In the gravitational potential energy equation E = −GMm/r, what do M and m represent?

M is the mass of the point mass creating the gravitational field; m is the mass of the object whose potential energy is being calculated

Why is gravitational potential energy given by E = −GMm/r always negative?

Because gravitational potential is defined as zero at infinity, and work must be done against the attractive gravitational force to move a mass from distance r to infinity, so the energy at r must be less than zero

How is the gravitational potential energy E of a mass m related to the gravitational potential V at that point?

E = mV, where V is the gravitational potential at that point

What happens to the gravitational potential energy of a mass m as it moves closer to a point mass M?

The gravitational potential energy becomes more negative (decreases)

What happens to the gravitational potential energy of a mass m as it moves further away from a point mass M towards infinity?

The gravitational potential energy increases (becomes less negative), approaching zero at infinity

OCR A-Level Physics A H556

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Gravitational Fields

Gravitational potential energy and escape velocity

2 things to know
Papers 1, 2 and 3

Overview

Recall questions on gravitational potential energy E = −GMm/r and its link to potential, how it changes with distance, the area under a force-distance graph, and deriving and calculating escape velocity.

What you need to know

Answer each one before you reveal it.

Your recallNot started

Key term

In the derivation of escape velocity, what relationship exists between kinetic energy and gravitational potential energy?

Key term

On a force–distance graph for a point or spherical mass, what does the area under the curve represent?

Questions from this subtopic

Each one with the model answer underneath.

1
State the formula for the gravitational potential energy of a mass m at a distance r from a point mass M.
Model answer
E = −GMm/r
2
In the gravitational potential energy equation E = −GMm/r, what do M and m represent?
Model answer
M is the mass of the point mass creating the gravitational field; m is the mass of the object whose potential energy is being calculated
3
Why is gravitational potential energy given by E = −GMm/r always negative?
Model answer
Because gravitational potential is defined as zero at infinity, and work must be done against the attractive gravitational force to move a mass from distance r to infinity, so the energy at r must be less than zero
4
How is the gravitational potential energy E of a mass m related to the gravitational potential V at that point?
Model answer
E = mV, where V is the gravitational potential at that point
5
What happens to the gravitational potential energy of a mass m as it moves closer to a point mass M?
Model answer
The gravitational potential energy becomes more negative (decreases)
6
What happens to the gravitational potential energy of a mass m as it moves further away from a point mass M towards infinity?
Model answer
The gravitational potential energy increases (becomes less negative), approaching zero at infinity

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