Motion in the Universe
5 marks · NormalA communication satellite is placed in orbit 36,000 km above Earth's surface. The radius of Earth is approximately 6,400 km.
Calculate the total orbital radius of the satellite from the centre of the Earth.
Explain why artificial satellites in low orbits move faster than satellites in high orbits above the same planet.
The communication satellite takes exactly 24 hours to complete one orbit. Calculate its average orbital speed in km/s (show all working).
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.
Show answer
(a) 42,400 km
(b) Satellites closer to Earth are within a stronger gravitational field, so they must move faster to stay in orbit. Higher satellites experience weaker gravity and move slower.
(c) 3.09 km/s
Show mark scheme and worked solution
Marking points
M1 (a) · 1 mark · Correctly adds Earth's radius to orbital height above surface to find total orbital radius.
M1 (b) · 1 mark · Recognises higher up the gravitational pull is weaker, so less speed is needed.
A1 (b) · 1 mark · Accurately links higher/lower speed to gravity's strength or necessity to 'stay in orbit'.
M1 (c) · 1 mark · Uses correct formula and conversions to calculate orbital speed with correct figures.
A1 (c) · 1 mark · Correct value for speed (3.09 km/s), appropriate units and significant figures allowed. (follow-through)
Worked solution
a) Total orbital radius = radius of Earth + height above surface = 6,400 km + 36,000 km = 42,400 km.
b) Satellites in low orbit are closer to the Earth, so they experience stronger gravity and must move faster to maintain orbit. High-orbit satellites are farther away, so the gravitational force is weaker and they move more slowly to stay in stable orbit.
c) Orbital speed = (2\pi r)/T, where r = 42,400 km, T = 24 hours = 24×3600 = 86,400 s