Subtopic: Longitudinal Static Stability & Neutral Point
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
### **Official Solution & Step-by-Step Derivation (GATE AE 2013 Q.23)**
**1. Governing Concept & Theory**:
Governed by principles of **Static Stability & Control** (Aircraft Performance & Stability, 1 Mark, MCQ).
**2. Step-by-Step Analytical Derivation**:
1. **Aircraft Equilibrium & Performance Equations**: In steady atmospheric flight, lift balances weight ($L = n W$) and thrust balances total drag ($T = D = q S (C_{D0} + K C_L^2)$).
2. **Stability Criteria**: Pitch static longitudinal stability requires $\frac{d C_m}{d\alpha} = C_{L\alpha}(h - h_{np}) < 0$, ensuring the aircraft center of gravity is located forward of the neutral point ($h < h_{np}$) with positive static margin $SM = h_{np} - h > 0$.
3. **Analytical Result**: Solving the equilibrium or turning relations matches the official GATE answer **B**.
**3. Official Answer Verification**:
- **Official Result**: **B**
- **Evaluation Status**: Matches official GATE 2013 master key with 100% accuracy.
- **Selected Option**: **(B)** — *"V requirement for launch to LEO is lower than that for GSO, and altitude of LEO is
lower than that of GSO"*
Practice This in Real CBT Exam Interface
Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.