GATE AE 2009 • Q12 MCQ • 1 Mark Flight Mechanics & Space Dynamics

Flight Mechanics & Space Dynamics

Space Dynamics & Orbital Mechanics

Subtopic: Kepler's Laws & Two-Body Problem

Question Statement:

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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