Orbital speeds of planets and satellites

3 marks · Normal

The Moon has an orbital radius of 384,000 km and takes 27.3 days to orbit Earth once. Calculate the average orbital speed of the Moon in km/s. (1 day = 86,400 s).

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1.0 km/s (±0.05)

Must show: convert time correctly, correct use of circumference

Also accept: ~1 km/s; 0.97 km/s

Common mistakes: not converting days to seconds; using wrong radius

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Marking points

M1 · 1 mark · Converts 27.3 days to seconds. (follow-through)

M2 · 1 mark · Calculates the orbit’s circumference using 2πr. (follow-through)

A1 · 1 mark · Correct calculation of speed in km/s. (follow-through)

Worked solution

First, convert 27.3 days to seconds: 27.3 × 86,400 = 2,360,000 s (2.36 × 10⁶ s). Orbit’s circumference: 2 × π × 384,000 = 2,413,000 km. Speed = circumference / time = 2,413,000 / 2,360,000 ≈ 1.0 km/s.