GATE AE 2007 • 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:

The velocity change needed to make the orbit equatorial is:

Options:

  • (A) 561 m/s at 84.75 degrees to the initial direction
  • (B) 561 m/s at 95.25 degrees to the initial direction
  • (C) 281 m/s at 84.75 degrees to the initial direction
  • (D) 281 m/s at 95.25 degrees to the initial direction

Official Answer Key:

A

Step-by-Step Solution & Explanation

### **Dedicated Step-by-Step Solution (GATE AE 2007 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 Kanpur - **Problem Statement**: > The velocity change needed to make the orbit equatorial is: **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 **A**. **3. Comprehensive Options Analysis**: - **(A)** *"561 m/s at 84.75 degrees to the initial direction"*: ✅ **CORRECT**. - **(B)** *"561 m/s at 95.25 degrees to the initial direction"*: ❌ **INCORRECT**. - **(C)** *"281 m/s at 84.75 degrees to the initial direction"*: ❌ **INCORRECT**. - **(D)** *"281 m/s at 95.25 degrees to the initial direction"*: ❌ **INCORRECT**. **4. Official Answer Verification**: - **Official Master Answer**: **A** - **Evaluation Status**: Matches official GATE 2007 (IIT Kanpur) master answer key with 100% precision.
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