1. Consider the simplest circular orbit and the general elliptical orbit.

It is assumed that the satellite monitoring and control stations are distributed on the surface of the earth parallel to the satellite orbit, and the satellite orbit is circular. The relationship between the number of TT&C stations required for full coverage and the satellite height is given by using the geometric relationship. such as

Satellite altitude 100 200 300 343 400 500

The number of observation stations is 24161212110.

When the satellite orbit is elliptical and one focus of the satellite orbit is at the center of the earth, the coverage of each monitoring station is given by using geometric relations. Then the measurement and control station is optimized by numerical method, and some concrete results (number and position) are given. Such as the number of monitoring stations below.

Perigee 200 200 200 300 400 400

Apogee 300 400 347 400 500 600

The number of observation stations is1413141210.

2. Space orbit

Under the influence of the earth's rotation, the satellite's downward trajectory is some curves on the earth's surface, so it is difficult to calculate the number of monitoring stations. A rough estimation method is to set up many monitoring stations so that they can cover all the airspace over which the satellite flies. Calculate the solid angle of this sphere covering the equator, and then remove the solid angle that an observation station can cover, and get the observation stations needed to cover at least this area (give the relationship model between the number of stations needed and the height and included angle). Give one or two examples. For example, the included angle between the orbital plane of Shenzhou VII and the equatorial plane of the earth is 42.2 degrees, which is 343 kilometers away from the ground. At least 55 observation stations are needed to cover this area. Considering that the area of the circle inscribed with a regular hexagon is only 0.827 of the area of the circle, at least 67 observation stations are needed.

3. Actual situation

(1) Collect launch or operation data of satellites or spacecraft: orbital inclination, altitude, etc.

(2) Collect the data of observation stations during satellite launch and operation: quantity, location, etc.

I hope that a good team can give the orbit of the satellite, the trajectory equation of the satellite downlink during the satellite operation, the measurement and control range of each station, and the range that the satellite or spacecraft can measure and control when it runs to a certain circle, and it is best to give the longest observation time.

Note: The data given here are for reference only. For example, 55 or 67 stations in 2 are the lower limit of Shenzhou VII's flight orbit under some simplified assumptions. The flight parameters of different satellites or spacecraft are different. Students should also build models and estimate the number of stations needed under different assumptions. It is suggested to judge and review according to students' specific conditions, and students' answers may not be completely consistent with these reference data.