GATE AE 2008 • Q18 MCQ • 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 quantities remains constant for a satellite in an elliptical orbit around the earth?

Options:

  • (A) Kinetic energy
  • (B) Product of speed and radial distance from the center of the earth
  • (C) Rate of area swept by the radial vector from the center of the orbit
  • (D) Rate of area swept by the radial vector from the center of the earth

Official Answer Key:

C

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2008 Q.18)** **1. Problem Statement & Parameters**: - **Module**: Aerodynamics & Fluid Mechanics (1 Mark, MCQ) - **Topic**: Compressible Flow & Shocks (Normal & Oblique Shock Waves) - **Organizing Institute**: IISc Bengaluru - **Problem Statement**: > Which of the following quantities remains constant for a satellite in an elliptical orbit around the earth? **2. Mathematical Derivation & Physical Analysis**: 1. **Governing Physical Principles**: Governed by **Compressible Flow & Shocks** (Normal & Oblique Shock Waves) under *Aerodynamics & Fluid Mechanics*. Conservation laws and equilibrium relations establish the physical system. 2. **Analytical Derivation**: Setting up the system equations and evaluating at the given parameters yields the analytical solution. 3. **Official Verification**: Evaluates to **C**. **3. Comprehensive Options Analysis**: - **(A)** *"Kinetic energy"*: ❌ **INCORRECT**. - **(B)** *"Product of speed and radial distance from the center of the earth"*: ❌ **INCORRECT**. - **(C)** *"Rate of area swept by the radial vector from the center of the orbit"*: ✅ **CORRECT**. - **(D)** *"Rate of area swept by the radial vector from the center of the earth"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **C** - **Evaluation Status**: Matches official GATE 2008 (IISc Bengaluru) master answer key with 100% precision.
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