CIRCULAR ORBITS. "IRIDIUM"

Travelling on the circle orbit of radius r the satellite is acted upon by the force of the earth's gravity g mM/r2, where g is the gravity constant, m is the mass of the satellite and M is the mass of the planet (earth in our case). According to second Newton law this force is equal to centripetal force mv2/r. From these two formulas we find the equation for the velocity of the satellite motion in the circle orbit:

v=(g M/r)1/2

The period of the satellite revolution around the earth Tsat is equal to the length of the orbit 2p r divided by the velocity of the satellite motion v:

Tsat=2p r/v=2p (r3/g M)1/2

If this orbit period Tsat is equal to the period of the globe spinning (about 24 hours), then the satellite will hang over the same equatorial region of the earth and such an orbit is called the geo-stationary orbit. The sky coordinates of the geo-stationary satellite are the same all the time and we can precisely orient/beam on it the parabolic antenna of our receiver.

On the contrary, if the radius of the satellite orbit is less than the radius of the geo-stationary orbit, then the satellite will outstrip the spinning of the globe and we can not direct the satellite dish on it. Nevertheless, satellites on the low orbits provide more a powerful signal as compared to the satellites on the geo-stationary orbit, and using several satellites on the same orbit, permanent telecommunication can be achieved.

This principle was used in the telecommunication satellite system "Iridium", which uses 66 Low Earth Orbit satellites: 11 satellites in 6 orbits, as shown in the animation. Every satellite covers the area on the globe shown by a light spot. We can see in this figure that the spots overlap, covering the entire surface of the globe. This means that this satellite system provides continuous telephone communication at every point of the globe.

Ref. in Internet:

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