Extended · Practice questions · Orbital speed

Round and round, measured.

Six original Cambridge-style questions on orbital speed: using v = 2(pi)r / T, rearranging it, and comparing orbits.

Original questions All questions on this page are original work, written in the Cambridge IGCSE style. They are not from past papers. They test the same concepts and skills the syllabus rewards.

What the examiner wants

Circumference over period.

Formula: v = 2(pi)r / T.
Units: r in metres, T in seconds, v in m/s.
Rearrange: to find r or T when needed.

Recall

[2 marks]

Write down the equation for orbital speed, and state what each symbol means.

v = 2(pi)r / T. ✓
r is the orbit radius, T is the period (time for one orbit), v is the orbital speed. ✓

Calculation

[3 marks]

A planet orbits a star in a circle of radius 6.0 x 10 to the 10 m, with a period of 2.0 x 10 to the 7 s. Calculate its orbital speed.

v = 2(pi)r / T = 2 x (pi) x (6.0 x 10 to the 10) / (2.0 x 10 to the 7)

v = 1.9 x 10 to the 4 m/s (about 19000 m/s)

Calculation

[3 marks]

A satellite moves at 7500 m/s in a circular orbit of radius 7.0 x 10 to the 6 m. Calculate its period.

T = 2(pi)r / v = 2 x (pi) x (7.0 x 10 to the 6) / 7500

T = 5900 s (to 2 significant figures)

Analysis

[2 marks]

Two satellites have the same period, but one orbits at twice the radius of the other. Compare their orbital speeds.

Speed is proportional to radius when the period is the same. ✓
The one at twice the radius moves at twice the speed. ✓

Application

[2 marks]

Explain why a satellite with a longer period, at the same orbital radius, moves more slowly.

It travels the same distance (2(pi)r) round the orbit. ✓
But it takes a longer time, so its speed (distance / time) is smaller. ✓

Calculation

[3 marks]

The Moon orbits the Earth at a radius of about 3.8 x 10 to the 8 m with a period of about 2.4 x 10 to the 6 s. Estimate its orbital speed.

v = 2(pi)r / T = 2 x (pi) x (3.8 x 10 to the 8) / (2.4 x 10 to the 6)

v = 1000 m/s (about 1.0 x 10 to the 3 m/s)

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.