Calculating Orbits.
When a satellinte orbits the Eath, the satellite's orbit will form an ellipse with the Earth located at one of the focal points of the ellipse. The satellite's orbit can be expressed in polar coordintaes as
r = p/(1 - \epsilon * cos( \theta ))
Where r and theta are the distance and angle of the satellite from the center of the earth, p is a parameter specifying the size of the orbit, and \epsilon is a parameter representing the eccentricity of the orbit. A circular orbit has an eccentricity of zero. An elliptical orbit has an eccentricity of 0 <= e <= 1. If \epsilon > 1, the satellite follows a hyperbolic path and escapes from Earth's gravitational field.
Consider a satellite with a size parameter p = 1200 km. Write a program to calculate the distance of the satellite from the center of the Earth as a function of theta if the satellite has an eccentricity of (a) e = 0; (b) e = 0.25; (c) e = 0.5. Write a single program in which r and e are both input values.
How close does each orbit come to the earth? How far away does each orbit get from the earth?