# 7.2.2 Calculating Gravitational Potential

### Calculating Gravitational Potential

• The equation for gravitational potential V is defined by the mass M and distance r: • Where:
• V = gravitational potential (J kg-1)
• G = Newton’s gravitational constant
• M = mass of the body producing the gravitational field (kg)
• r = distance from the centre of the mass to the point mass (m)
• The gravitational potential always is negative near an isolated mass, such as a planet, because:
• The potential when r is at infinity (∞) is defined as 0
• Work must be done to move a mass away from a planet (V becomes less negative)
• It is also a scalar quantity, unlike the gravitational field strength which is a vector quantity

• Gravitational forces are always attractive, this means as r decreases, positive work is done by the mass when moving from infinity to that point
• When a mass is closer to a planet, its gravitational potential becomes smaller (more negative)
• As a mass moves away from a planet, its gravitational potential becomes larger (less negative) until it reaches 0 at infinity
• This means when the distance (r) becomes very large, the gravitational force tends rapidly towards 0 at a point further away from a planet Gravitational potential increases and decreases depending on whether the object is travelling towards or against the field lines from infinity

#### Worked Example

A planet has a diameter of 7600 km and a mass of 3.5 × 1023 kg.

A rock of mass 528 kg accelerates towards the planet from infinity.

At a distance of 400 km above the planet’s surface, calculate the gravitational potential of the rock.

Step 1: Write the gravitational potential equation Step 2: Determine the value of r

• r is the distance from the centre of the planet

Radius of the planet = planet diameter ÷ 2 = 7600 ÷ 2  = 3800 km

r = 3800 + 400 = 4200 km = 4.2 × 106 m

Step 3: Substitute in values #### Exam Tip

Remember to keep the negative sign in your solution for the gravitational potential at a point. However, if you’re asked for the ‘change in’ gravitational potential, no negative sign needs to be included since you are finding a difference in values and just the magnitude is normally required.

Remember to also calculate r as the distance from the centre of the planet, and not just the distance above the planet’s surface ### 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.
Close Close

# ## Download all our Revision Notes as PDFs

Try a Free Sample of our revision notes as a printable PDF.

Already a member?