Motion in the Universe
4 marks · EasyA satellite is placed in orbit at a height where the gravitational field strength is much smaller than on Earth’s surface.
Explain why the satellite stays in orbit instead of falling straight towards the Earth.
Calculate the orbital speed of the satellite if it travels along a circular path of radius m and completes one orbit in 24 hours. Give your answer in to two significant figures.
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) Because it has a high sideways (tangential) speed, gravity keeps pulling it toward Earth but its speed keeps it moving around Earth in a curved path. · must show Satellite has forward (sideways) speed, Gravity pulls it inward, Both combine to create orbit (falls around Earth)
(b) 7.3 km/s · must show Converts time to seconds (24 hours = 86400 s), Calculates circumference (2πr), Divides distance by time
Common mistakes: Using the diameter instead of the radius; Not converting hours to seconds
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · States satellite has enough sideways/forward speed.
A1 (a) · 1 mark · Explains that gravity pulls it inward, making it curve rather than fall straight down. Credit 'falls around Earth'.
M2 (b) · 1 mark · Correct calculation for circumference and time. Substitutes values into .
A2 (b) · 1 mark · Correct final answer (7.3 km/s), 2 significant figures, with correct unit.
Worked solution
a) The satellite moves sideways very fast. Gravity pulls it towards Earth, but because of its speed, it keeps missing and stays in orbit, continuously falling around Earth instead of dropping straight down.
b) Orbital speed
Final answer: 2.9 km/s (rounded to two significant figures; mark 2.9 km/s as correct for full method).