GATE AE 2024 • Q26 MSQ • 1 Mark Flight Mechanics & Space Dynamics

Flight Mechanics & Space Dynamics

Space Dynamics & Orbital Mechanics

Subtopic: Kepler's Laws & Two-Body Problem

Question Statement:

Which of the following statements is/are correct about a satellite moving in a geostationary orbit?

Options:

  • (A) The orbit lies in the equatorial plane
  • (B) The orbit is circular about the center of the Earth
  • (C) The time period of motion is 90 minutes
  • (D) The satellite is visible from all parts of the Earth

Official Answer Key:

A, B

Step-by-Step Solution & Explanation

### **Detailed Step-by-Step Solution (GATE AE 2024 Q.26)** **1. Properties of a Geostationary Orbit (GEO)**: A geostationary orbit is a specific geosynchronous orbit that appears stationary with respect to a fixed point on Earth's surface: 1. **Orbital Plane**: Must lie strictly in the equatorial plane (inclination $i = 0^\circ$) so that the satellite does not oscillate North-South. $\implies$ Option (A) is TRUE. 2. **Orbital Shape**: Must be circular ($e = 0$) with radius $r \approx 42,164\text{ km}$ from the center of Earth so that orbital speed equals Earth's rotational speed at all times. $\implies$ Option (B) is TRUE. 3. **Orbital Period**: The orbital period equals one sidereal day ($23\text{ h } 56\text{ m } 4\text{ s}$, approximately 1436 minutes, NOT 90 minutes; 90 minutes is typical for Low Earth Orbit). $\implies$ Option (C) is FALSE. 4. **Coverage**: A single GEO satellite cannot view the high polar regions (latitudes $\gtrsim 81^\circ$) due to Earth's curvature. $\implies$ Option (D) is FALSE. **2. Conclusion**: Only **A** and **B** are correct. **3. Official Master Key**: - **Official Answer Key**: **A, B** - **Exam Takeaway**: GEO requires zero inclination ($i=0^\circ$), zero eccentricity ($e=0$), and period equal to one sidereal day ($T \approx 24\text{ hours}$).
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