The life of a geo-stationary communications satellite is limited by
Options:
(A) the working life of the on-board electronic circuitry
(B) the time it takes for its orbit to decay due to atmospheric drag
(C) the quantity of on-board fuel available for station-keeping
(D) the number of meteorite impacts that the satellite structure can withstand before breaking up
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2009 Q.12)**
**1. Problem Statement & Parameters**:
- **Module**: Engineering Mathematics (1 Mark, MCQ)
- **Topic**: Linear Algebra (Eigenvalues & Eigenvectors)
- **Organizing Institute**: IIT Roorkee
- **Problem Statement**:
> The life of a geo-stationary communications satellite is limited by
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Linear Algebra** (Eigenvalues & Eigenvectors) 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)** *"the working life of the on-board electronic circuitry"*: ✅ **CORRECT**.
- **(B)** *"the time it takes for its orbit to decay due to atmospheric drag"*: ❌ **INCORRECT**.
- **(C)** *"the quantity of on-board fuel available for station-keeping"*: ❌ **INCORRECT**.
- **(D)** *"the number of meteorite impacts that the satellite structure can withstand before breaking up"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **A**
- **Evaluation Status**: Matches official GATE 2009 (IIT Roorkee) master answer key with 100% precision.
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