I solved for the gravitational acceleration on the surface of the moon= 1.62 m/s^2

An object on Earth weighs 64 N.

b) What is the weight of this same object on the moon? Answer: 10.568 N

I am stuck on part c. of the problem...
c) How many Earth radii must this same object be from the surface of the Earth if it is to weigh the same as it does on the surface of the moon?

Homework Equations

g= GMe/Re^2

The Attempt at a Solution

What I did was, I tried to use the g(moon)= 1.62= GMe/(nRe)^2
where G= 6.67e-11
Me= 5.97e24
Re=6.37e6

And solved for n= number of Earth radii= 2.461, but that isn't correct.

Can someone tell me what I did wrong? Thank you.

 

[The Bob]

I am stuck on part c. of the problem...
c) How many Earth radii must this same object be from the surface of the Earth if it is to weigh the same as it does on the surface of the moon?

[...]n= number of Earth radii= 2.461, but that isn't correct.

It seems that what is wrong is that you're including the radius of the Earth itself, where as the question asks how many radii is it from the surface of the Earth and not its centre.

The Bob

 

[physics817]

is that the right way to solve the problem then? Since it asks for how many Earth radii from the surface of the earth..and I included one radius of the eart in my answer..all I do is minus 1 to get the answer?

Thanks.

 

[The Bob]

I can't see anything wrong with your method apart from the fact it includes the radius of the Earth itself rather than from the surface. I believe simply taking away 1 will give you the correct solution. If not, let us know.

The Bob

 

[physics817]

I did get the correct answer after subtracting one..I was unsure as to whether the problem-solving was correct of if I got to the answer by chance. Thank you very much for your help!

 

[The Bob]

Cool, no problem. Glad to help. All the best,

The Bob