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
- 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
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- '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
Examiner 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.
