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A satellite passes over a fixed location on the equator once every 8 hours when it orbits in the direction opposite to Earth's rotation. Find the time interval between successive passes over the same location if the satellite instead orbits in the same direction as Earth's rotation.
- 8 hours
- 12 hours
- 24 hours
- 6 hours
Correct answer: 24 hours
Solution
Let satellite angular speed be ws and Earth's we = 2pi/24 per hour. When motions are opposite, relative angular speed = ws + we = 2pi/8, so ws = 2pi/8 - 2pi/24 = 2pi(3-1)/24 = 2pi*2/24 = 2pi/12, i.e. ws = 2pi/12 (period 12 h). When in the same direction, relative = ws - we = 2pi/12 - 2pi/24 = 2pi(2-1)/24 = 2pi/24. So observed period T = 24 hours.
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