Astrophysics
4 marks · EasyA weather satellite completes an orbit around Earth every 6 hours at an average orbital radius of 12,000 km.
State the SI unit for the orbital radius in this context.
Write the formula for calculating the speed of an orbiting satellite using its orbital radius and time period.
Calculate the orbital speed of the satellite. Give your answer to 2 significant figures.
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Show answer
(a) metre (m)
(b) v = (2 π r) / T
(c) v ≈ 3.5 km/s
Show mark scheme and worked solution
Marking points
B1 (a) · 1 mark · Correct SI unit 'metre (m)'.
B1 (b) · 1 mark · Correct orbital speed formula (accept variants: v=distance/time, with distance=2πr, T for period).
M1 (c) · 1 mark · Substitutes r=12,000 km, T=6 h (=21,600 s) into v = 2πr / T formula.
A1 (c) · 1 mark · Evaluates and gives answer: 3.5 km/s (to 2 s.f.).
Worked solution
(a) The SI unit for radius is metre (m).
(b) The speed of the satellite: v = (2 π r) / T
(c) r = 12,000 km = 12,000,000 m; T = 6 h = 21,600 s