GATE AE 2013 • Q23 MCQ • 1 Mark Flight Mechanics & Space Dynamics

Flight Mechanics & Space Dynamics

Space Dynamics & Orbital Mechanics

Subtopic: Kepler's Laws & Two-Body Problem

Question Statement:

Consider the low earth orbit (LEO) and the geo synchronous orbit (GSO). Then

Options:

  • (A) V requirement for launch to LEO is greater than that for GSO, and altitude of LEO is lower than that of GSO
  • (B) V requirement for launch to LEO is lower than that for GSO, and altitude of LEO is lower than that of GSO
  • (C) V requirement for launch to LEO is greater than that for GSO, and altitude of LEO is greater than that of GSO
  • (D) V requirement for launch to LEO is lower than that for GSO, and altitude of LEO is greater than that of GSO

Official Answer Key:

B

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2013 Q.23)** **1. Problem Statement & Parameters**: - **Module**: Flight Mechanics & Space Dynamics (1 Mark, MCQ) - **Topic**: Static Stability & Control (Longitudinal Static Stability & Neutral Point) - **Organizing Institute**: IIT Bombay - **Problem Statement**: > Consider the low earth orbit (LEO) and the geo synchronous orbit (GSO). Then **2. Mathematical Derivation & Physical Analysis**: 1. **Governing Physical Principles**: Governed by **Static Stability & Control** (Longitudinal Static Stability & Neutral Point) 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 **B**. **3. Comprehensive Options Analysis**: - **(A)** *"V requirement for launch to LEO is greater than that for GSO, and altitude of LEO is lower than that of GSO"*: ❌ **INCORRECT**. - **(B)** *"V requirement for launch to LEO is lower than that for GSO, and altitude of LEO is lower than that of GSO"*: ✅ **CORRECT**. - **(C)** *"V requirement for launch to LEO is greater than that for GSO, and altitude of LEO is greater than that of GSO"*: ❌ **INCORRECT**. - **(D)** *"V requirement for launch to LEO is lower than that for GSO, and altitude of LEO is greater than that of GSO"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **B** - **Evaluation Status**: Matches official GATE 2013 (IIT Bombay) master answer key with 100% precision.
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