The angular momentum, about the centre of mass of the earth, of an artificial satellite in a highly eiliptical orbit is
Options:
(A) a maximum when the satellite is farthest from the earth
(B) a constant
(C) proportional to the speed of the satellite
(D) proportional to the square of the speed of the satellite
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2010 Q.11)**
**1. Problem Statement & Parameters**:
- **Module**: Engineering Mathematics (1 Mark, MCQ)
- **Topic**: Linear Algebra (Matrices & Determinants)
- **Organizing Institute**: IIT Guwahati
- **Problem Statement**:
> The angular momentum, about the centre of mass of the earth, of an artificial satellite in a highly eiliptical orbit is
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Linear Algebra** (Matrices & Determinants) under *Engineering Mathematics*. 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 **A**.
**3. Comprehensive Options Analysis**:
- **(A)** *"a maximum when the satellite is farthest from the earth"*: ✅ **CORRECT**.
- **(B)** *"a constant"*: ❌ **INCORRECT**.
- **(C)** *"proportional to the speed of the satellite"*: ❌ **INCORRECT**.
- **(D)** *"proportional to the square of the speed of the satellite"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **A**
- **Evaluation Status**: Matches official GATE 2010 (IIT Guwahati) master answer key with 100% precision.
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