Consider a high Earth-orbiting satellite of angular momentum per unit mass ℎሬ⃗ and
eccentricity e.
The mass of the Earth is M and G is the universal gravitational constant.
The distance between the satellite's center of mass and the Earth's center of mass
is r, the true anomaly is 𝜃, and the phase angle is zero.
Which of the following statements is/are true?
Options:
(A) The trajectory equation is r = r(𝜃) =
หሬሬ⃗ห
ீெ(ଵା ௦ ఏ)
(B) The trajectory equation is r = r(𝜃) =
หሬሬ⃗ห
మ
ீெ(ଵା ௦ ఏ)
(C) ℎሬ⃗ is conserved
(D) The sum of potential energy and kinetic energy of the satellite is conserved
Official Answer Key:
A
Step-by-Step Solution & Explanation
### **Official Solution & Step-by-Step Derivation (GATE AE 2022 Q.46)**
**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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