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Gravitational Fields

Orbital speed, period and geostationary satellites

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Overview

Recall questions on what supplies the centripetal force, deriving orbital speed and period, the period-radius relationship, and the conditions for a geostationary orbit.

What you need to know

Answer each one before you reveal it.

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Numbers

What relationship links orbital period to orbital radius, how do a satellite's speed and period change in a higher orbit, and does a heavier satellite need to travel faster in a given orbit?

Questions from this subtopic

Each one with the model answer underneath.

  1. 1

    What provides the centripetal force that keeps a satellite in orbit?

    Model answer

    The gravitational attraction between the satellite and the body it orbits provides the centripetal force.

  2. 2

    How is the expression for the orbital speed of a satellite in a circular orbit of radius r around a body of mass M obtained?

    Model answer

    Equating GMm/r² to mv²/r and cancelling m and one factor of r gives v² = GM/r, so v = √(GM/r).

  3. 3

    How is the expression for the orbital period of a satellite in a circular orbit of radius r obtained?

    Model answer

    Substituting v = 2πr/T into v² = GM/r gives 4π²r²/T² = GM/r, so T² = 4π²r³/(GM).

  4. 4

    What relationship between orbital period and orbital radius follows from that derivation?

    Model answer

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

  5. 5

    Does a heavier satellite need to travel faster in a given orbit than a lighter one?

    Model answer

    No, because the satellite's mass cancels from the equation, so orbital speed depends only on the central mass and the orbital radius.

  6. 6

    How do the speed and the period of a satellite change if it is moved into a higher orbit?

    Model answer

    Its orbital speed decreases because v = √(GM/r), while its period increases because T² is proportional to r³.

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