GATE AE 2010 • Q11 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 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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