Calculating Orbital Speeds (Cambridge (CIE) O Level Physics): Revision Note

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.

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

$v=\frac{2\mathrm{\pi }r}{T}$

Step 3: Calculate the orbital radius, r

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

$r=R+h$

$r=6400+560=6960\mathrm{km}$

Step 4: Convert any units

• The time period needs to be in seconds

$1\mathrm{minute}=60\mathrm{seconds}$

$96\mathrm{minutes}=60\times 96=5760\mathrm{s}$

• The radius needs to be in metres

$1\mathrm{km}=1000\mathrm{m}$

$6960\mathrm{km}=6960000\mathrm{m}$

Step 5: Substitute values into the orbital speed equation

$v=\frac{2\mathrm{\pi }\times 6960000}{5760}=7592.18=7590\mathrm{m}/\mathrm{s}$

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!