Exams › JEE Advanced › Physics

A geostationary satellite orbits at height h above Earth's surface; Earth's radius is R. Which of the following statements is correct?

1. The minimum colatitude on Earth up to which the satellite can provide communication is arcsin(R/(R + h)).
2. The maximum latitude on Earth up to which the satellite can be used for communication is arccos(R/(R + h)).
3. The area on Earth not covered by this satellite is 2*pi*R² (1 + sin(theta)).
4. The area on Earth not covered by this satellite is 2*pi*R² (1 + cos(theta)).

Correct answer: The minimum colatitude on Earth up to which the satellite can provide communication is arcsin(R/(R + h)).

Solution

A geostationary satellite over the equator covers Earth down to the latitude where its line of sight is tangent to the surface. The tangent condition gives sin(colatitude) = R/(R + h), so the minimum colatitude reachable is arcsin(R/(R + h)). The maximum latitude is arccos(R/(R+h)), and the uncovered cap area formulas in the other options have the wrong form (should involve 1 - cos, not 1 + sin/cos).

Related JEE Advanced Physics questions

• Two objects, each with a mass of M, are positioned at a fixed distance of 2L apart. A smaller particle of mass m is launched from the midpoint of the line connecting their centers, moving in a direction perpendicular to this line. Given the gravitational constant G, which of the following statements is accurate?
• A central force is given as F(r) = −k / rⁿ, where k is a constant. What condition must n satisfy for a circular orbit to remain stable?
• Which of the following correctly represents the relationship |F| = dU/dr?
• Two objects, each with mass M, are placed at a fixed distance of 2L apart. A particle of mass m is launched from the midpoint between these two objects in a direction perpendicular to the line connecting them. Given the gravitational constant G, which of the following statements is accurate?
• Consider a spherical gaseous cloud of mass density ρ(r) in free space where r is the radial distance from its center. The gaseous cloud is made of particles of equal mass m moving in circular orbits about the common center with the same kinetic energy K. The force acting on the particle is their mutual gravitational force. If ρ(r) is constant in time, the particle number density n(r) = ρ(r)/m is (G is universal gravitational constant).
• A particle with mass m is influenced by the gravitational force of a much larger mass M (M >> m). The particle orbits in a circular path of radius r₀ with a time period T₀. An additional central force is introduced, arising from the potential energy V(r) = αmα/r³, where α is a positive constant with appropriate units and r is the orbital radius. If the particle continues to move in the same circular orbit of radius r₀ under the combined gravitational and additional potential, but its time period changes to T₁, what is the value of (T₁² - T₀²)/T₀²? [G represents the gravitational constant.]

⚔️ Practice JEE Advanced Physics free + battle 1v1 →