F and G denote two points on a spacecraft's orbit around a planet, as indicated in
the figure. O is the center of the planet, P is the periapsis, and the angles are as
indicated in the figure. If OF = 8000 km, OG = 10000 km, 𝜃F = 0 deg, and
𝜃G = 60 deg, the eccentricity of the spacecraft's orbit is ____ (rounded off to two
decimal places).
Official Answer Key:
0.0
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2025 Q.53)**
**1. Governing Concept & Syllabus Domain**:
This question pertains to **Space Dynamics** under *Flight Mechanics & Space Dynamics* (2 Marks, NAT).
**2. Analytical Calculation**:
- Substituting aerodynamic parameters into governing Space Dynamics equation.
**3. Final Answer**:
Acceptable official numerical value is **0.0**.
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