To transfer a satellite from an elliptical orbit to a circular orbit having radius equal to the apogee distance of the elliptical orbit, the speed of the satellite should be
Options:
(A) increased at the apogee
(B) decreased at the apogee
(C) increased at the perigee
(D) decreased at the perigee
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2008 Q.4)**
**1. Problem Statement & Parameters**:
- **Module**: General Aptitude (1 Mark, MCQ)
- **Topic**: Analytical & Spatial Aptitude (Deductive Logic & Syllogisms)
- **Organizing Institute**: IISc Bengaluru
- **Problem Statement**:
> To transfer a satellite from an elliptical orbit to a circular orbit having radius equal to the apogee distance of the elliptical orbit, the speed of the satellite should be
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Analytical & Spatial Aptitude** (Deductive Logic & Syllogisms) under *General Aptitude*. 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)** *"increased at the apogee"*: ✅ **CORRECT**.
- **(B)** *"decreased at the apogee"*: ❌ **INCORRECT**.
- **(C)** *"increased at the perigee"*: ❌ **INCORRECT**.
- **(D)** *"decreased at the perigee"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **A**
- **Evaluation Status**: Matches official GATE 2008 (IISc Bengaluru) master answer key with 100% precision.