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Orbits Edexcel International A Level Physics revision

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In plain words

A satellite is falling all the time. It is also moving sideways so fast that the ground curves away beneath it as quickly as it falls, so it never gets any closer. Gravity supplies exactly the centripetal force the circle needs.

Three things to know

  1. For a circular orbit, the gravitational force is the centripetal force: GMm ÷ r² = mv² ÷ r, so v² = GM ÷ r. The satellite's own mass cancels out.
  2. Putting v = 2πr ÷ T gives T² = 4π²r³ ÷ GM. The period depends only on the radius of the orbit and the mass at the centre. Bigger orbits are slower and take longer.
  3. A geostationary satellite stays above the same point on the Earth. Its orbit must have a period of 24 hours, be directly above the Equator, and go from west to east, the way the Earth spins.

Worked example

Find the speed of a satellite in a circular orbit 400 km above the Earth's surface. (For the Earth, GM = 3.98 × 10¹⁴ N m² kg⁻¹ and the radius is 6.37 × 10⁶ m.)

  1. Radius of the orbit r = 6.37 × 10⁶ + 0.40 × 10⁶ = 6.77 × 10⁶ m.
  2. v² = GM ÷ r = 3.98 × 10¹⁴ ÷ 6.77 × 10⁶ = 5.88 × 10⁷.
  3. v = 7.7 × 10³ m/s.

Tips and tricks

  • Start every orbit question by writing "gravitational force = centripetal force".
  • Astronauts in orbit feel weightless because they and their spacecraft are falling together, not because gravity has gone.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Orbits: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. A satellite is moved to a higher circular orbit. What happens to its speed?
    • It decreases. (the answer)
    • It increases.
    • It stays the same.
    • It becomes zero.

    v² = GM ÷ r.

  2. What is the period of a geostationary satellite?
    • 90 minutes
    • 12 hours
    • 24 hours (the answer)
    • 1 month

    It keeps pace with the turning Earth.

  3. Above which part of the Earth must a geostationary satellite orbit?
    • the Equator (the answer)
    • the North Pole
    • the South Pole
    • anywhere

    Only an orbit above the Equator stays over one point.

  4. Two satellites of different mass share the same circular orbit. How do their speeds compare?
    • They are the same. (the answer)
    • The heavier one is faster.
    • The lighter one is faster.
    • It depends on their shapes.

    The satellite's mass cancels out of the equation.

  5. The radius of a satellite's orbit is increased. What happens to its period?
    • It increases. (the answer)
    • It decreases.
    • It stays the same.
    • It halves.

    T² is proportional to r³.

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