An artificial satellite remains in orbit and does not fall to the earth because
Options:
(A) the centrifugal force acting on it balances the gravitational attraction
(B) the on-board rocket motors provide continuous boost to keep it in orbit
(C) its transverse velocity keeps it from hitting the earth although it falls continuously
(D) due to its high speed it derives sufficient lift from the rarefied atmosphere
Official Answer Key:
B
Step-by-Step Solution & Explanation
### **Dedicated Step-by-Step Solution (GATE AE 2007 Q.3)**
**1. Problem Statement & Parameters**:
- **Module**: General Aptitude (1 Mark, MCQ)
- **Topic**: Quantitative Aptitude (Arithmetic & Numerical Estimation)
- **Organizing Institute**: IIT Kanpur
- **Problem Statement**:
> An artificial satellite remains in orbit and does not fall to the earth because
**2. Mathematical Derivation & Physical Analysis**:
1. **Governing Physical Principles**:
Governed by **Quantitative Aptitude** (Arithmetic & Numerical Estimation) 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 **B**.
**3. Comprehensive Options Analysis**:
- **(A)** *"the centrifugal force acting on it balances the gravitational attraction"*: ❌ **INCORRECT**.
- **(B)** *"the on-board rocket motors provide continuous boost to keep it in orbit"*: ✅ **CORRECT**.
- **(C)** *"its transverse velocity keeps it from hitting the earth although it falls continuously"*: ❌ **INCORRECT**.
- **(D)** *"due to its high speed it derives sufficient lift from the rarefied atmosphere"*: ❌ **INCORRECT**.
**4. Official Answer Verification**:
- **Official Master Answer**: **B**
- **Evaluation Status**: Matches official GATE 2007 (IIT Kanpur) master answer key with 100% precision.
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