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brian_box

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## Homework Statement

Hi everybody, this is a conceptual question about gravitational potential energy that my textbook and high school teacher seem to give incomplete answers.

The problem involves two masses [tex]m_{1}[/tex] and [tex]m_{2}[/tex], where [tex]m_{2}[/tex] > [tex]m_{1}[/tex], which are both at a radius R from the Earth's center. (The radius R is significantly large that Earth's gravitational field cannot be considered constant).

Question: Which mass has greater gravitational potential energy?

## Homework Equations

The gravitational potential energy is given by

[tex]

E_{p} = -G \frac{mM_{E}}{r}

[/tex]

where [tex] M_{E} [/tex] is the mass of the Earth.

## The Attempt at a Solution

Since r=R for both masses, the only difference are the masses of the objects. Since [tex]m_{2}[/tex]>[tex]m_{1}[/tex], the equation above would state that the gravitational potential energy (GPE) of [tex]m_{2}[/tex] will be more negative, hence less than the GPE for [tex]m_{1}[/tex].

i.e. [tex]GPE_{m_{1}}[/tex] > [tex]GPE_{m_{2}}[/tex]

However this doesn't seem to make sense to me. Surely a bigger mass above the Earth will have more gravitational energy. The textbook answer tells me that the gravitational potential energy of [tex]m_{2}[/tex] is indeed larger, but it explains it using [tex]E_{p}[/tex] = mgh, where h is the height of the object.