Question Statement:
Consider a high Earth-orbiting satellite of angular momentum per unit mass $h$ 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 $\theta$, and the phase angle is zero. Which of the following statements is/are true?
Scientific schematic diagram reproduced from official IIT paper
Options:
- (A) The trajectory equation is $r = r(\theta) = \frac{h}{GM(1 + e \cos\theta)}$
- (B) The trajectory equation is $r = r(\theta) = \frac{h^2}{GM(1 + e \cos\theta)}$
- (C) $\vec{h}$ is conserved
- (D) The sum of potential energy and kinetic energy of the satellite is conserved