A geostationary satellite above the equator is orbiting around the earth at a fixed distance from the center of the earth. A second satellite is orbiting in the equatorial plane in the opposite direction to the earth's rotation, at a distance from the center of the earth, such that . The time period of the second satellite as measured from the geostationary satellite is hours. The value of is _____.
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JEE Advanced 2025 · Paper 2, Physics question 12
Answer and worked solution
Official answer: 2.3
Period of the second satellite. By Kepler's third law,
Relative motion. The two orbit in opposite directions, so their angular velocities add:
So .