A spacecraft is in an elliptical orbit around the earth. At the time t=0 hours, it is at its apogee (highest point), d=1000 km above the earth's surface. It is at its perigee (lowest point) d=100 km above the surface 50 minutes later.

Question

A spacecraft is in an elliptical orbit around the earth. At the time t=0 hours, it is at its apogee (highest point), d=1000 km above the earth's surface. It is at its perigee (lowest point) d=100 km above the surface 50 minutes later. 
a. Assuming that d varies sinusoidally with time, write an equation expressing d in terms of t. 
b. Find the first 3 positive values of t for which the spacecraft is 200 km from the surface. 
c. In order to transmit information back to the earth, the spacecraft must be within 700 km of the surface. For how many consecutive minutes will the spacecraft be able to transmit?