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Out Into Space

Circular gravitational orbits

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

Overview

Recall questions on gravity supplying the centripetal force, deriving orbital speed and the period–radius relation, why satellite mass drops out, geostationary and polar orbits, and decaying low orbits.

What you need to know

Answer each one before you reveal it.

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Key term

Why does orbital speed not depend on the mass of the satellite?

Key term

State the relationship between the period and the radius of a circular orbit in words.

Key term

A satellite of orbital radius 6.77 × 10⁶ m travels at 7.7 × 10³ m s⁻¹. What is its period?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    How does the gravitational force provide the centripetal force for a circular orbit?

    Model answer

    The gravitational attraction GMm/r² acts towards the centre and is exactly the force mv²/r needed to hold the satellite on its circular path.

  2. 2

    Derive an expression for the orbital speed of a satellite in a circular orbit of radius r.

    Model answer

    Setting GMm/r² equal to mv²/r and cancelling m gives v = √(GM/r).

  3. 3

    Why does orbital speed not depend on the mass of the satellite?

    Model answer

    The satellite's mass appears on both sides of GMm/r² = mv²/r and cancels.

  4. 4

    How does orbital speed vary with orbital radius?

    Model answer

    It is proportional to 1/√r, so a satellite in a larger orbit moves more slowly.

  5. 5

    Derive the relationship between orbital period and orbital radius.

    Model answer

    Substituting v = 2πr/T into v² = GM/r gives T² = 4π²r³/GM.

  6. 6

    State the relationship between the period and the radius of a circular orbit in words.

    Model answer

    The square of the period is proportional to the cube of the orbital radius.

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