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Gravitational Fields

Orbital period and geostationary orbits

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

Overview

Recall questions on T² ∝ r³, and on the conditions for and uses of a geostationary orbit.

What you need to know

Answer each one before you reveal it.

Your recallNot started
Numbers

Write the equation relating orbital period T to orbital radius r for a body orbiting a central mass M.

Numbers

After substituting v = 2πr/T into v² = GM/r, what final rearrangement gives the orbital period equation?

Key term

What substitution for orbital speed v is made when deriving the relationship between T and r?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    Write the equation relating orbital period T to orbital radius r for a body orbiting a central mass M.

    Model answer

    T² = (4π²/GM)r³

  2. 2

    What substitution for orbital speed v is made when deriving the relationship between T and r?

    Model answer

    Substitute v = 2πr/T into the equation.

  3. 3

    After substituting v = 2πr/T into v² = GM/r, what final rearrangement gives the orbital period equation?

    Model answer

    Rearrange to obtain T² = (4π²/GM)r³.

  4. 4

    Does Kepler's third law relationship T² ∝ r³ apply only to planets orbiting the Sun?

    Model answer

    No, it applies to any system of orbiting bodies, where M is the mass of the central body being orbited.

  5. 5

    Define a geostationary orbit.

    Model answer

    An orbit in which a satellite remains above the same point on the Earth's surface at all times.

  6. 6

    What orbital period must a geostationary satellite have?

    Model answer

    One day (about 24 hours), equal to Earth's rotational period.

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