Gravitational Potential Energy (OCR A Level Physics)

Revision Note

Test Yourself




Physics Project Lead

Gravitational Potential Energy

  • The gravitational potential Vg at a point is given by:

V subscript g equals fraction numerator negative G M over denominator r end fraction

  • Recall that potential V is defined as the energy required to bring unit mass m from infinity to a defined point in the field
    • Recall that the gravitational field is usually caused by 'big mass', M

  • Therefore, the potential energy E  is given by:


  • Substituting the equation for gravitational potential Vg gives the equation for the gravitational potential energy E between two masses M and m:

E equals fraction numerator negative G M m over denominator r end fraction

  • Where: 
    • G = Universal Gravitational Constant (N m2 kg2)
    • M = mass causing the field (kg)
    • m = mass moving within the field of M (kg)
    • r = distance between the centre of m and M (m)

Calculating Changes in Gravitational Potential Energy

  • When a mass is moved against the force of gravity, work is required
    • This is because gravity is attractive, therefore, energy is needed to work against this attractive force

  • The work done (or energy transferred) ∆W to move a mass m between two different points in a gravitational potential ∆V is given by:

W = m V

  • Where:
    • W = work done or energy transferred (J)
    • m = mass (kg)
    • Vchange in gravitational potential (J kg-1)


  • This work done, or energy transferred, is the change in gravitational potential energy (G.P.E) of the mass
    • When ∆V = 0, then the the change in G.P.E = 0

  • The change in G.P.E, or work done, for an object of mass m at a distance r1 from the centre of a larger mass M, to a distance of r2 further away can be written as:

  • Where:
    • M = mass that is producing the gravitational field (e.g., a planet) (kg)
    • m = mass that is moving in the gravitational field (e.g., a satellite) (kg)
    • r1initial distance of m from the centre of M (m)
    • r2 = final distance of m from the centre of (m)

  • Work is done when an object in a planet's gravitational field moves against the gravitational field lines, i.e., away from the planet
    • This is, again, because gravity is attractive
    • Therefore, energy is required to move against gravitational field lines

Change in GPE, downloadable AS & A Level Physics revision notes

Gravitational potential energy increases as a satellite leaves the surface of the Moon

Worked example

A spacecraft of mass 300 kg leaves the surface of Mars to an altitude of 700 km.Calculate the work done by the spacecraft.Radius of Mars = 3400 km

Mass of Mars = 6.40 × 1023 kg

Step 1:            Write down the work done (or change in G.P.E) equation

Worked Example G.P.E equation

Step 2:            Determine values for r1 and r2

r1 is the radius of Mars = 3400 km = 3400 × 103 m

r2 is the radius + altitude = 3400 + 700 = 4100 km = 4100 × 103 m

Step 3:            Substitute in values

Worked Example G.P.E Calculation

ΔG.P.E =  643.076 × 10= 640 MJ (2 s.f.)

Exam Tip

Make sure to not confuse the ΔG.P.E equation with

ΔG.P.E = mgΔh

The above equation is only relevant for an object lifted in a uniform gravitational field (close to the Earth’s surface). The new equation for G.P.E will not include g, because this varies for different planets and is no longer a constant (decreases by 1/r2) outside the surface of a planet.

You've read 0 of your 0 free revision notes

Get unlimited access

to absolutely everything:

  • Downloadable PDFs
  • Unlimited Revision Notes
  • Topic Questions
  • Past Papers
  • Model Answers
  • Videos (Maths and Science)

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

Did this page help you?


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.

Join over 500 thousand students
getting better grades