A geostationary satellite orbits at radius r₁. A second satellite moves in the equatorial plane in the opposite direction at radius r₂, where r₁ = 1.21r₂. The period of the second satellite as measured from the geostationary satellite is 24/p hours. Find p.
Physics · Circular Motion
JEE Advanced 2025 Paper 2

Question

A geostationary satellite orbits at radius r₁. A second satellite moves in the equatorial plane in the opposite direction at radius r₂, where r₁ = 1.21r₂. The period of the second satellite as measured from the geostationary satellite is 24/p hours. Find p.

Physics · Circular Motion

JEE Advanced 2025 Paper 2

G1 Physics · Accepted Answer

The geostationary period is 24 h. By Kepler's third law, T ∝ r³ᐟ². Since r₁/r₂ = 1.21 = 1.1², the period ratio is T₁/T₂ = (1.21)³ᐟ² = 1.1³ = 1.331. The satellites move in opposite directions, so their relative angular speeds add: 1/(relative period) = 1/24 + 1/T₂ = (1 + 1.331)/24 = 2.331/24. Therefore relative period = 24/2.331 h. Comparing with 24/p gives p = 2.331.