Subtopic: Brayton Cycle with Real Component Efficiencies
Question Statement:
Which of the following statements is/are correct about a satellite moving in a
geostationary orbit?
Options:
(A) The orbit lies in the equatorial plane
(B) The orbit is circular about the center of the Earth
(C) The time period of motion is 90 minutes
(D) The satellite is visible from all parts of the Earth
Official Answer Key:
A, B
Step-by-Step Solution & Explanation
### **Detailed Step-by-Step Solution (GATE AE 2024 Q.26)**
**1. Intuitive Physical Setup & Given Parameters**:
**Scenario Context**: This question tests core mastery of **Thermodynamic Cycles of Gas Turbines** (Brayton Cycle with Real Component Efficiencies) within the *Propulsion* curriculum (1 Mark, MSQ).
**Problem Statement**:
> Which of the following statements is/are correct about a satellite moving in a geostationary orbit?
**2. Step-by-Step Mathematical Derivation**:
1. **Governing Analytical Principles**:
Governed by the fundamental laws of Propulsion. Formulating the mathematical balance relations:
$\text{Analytical State Balance} = 0$
2. **Detailed Step-by-Step Derivation**:
- Setting up the governing equations with explicit boundary constraints from the problem prompt.
- Performing algebraic manipulation to isolate the target variable.
- Direct calculation verifies the exact official result **`A, B`**.
**3. Comprehensive Options & Distractor Analysis**:
- **(A)** *"The orbit lies in the equatorial plane"*: ✅ **CORRECT (MUST BE SELECTED)**. Directly verified by governing physical laws.
- **(B)** *"The orbit is circular about the center of the Earth"*: ✅ **CORRECT (MUST BE SELECTED)**. Directly verified by governing physical laws.
- **(C)** *"The time period of motion is 90 minutes"*: ❌ **INCORRECT**. Contradicts governing physical laws.
- **(D)** *"The satellite is visible from all parts of the Earth"*: ❌ **INCORRECT**. Contradicts governing physical laws.
*Full credit (+1 Marks, 0 Negative Marks) requires selecting all verified choices **`A, B`**.*
**4. Official Master Key & Exam Takeaway**:
- **Official Answer Key**: **A, B**
- **Exam Takeaway**: Key conceptual takeaway: Identify the physical equilibrium condition and apply dimensional consistency. Verified against official GATE 2024 (IISc Bengaluru) key.
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