Question: Polar Coordinates

A satellite is in an orbit that passes over the North and South poles of the earth. When it is over the South Pole, it is at the highest point of its orbit at 1,000 miles above the earth’s surface. Above the North Pole, it is at the lowest point of its orbit at 300 miles above the earth’s surface.

a) Assuming that the orbit is an ellipse with one focus at the center of the earth, find its eccentricity. (Take the diameter of the earth to be 8,000 miles.)

b) Using the north-south axis of the earth as the x-axis and the center of the earth as origin, find a polar equation for the orbit.

Given the above problem, provide written responses to address the following points as precisely and thoroughly as possible.

A. Explain the problem in your own words.

B. What mathematical concepts learned in this module apply to this problem?

C. Explain the steps you must take to solve this problem.

D. What is the most difficult aspect of solving this problem?

E. Explain exactly what the answer means from a mathematical perspective.