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Gravitational Fields

The field of a point mass and calculations with g

  • 1 thing to know
  • Papers 2 and 3

Overview

Recall questions on the derivation of g = Gm/r², treating a sphere as a point mass, how g varies outside a planet, and finding g at a planet's surface or at orbital radius.

What you need to know

Answer each one before you reveal it.

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Numbers

How does g vary with distance from the centre of a planet, outside its surface?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Why may a uniform sphere be treated as a point mass when calculating its field?

    Model answer

    Outside the sphere its whole mass behaves as though concentrated at its centre, so the field depends only on the distance from that centre.

  2. 2

    How does g vary with distance from the centre of a planet, outside its surface?

    Model answer

    It obeys an inverse square relationship, so g is proportional to 1/r².

  3. 3

    What are the value and unit of the universal gravitational constant?

    Model answer

    G = 6.67 × 10⁻¹¹ N m² kg⁻².

  4. 4

    The Earth has a mass of 5.97 × 10²⁴ kg and a radius of 6.37 × 10⁶ m. What is g at its surface?

    Model answer

    g = 6.67 × 10⁻¹¹ × 5.97 × 10²⁴ ÷ (6.37 × 10⁶)² = 9.81 N kg⁻¹.

  5. 5

    A planet of radius 3.39 × 10⁶ m has a surface gravitational field strength of 3.7 N kg⁻¹. What is its mass?

    Model answer

    m = gr²/G = 3.7 × (3.39 × 10⁶)² ÷ (6.67 × 10⁻¹¹) = 6.4 × 10²³ kg.

  6. 6

    A satellite orbits at a distance of three Earth radii from the Earth's centre. What is the field strength there if surface g is 9.81 N kg⁻¹?

    Model answer

    The distance is three times greater, so g falls by a factor of 9 to 1.09 N kg⁻¹.

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