AQA A Level Physics

Revision Notes

7.2.2 Calculating Gravitational Potential

Calculating Gravitational Potential

  • The equation for gravitational potential V is defined by the mass M and distance r:

Gravitational Potential Equation_2

  • 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 diagram, downloadable AS & A Level Physics revision notes

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

Gravitational Potential Equation_2

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

Gravitational Potential Worked Example Step 3_2

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

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