Motion in the Universe
5 marks · NormalConsider a comet with a highly elliptical orbit around the Sun, and a moon with a nearly circular orbit around a planet.
State two differences between the orbit of a comet and that of a moon in our solar system.
Explain why the speed of a comet changes as it moves along its orbit, while the speed of a moon remains nearly constant.
The average orbital radius of the moon is 400,000 km. If it takes 28 days to complete one orbit, calculate the average orbital speed of the moon. Give your answer in km/s.
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(a) 1. Comet orbits are highly elliptical, moon orbits are nearly circular. 2. Comets orbit the Sun, moons orbit planets.
(b) Comet speed varies because its distance from the Sun changes; gravity is stronger when closer, making it move faster. In contrast, a moon's distance from its planet stays nearly constant, so its speed remains nearly constant.
(c) 1.04 km/s
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Marking points
B1 (a) · 1 mark · States the difference in orbit shapes (elliptical vs. circular).
B1 (a) · 1 mark · States the difference in what body they orbit (Sun vs. planet).
M1 (b) · 1 mark · Explains comet's speed changes as distance from Sun varies due to elliptical orbit.
A1 (b) · 1 mark · Correctly links moon's almost constant speed to circular orbit and nearly constant distance from planet.
M1 (c) · 1 mark · Substitutes correct values; calculates speed using formula and appropriate conversions. (follow-through)
Worked solution
a) Differences: (1) The orbit of a comet is highly elliptical, while the orbit of a moon is nearly circular. (2) Comets orbit the Sun, moons orbit planets.
b) The speed of a comet changes because as it moves closer to the Sun, the gravitational force increases, pulling it faster; as it moves away, the force weakens and it slows down. In a moon's nearly circular orbit, the distance from the planet is almost constant, so gravity and speed remain nearly constant.
c) Orbital speed = (2 \pi r) / T
r = 400,000 km; T = 28 days = 28 × 24 × 3600 = 2,419,200 s