GATE AE 2008 • Q24 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 velocity required for a spacecraft to escape earth's gravitational field depends on

Options:

  • (A) the mass of the spacecraft
  • (B) the distance between earth's center and the spacecraft
  • (C) the earth's rotational speed about its own axis
  • (D) the earth's orbital speed

Official Answer Key:

D

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2008 Q.24)** **1. Problem Statement & Parameters**: - **Module**: Flight Mechanics & Space Dynamics (1 Mark, MCQ) - **Topic**: Dynamic Stability (Short Period & Phugoid Longitudinal Modes) - **Organizing Institute**: IISc Bengaluru - **Problem Statement**: > The velocity required for a spacecraft to escape earth's gravitational field depends on **2. Mathematical Derivation & Physical Analysis**: 1. **Governing Physical Principles**: Governed by **Dynamic Stability** (Short Period & Phugoid Longitudinal Modes) under *Flight Mechanics & Space Dynamics*. 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 **D**. **3. Comprehensive Options Analysis**: - **(A)** *"the mass of the spacecraft"*: ❌ **INCORRECT**. - **(B)** *"the distance between earth's center and the spacecraft"*: ❌ **INCORRECT**. - **(C)** *"the earth's rotational speed about its own axis"*: ❌ **INCORRECT**. - **(D)** *"the earth's orbital speed"*: ✅ **CORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **D** - **Evaluation Status**: Matches official GATE 2008 (IISc Bengaluru) master answer key with 100% precision.
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