Question 1 [20 points]
In class, we saw that the equation of a conic section is given by:
r = \frac{p}{1 + e \cos(\theta^*)}
(1)
where $p = a(1 - e^2)$ is a geometrical constant of the conic called the \"parameter\" or \"semi-latus rectum\", e is the eccentricity, and $\theta^*$ is the true anomaly.
Your team launches a satellite into an orbit with a perigee altitude of $h_p$ and an
eccentricity of e.
PART 1: Derive expressions for the following quantities in terms of the perigee
altitude ($h_p$), eccentricity (e), Earth's radius ($R_E$), and Earth's gravitational constant
(GM):
(a) The apogee radius
(b) The semimajor axis
(c) The period of the orbit
(d) The velocity of the satellite at perigee
(e) The velocity of the satellite at apogee
