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Out Into Space

Gravitational potential and equipotentials

  • 3 things to know
  • Components 01, 02 and 03

Overview

Recall questions on gravitational potential V = −GM/r and its unit, its link to potential energy, potential as a scalar, the potential at the Earth's surface, equipotential surfaces around a planet and why moving along one needs no work, their relation to field lines, escape energy per kilogram, the energy to move a probe, equipotential spacing, and which way a released mass moves.

What you need to know

Answer each one before you reveal it.

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Key term

How is gravitational potential related to gravitational potential energy?

Key term

What is the gravitational potential at a distance r from a point mass M?

Numbers

Calculate the gravitational potential at the surface of an Earth with GM = 3.98 × 10¹⁴ N m² kg⁻¹ and radius 6.37 × 10⁶ m.

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Define gravitational potential at a point.

    Model answer

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

  2. 2

    How is gravitational potential related to gravitational potential energy?

    Model answer

    The potential is the potential energy per unit mass, V = E/m.

  3. 3

    What is the gravitational potential at a distance r from a point mass M?

    Model answer

    The potential is V = −GM/r.

  4. 4

    State the unit of gravitational potential.

    Model answer

    It is measured in J kg⁻¹.

  5. 5

    Is gravitational potential a scalar or a vector?

    Model answer

    It is a scalar, so the potentials due to several masses are simply added arithmetically.

  6. 6

    Calculate the gravitational potential at the surface of an Earth with GM = 3.98 × 10¹⁴ N m² kg⁻¹ and radius 6.37 × 10⁶ m.

    Model answer

    V = −GM/r = −6.25 × 10⁷ J kg⁻¹.

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