Solve Orbit Calculations Homework: Find Altitude 30 min After Perigee Passage

[Logarythmic]

Homework Statement

The given data is the perigee altitude $r_p$, the apogee altitude $r_a$ and the period T. Mission: find the altitude 30 min after perigee passage.

Homework Equations

Semi-major axis a is calculated.
Kepler's equation gives a relation for the eccentric anomaly E:

$$E - \epsilon \sin{E} = \frac{2 \pi}{T} \left( t - t_p \right)$$

The radius of the orbit is given by

$$r = a \left( 1 - \epsilon \cos{E} \right)$$

The Attempt at a Solution

How do I solve for the eccentric anomaly E so I can use the formula for the radius? Or should I use another approach?

 

[D H]

There are a number of ways to solve Kepler's equation for the eccentric anomaly given either the mean anomaly or time since periapsis, Newton's method being one of them.