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Gravitational Fields

Gravitational potential

  • 4 things to know
  • Papers 1, 2 and 3

Overview

Recall questions on gravitational potential and why it is negative, V = −GM/r, its unit and where it applies, and finding and calculating the change in potential between two points.

What you need to know

Answer each one before you reveal it.

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Key term

In the gravitational potential energy equation E = −GMm/r, what do M, m and r represent?

Key term

Define gravitational potential at a point.

Key term

In the equation V = −GM/r, what does G represent?

Numbers

State the equation for gravitational potential at distance r from a point mass M.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Define gravitational potential at a point.

    Model answer

    The work done per unit mass in bringing a small test mass from infinity to that point.

  2. 2

    What is the value of gravitational potential at infinity?

    Model answer

    Zero.

  3. 3

    Why is gravitational potential always negative?

    Model answer

    Because work must be done against the gravitational field to move a mass from any point to infinity; since potential is zero at infinity and energy is released when moving towards a mass, all finite positions have negative potential.

  4. 4

    State the equation for gravitational potential at distance r from a point mass M.

    Model answer

    V = −GM/r

  5. 5

    Calculate the change in gravitational potential when gravitational constant = 6.67 × 10⁻¹¹ N m² kg⁻², mass of body = 5.97 × 10²⁴ kg, initial distance = 6.37 × 10⁶ m, final distance = 4.22 × 10⁷ m.

    Model answer

    Change in gravitational potential = −6.67 × 10⁻¹¹ × 5.97 × 10²⁴ × (1 ÷ (4.22 × 10⁷) − 1 ÷ (6.37 × 10⁶)) = 5.31 × 10⁷ J kg⁻¹.

  6. 6

    What is the SI unit of gravitational potential?

    Model answer

    Joules per kilogram (J kg⁻¹).

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