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A geostationary satellite orbits at height h above Earth's surface (Earth radius R). Which of the following statements are correct? (A) The minimum co-latitude on Earth up to which the satellite can be used for communication is sin⁻¹(R / (R + h)). (B) The maximum latitude on Earth up to which the satellite can be used for communication is cos⁻¹(R / (R + h)). (C) The area on Earth not covered by this satellite is 2*pi*R²*(1 + sin(theta)). (D) The area on Earth not covered by this satellite is 2*pi*R²*(1 + cos(theta)).

1. A and B only
2. A, B and C
3. A, B and D
4. B and D only

Correct answer: A and B only

Solution

For a geostationary satellite at height h, the satellite-to-tangent-point line is tangent to Earth. The angle subtended at Earth's centre between the nadir (equatorial sub-satellite point) and the tangent point satisfies cos(angle) = R/(R+h). This angle equals the maximum geographic latitude reachable. So max latitude = cos⁻¹(R/(R+h)) — Statement B is correct. Minimum co-latitude = 90 deg - max latitude = sin⁻¹(R/(R+h)) — Statement A is correct. The uncovered polar caps each have area 2*pi*R²*(1 - cos(theta)) where theta = co-latitude of boundary. Neither option C nor D matches this standard formula for the spherical cap area, so only A and B are correct.

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