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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