# 7.2.1 Gravitational Potential

### Gravitational Potential

• 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

• 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 is only used for objects that are within the Earth’s surface
• However, outside the Earth’s surface, G.P.E can be defined as:

The energy an object possess due to its position in a gravitational field

• The gravitational potential at a point is the gravitational potential energy per unit mass at that point
• Therefore, it is defined as:

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

• It is represented by the symbol, V and is measured in J kg-1
• The gravitational potential is always a negative value. This is because:
• It is defined as zero at infinity
• Since the gravitational force is attractive, work must be done on a mass to reach infinity
• This means that the gravitational potential is negative on the surface of a mass (such as a planet), and increases with distance from that mass (becomes less negative)
• Work has to be done against the gravitational pull of the planet to take a unit mass away from the planet
• The gravitational potential at a point depends on the mass of the object producing the gravitational field and the distance the point is from that mass

Gravitational potential decreases as the satellite moves closer to the Earth

#### Exam Tip

Remember to memorise the gravitational potential definition and the reason why it is negative, as these are very common exam questions

### Gravitational Potential Difference

• Two points at different distances from a mass will have different gravitational potentials
• This is because the gravitational potential increases with distance from a mass
• Therefore, there will be a gravitational potential difference between the two points
• This is represented by the symbol ΔV
• Δis normally given as the equation

ΔV = Vf – Vi

• Where:
• Vf = final gravitational potential (J kg-1)
• Vi = initial gravitational potential (J kg-1)
• A difference in gravitational potential will give a difference in gravitational potential energy, that can also be calculated

#### Exam Tip

When exam questions ask for the ‘difference’ or ‘change in’ a value (denoted by Δ), they are asking for the magnitude. Therefore, don’t worry too much about negative or positive signs. As long as you consistently calculate the difference in two values as ‘final value – initial value‘, a negative difference will mean that the value is decreasing and vice versa

### Author: Ashika

Ashika graduated with a first-class Physics degree from Manchester University and, having worked as a software engineer, focused on Physics education, creating engaging content to help students across all levels. Now an experienced GCSE and A Level Physics and Maths tutor, Ashika helps to grow and improve our Physics resources.
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