IGCSE Physics / Motion in the universe
Orbital speed
Edexcel International GCSE Physics (4PH1), chapter 26: Motion in the universe, specification point 8.6. Free lesson.
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Orbital speed is the distance travelled in one complete orbit divided by the time taken. The distance is the orbit's circumference, so you use 2πr and convert the period into seconds before calculating.
What the orbital speed equation means
An orbit is one complete trip around a circle. Its circumference is 2πr, so orbital speed is circumference divided by the time for one orbit. The radius is measured from the centre of the larger body to the orbiting object. v is orbital speed, measured in m/s. r is orbital radius, measured in metres (m). If you are given a diameter, halve it to find the radius. Do not halve a radius. T is the time period for one complete orbit, measured in seconds (s). The equation is v = (2 × π × r)/T. Keep the 2π because the object travels the whole circumference.
How to convert a period into seconds
Periods are often given in days or years, but the equation needs T in seconds. Convert the period before substituting it into the equation.
How to calculate orbital speed
Use the circumference as the distance travelled in one orbit, then divide by the period in seconds. Write the equation first and show your substitution, which helps make your method clear.
How to rearrange the equation to find T
If the speed and radius are known, substitute them into the equation before rearranging. This makes it clear that the correct values have been used.