Astrophysics
4 marks · NormalA planet named Xon is discovered with a moon that orbits at a radius of 120,000 km and takes 40 days for one complete orbit. The gravitational field strength at the moon's surface is also measured.
Calculate the orbital speed of the moon. Give your answer in km/s.
The moon has a gravitational field strength of 2.5 N/kg. What is the weight of a 50 kg object on the surface of this moon?
Work this out on paper, then compare with the answer and worked solution below. With a free account you can submit written answers for marking.
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(a) Orbital speed v = 2πr / T = 2 × π × 120,000 km / (40 × 24 × 3600 s) ≈ 0.218 km/s. km/s
(b) 125 N
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Marking points
M1 (a) · 1 mark · Selects correct formula: v = 2πr / T
M2 (a) · 1 mark · Correct substitution for r and T (with T converted to seconds)
A1 (a) · 1 mark · Correct calculation and answer, 0.218 km/s (accept values to 2 dp) (follow-through)
A2 (b) · 1 mark · Correct weight calculated: 125 N
Worked solution
a) Orbital speed , where r = 120,000 km, T = 40 days.
Convert T to seconds: T = 40 × 24 × 3600 = 3,456,000 s
b) Weight = mass × g = 50 × 2.5 = 125 N