# Gravitational Potential(OCR A Level Physics)

Author

Katie M

Expertise

Physics

## Gravitational Potential

#### Near the Earth's Surface

• The gravitational potential energy (G.P.E) is the energy an object has when lifted off the ground given by the familiar equation:

G.P.E = mgΔh

• When using this equation, the G.P.E on the surface of the Earth is taken to be zero
• This means work is done to lift the object

• This equation can only be used for objects that are near the Earth's surface
• This is because, near Earth's surface, the gravitational field is approximated to be uniform
• Far away from the Earth's surface, the gravitational field is radial because the Earth is a sphere

• In a radial field, G.P.E is defined as the energy an object possesses due to its position in a gravitational field
• The gravitational potential at a point is the gravitational potential energy per unit of mass for an object at that point
• Gravity is always attractive, so work must be done on a mass to move it away to a point infinitely far away from every other mass
• 'Infinity' is the point at which the gravitational potential is zero
• Therefore, since the potential energy of all masses increases as work is done on them to move them infinitely far away, the value of the potential is always negative

• Gravitational potential is formally defined as:

The work done per unit of mass in bringing a mass from infinity to a defined point

Gravitational potential decreases as the satellite moves closer to the Earth. It increases if it moves further away, towards infinity, where gravitational potential is zero

#### Exam Tip

A common exam question requires you to explain the 'negative sign' for values of gravitational potential. Remember the two key facts:

• Gravitational fields are always attractive
• It requires work to move a mass to infinity, where potential is defined as zero

Since the potential energy of a mass therefore increases as it moves toward infinity (where V = 0), the value of the potential everywhere else must be negative

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