An Interesting Question from 2009 China University Mathematics Modeling Competition

Applied Mathematics often involves what we call "Mathematics Modeling", namely, using maths language to describe (and often idealise) a system at work and solves it in a systematic way.

Recently, I took a peep at the 09 China University Maths Modeling Competition. It has 4 questions and contestants can only answer one of them. They cover quite a number of disciplines, including mechanism, astrophysics, and some seemingly mundane everyday problems (but very HARD!) like arranging a meeting to achieve opitimality in saving time, etc. Here, I quote the third question, the one I find most intriguing and hope to hear from your novel ways of modeling this question: (translated from Chinese)

"Satellites and manned spacecraft are playing more and more important roles in our life. However, there are problems with tracking them from the ground for all time.

"Usually, a radar can only receive signals from a satellite when the angle of the satellite above the ground is larger than 3 degrees. Hence, it is impossible for one radar fixed at one point to track the satellite at all time when it revolves around the Earth. Very often, multiple radars in different positions are deployed to track one satellite/spacecraft, like the case of the Shenzhou VII Spacecraft (see the diagram attached)

"Please design a mathematical model to describe the method in tracking a satellite/spacecraft, and here are some specific questions for consideration:

"(1) If all the radars (at different positions, of course) are on the same plane to plane of the orbit of the satellite/spacecraft, at least how many radars must be deployed?

"(2) Assume the plane of orbit of the satellite/spacecraft has a fixed angle to the plane of the Equator, and they have a constant height H above the ground. Also assume the satellite/spacecraft has a constant period of revolution and the earth is perfectly spherical. At least how many radars must be used?

*Don't forget that the Earth is also spinning at 1 revolution per day!

"(3) Use your model and your collected data from a real case study of the radar deployment in tracking satellite/manned spacecraft, assess your model thoroughly. "

And another reminder is that this is not "solving" a question, but rather provide a viable model to solve the question. Distinguish between these two!

Good Luck :)