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Physics · Space physics

Orbital motion and satellites

Explain how a satellite can move at constant speed but with changing velocity, and how orbital radius and speed are linked (Higher tier only; Physics only).

  • Higher
  • 6 key terms
  • All boards
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Warm-up

Answer each one, then check.

  1. 1

    What is speed?

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    Distance travelled per unit time

  2. 2

    What is velocity?

    Show answerHide answer

    Speed in a given direction

  3. 3

    What is gravity?

    Show answerHide answer

    An attractive force between masses

  4. 4

    What is an orbit?

    Show answerHide answer

    The curved path round a planet or star

  5. 5

    What is a satellite?

    Show answerHide answer

    An object that orbits a larger object

Learning Objectives

  1. 1Explain why an object moving in a circle at constant speed has a changing velocity.
  2. 2Explain that gravity provides the force for circular orbits.
  3. 3Explain how orbital radius, speed and time for an orbit are linked.
  4. 4Describe what happens if a satellite's speed changes.

CIRCULAR ORBITS

An object in a circular orbit moves at constant speed but its velocity is always changing because its direction is changing. The resultant force is gravity, which acts towards the centre of the orbit.

For an orbit of a given radius, the speed must be a particular value. If the speed changes, the radius changes.

Orbits at Different Heights

Learn the links.

  • Low orbit (closer)

    Speed: Faster. Time for one orbit: Shorter

  • High orbit (further away)

    Speed: Slower. Time for one orbit: Longer

  • Geostationary (about 36 000 km)

    Speed: Matches the Earth's rotation. Time for one orbit: 24 hours

  • If the speed changes

    Speed: Radius must change too. Time for one orbit: Time changes

Constant Speed, Changing Velocity

Explain why a satellite moving at constant speed in a circle is accelerating.

Show the solutionHide the solution
  1. 1 Speed Constant
  2. 2 Direction Always changing
  3. 3 Velocity Has speed and direction, so it changes
  4. 4 Acceleration A change in velocity is an acceleration, towards the centre

AnswerVelocity changes because direction changes, so it accelerates.

Orbital Speed

A satellite orbits at a radius of 7000 km and completes one orbit in 5800 s. Calculate its speed.

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  1. 1 Distance circumference \(= 2\pi r = 2 \times \pi \times 7.0 \times 10^6 = 4.4 \times 10^7\) m
  2. 2 Speed \(v = d \div t = 4.4 \times 10^7 \div 5800\)
  3. 3 Answer \(v \approx 7600\) m/s

AnswerAbout 7600 m/s.

Key Points

Learn these.

  • Gravity

    Provides the force towards the centre.

  • Constant speed

    But velocity changes.

  • Closer orbit

    Faster and a shorter orbit time.

  • Change of speed

    Changes the radius of the orbit.

Orbit Sums

Explain why a satellite does not fall to Earth even though gravity pulls on it. Then calculate its speed if one orbit of radius 7000 km takes 5800 s.

1. Speed = distance ÷ time.

A good answer shows: It is falling but moves sideways fast enough to keep missing the Earth. v = 2π × 7.0 × 10^6 ÷ 5800 ≈ 7600 m/s.

Can I...?

  1. 1Define orbit.
  2. 2Explain changing velocity.
  3. 3Explain the force.
  4. 4Link radius and speed.
  5. 5Describe geostationary.
  6. 6Calculate orbital speed.
  7. 7Explain a change in speed.
  8. 8Give examples.

Summary & Exam Focus

  • Constant speed but changing direction means changing velocity.
  • Gravity acts towards the centre.
  • Lower orbit: faster; higher orbit: slower.
  • Change of speed gives a change of radius.

Exam focus

Explain why the velocity of a satellite moving at constant speed is changing. (2 marks) (2 marks)

Direction changes.

Key terms

The vocabulary this lesson expects you to use. Each one is linked from the first place it appears above.

Orbit
The curved path of an object round a planet or star.
Orbital speed
The speed of an object as it moves in its orbit.
Velocity
Speed in a given direction.
Geostationary orbit
An orbit with a period of 24 hours, so the satellite stays above one point on Earth.
Acceleration
A change in velocity.
Satellite
An object in orbit around a larger object.

Practice questions

Have a go at each one before you open its answer.

  1. Question 1 Explain 2 marks

    A satellite orbits the Earth at constant speed. Explain why its velocity is not constant.

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    Model answer

    Velocity is speed in a given direction. The direction of motion is always changing, so the velocity changes even though the speed is constant.

    Mark scheme

    • Velocity has direction — 1 mark
    • Direction is changing — 1 mark
  2. Question 2 Explain 3 marks

    Explain what provides the force that keeps a satellite in a circular orbit and state the direction of the force.

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    Model answer

    The force is gravity between the Earth and the satellite. It acts towards the centre of the orbit (the centre of the Earth).

    Mark scheme

    • Gravity — 1 mark
    • Between Earth and satellite — 1 mark
    • Towards the centre — 1 mark
  3. Question 3 Calculate 3 marks

    A satellite completes one circular orbit of circumference 4.4 × 10^7 m in 5800 s. Calculate its orbital speed.

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    Model answer

    \(v = 4.4 \times 10^7 \div 5800 = 7600\) m/s (about)

    Mark scheme

    • Distance ÷ time — 1 mark
    • Correct substitution — 1 mark
    • About 7600 m/s — 1 mark
  4. Question 4 Explain 3 marks

    Satellite A orbits the Earth at a smaller radius than satellite B. Compare the orbital speeds and the times taken for one orbit, and explain the difference in speed.

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    Model answer

    A moves faster than B and takes less time to complete an orbit. Gravity is stronger closer to the Earth, so a greater orbital speed is needed for a stable orbit at a smaller radius; A also has a shorter path.

    Mark scheme

    • A faster than B — 1 mark
    • A has a shorter orbit time — 1 mark
    • Gravity is stronger at smaller radius, so a higher speed is needed — 1 mark
  5. Question 5 Explain 2 marks

    A geostationary satellite stays above the same point on the Earth. State the time taken for one orbit and explain why this is useful.

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    Model answer

    24 hours. It stays above one place, so a fixed dish can communicate with it.

    Mark scheme

    • 24 hours — 1 mark
    • Fixed position above the Earth: useful for communications — 1 mark

Quick check

  1. A satellite in a circular orbit has constant...

    1. Avelocity
    2. Bacceleration
    3. Cdirection
    4. Dspeed
    Show answerHide answer

    D: speed

    Speed is constant.

  2. The force keeping a satellite in orbit is...

    1. Agravity
    2. Bfriction
    3. Cmagnetism
    4. Dair resistance
    Show answerHide answer

    A: gravity

    Attracts to the centre.

  3. The force acts...

    1. Aalong the path
    2. Btowards the centre of the orbit
    3. Caway from the centre
    4. Din no direction
    Show answerHide answer

    B: towards the centre of the orbit

    Centripetal.

  4. A lower orbit has a...

    1. Alonger orbit time
    2. Bslower speed
    3. Cshorter orbit time
    4. Dzero speed
    Show answerHide answer

    C: shorter orbit time

    Faster.

  5. A geostationary orbit takes...

    1. A1 hour
    2. B365 days
    3. C12 hours
    4. D24 hours
    Show answerHide answer

    D: 24 hours

    Same as Earth's rotation.

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