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O LevelPhysicsCambridgeRevision Notes6. Space Physics6.1 Earth & The Solar SystemCalculating Orbital Speeds

Calculating Orbital Speeds (Cambridge O Level Physics)

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Katie M

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Orbital Speed

  • When planets move around the Sun, or a moon moves around a planet, they orbit in circular motion
    • This means that in one orbit, a planet travels a distance equal to the circumference of a circle (the shape of the orbit)
    • This is equal to 2πr where r is the radius of a circle 

  • The relationship between speed, distance and time is:

s p e e d space equals space fraction numerator d i s t a n c e over denominator t i m e end fraction

  • the average orbital speed of an object can be defined by the equation:

v space equals space fraction numerator 2 straight pi r over denominator T end fraction

  • Where:
    • v = orbital speed in metres per second (m/s)
    • r = average radius of the orbit in metres (m)
    • T = orbital period in seconds (s)

  • This orbital period (or time period) is defined as:

The time taken for an object to complete one orbit

  • The orbital radius r is always taken from the centre of the object being orbited to the object orbiting

Orbital Motion

Orbital Period, downloadable IGCSE & GCSE Physics revision notes

Orbital radius and orbital speed of a planet moving around a Sun

Worked example

The Hubble Space Telescope (HST) moves in a circular orbit around the Earth. Its distance above the Earth’s surface is 560 km and the radius of the Earth is 6400 km. The HST completes one orbit in 96 minutes.

6-1-2-worked-example-question-cie-igcse-23-rn

Calculate the orbital speed of the HST in m/s.

Answer:

Step 1: List the known quantities

  • Radius of the Earth, R = 6400 km
  • Distance of the telescope above the Earth's surface, h = 560 km
  • Time period, T = 96 minutes

Step 2: Write the relevant equation

v space equals space fraction numerator 2 straight pi r over denominator T end fraction

Step 3: Calculate the orbital radius, r

  • The orbital radius is the distance from the centre of the Earth to the telescope

r space equals space R space plus space h

6-1-2-worked-example-solution-cie-igcse-23-rn

r space equals space 6400 space plus space 560 space equals space 6960 space km

Step 4: Convert any units

  • The time period needs to be in seconds

1 space minute space equals space 60 space seconds

96 space minutes space equals space 60 space cross times space 96 space equals space 5760 space straight s

  • The radius needs to be in metres

1 space km space equals space 1000 space straight m

6960 space km space equals space 6 space 960 space 000 space straight m

Step 5: Substitute values into the orbital speed equation

v space equals space fraction numerator 2 straight pi space cross times space 6 space 960 space 000 over denominator 5760 end fraction space equals space 7592.18 space equals space 7590 space straight m divided by straight s

Examiner Tip

Remember to check that the orbital radius r given is the distance from the centre of the Sun (if a planet is orbiting a Sun) or the planet (if a moon is orbiting a planet) and not just from the surface. If the distance is a height above the surface you must add the radius of the body, to get the height above the centre of mass of the body.

This is because orbits are caused by the mass, which can be assumed to act at the centre, rather than the surface.

Don't forget to check your units and convert any if required!

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    Katie M

    Author: Katie M

    Expertise: Physics

    Katie has always been passionate about the sciences, and completed a degree in Astrophysics at Sheffield University. She decided that she wanted to inspire other young people, so moved to Bristol to complete a PGCE in Secondary Science. She particularly loves creating fun and absorbing materials to help students achieve their exam potential.