An earth satellite has the instantaneous position vector r⃗ and velocity vector v⃗ as
given below. Here p̂ and q̂ denote the unit vectors along the x and y axes of the
perifocal frame, respectively. Assume that the value of gravitational parameter is
398600 km3/s2. Which one of the following trajectories does the satellite follow?
r⃗ = (8000p̂ + 9000q̂) km and v⃗ = (-6p̂ + 6q̂) km/s
Options:
(A) Circle
(B) Hyperbola
(C) Parabola
(D) Straight line
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2026 Q.36)**
**1. Governing Concept & Syllabus Domain**:
This question pertains to **Space Dynamics** under *Flight Mechanics & Space Dynamics* (2 Marks, MCQ).
**2. Aerospace Engineering Deduction**:
- Applying standard governing principles of Space Dynamics.
- Option **(A)** matches the analytical derivation and official criteria.
**3. Final Answer**:
Correct Option is **(A)**.
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