Many artificial satellites for communication, broadcast, meteorology, etc, are orbiting a circle called geostationary orbit.
The satellites in the orbit look 'stationary' from the Earth because the angular velocity of them exactly matches that of Earth rotation.
The 36,000-km-altitude orbit is so useful that hundreds of satellites are placed by a number of worldwide countries.

As the geostationary orbit continues to get more crowded, the demand for communication satellites using different orbits has increased. Moreover, if these new communication satellites can transmit radio signals from the zenith of the sky, it will be very useful for a number of applications including mobile communications and navigation systems.
An eight figure satellite is one possible solution.
The radius of its orbit is the same as geostationary satellites, but its orbital plane is tilted about 45 degrees. Its subsatellite point traces a figure eight on the globe. It stays near the zenith of Japan about 8 hours per day.
Therefore, if we launch three such satellites and adjust their orbital planes, then there will be one of three satellites with high elevation angles above Japan at all times.

[ Play Movie ]

This is a machine for detecting satellite orbital positions by receiving satellite microwaves.
The use of movable mirrors mounted on a rotary arm has made accurate detection possible, though its receiving antennas are small.
This technique is unique in the world.
A scaled model for the machine shows how the arm and mirrors
move in order to guide satellite microwaves.

All objects interact with each other by universal gravitation.
If there are only two objects in the universe, motion is simple because each object is attracted only to the other.
If there are three objects, each object is attracted by the other two objects.
Their motion is radically different, which is probably chaotic.
Please come in to operate the simulator.
You can watch a movie of three objects in motion by clicking on any of the three positions on the screen as you like.
The dynamics of three objects are computed and their orbital paths are drawn immediately.
Which motion did you click on?