Orbits of Planets & Satellites

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Orbital Period and Radius

When an object orbits a more massive body it has a set period and radius which depend on each other.

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Orbital period

  • The time taken for an object to do one full orbit is called the period.
  • Even if the orbit is elliptical the period will remain constant.
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Orbital radius

  • The orbital radius is the average distance between the centre of the body and the centre of the object.
  • For the circle, the radius is always the same.
  • For an elliptical orbit, the radius changes.
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  • Orbital period and radius have the following relationship:
    • The period squared is proportional to the radius cubed.
    • T2  α  r3T^2\; \alpha \; r^3
  • The constant of proportionality can be found by finding the gradient of a graph of period squared against radius cubed.
  • This is Kepler's third law.

Energies of Orbiting Objects

Sometimes, considering the total energy of a system, such as a satellite orbiting a planet, can be much easier than thinking about the resultant force and acceleration of an object.

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Circular orbits

  • In a circular orbit around a planet, the satellite is always on the same equipotential and so the total energy of an orbiting satellite is constant.
    • The planet does no work on the satellites, so there is no loss in potential and no loss in gravitational potential energy (GPE).
    • The radius of the orbit does not change.
    • The satellite does not change kinetic energy (KE) and so has a constant speed.
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Non-circular orbits

  • This approach also works for non-circular orbits such as ellipses and parabolas.
  • This is because we can show that the total energy of an orbiting satellite is always equal to half of the gravitational potential energy of the satellite.
  • This is because gravitational field strength follows an inverse-square law.

Jump to other topics

1Measurements & Errors

2Particles & Radiation


4Mechanics & Materials


6Further Mechanics & Thermal Physics (A2 only)

7Fields & Their Consequences (A2 only)

8Nuclear Physics (A2 only)

9Option: Astrophysics (A2 only)

10Option: Medical Physics (A2 only)

11Option: Engineering Physics (A2 only)

12Option: Turning Points in Physics (A2 only)

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