Orbital Speed Equation

Extended tier only

When planets orbit around the Sun, or a moon moves around a planet, they move in circular orbits
In one complete orbit, a planet travels a distance equal to the circumference of a circle
- This is equal to $2 π r$ , where $r$ is the radius of the circular path

The relationship between speed, distance and time is:

$speed = \frac{distance}{time} = \frac{circumference of orbit}{orbital period}$

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

$v = \frac{2 π r}{T}$

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 speed of a planet

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 moves in a circular orbit. Its height above the Earth’s surface is 560 km and the radius of the Earth is 6400 km. It completes one orbit in 96 minutes.

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

Calculate its orbital speed in m/s.

Answer:

Step 1: List the known quantities

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

Step 2: Write the relevant equation

$v = \frac{2 π r}{T}$

Step 3: Calculate the orbital radius, r

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

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

$r = R + h$

$r = 6400 + 560 = 6960 km$

Step 4: Convert any units

The time period needs to be in seconds

$1 minute = 60 seconds$

$96 minutes = 60 \times 96 = 5760 s$

The radius needs to be in metres

$1 km = 1000 m$

$6960 km = 6 960 000 m$

Step 5: Substitute values into the orbital speed equation

$v = \frac{2 π \times 6 960 000}{5760} = 7592.18 = 7590 m / s$

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!

Orbital Speed Equation (CIE IGCSE Physics: Co-ordinated Sciences (Double Award))

Revision Note