There is only one main force acting on a satellite when it is in orbit, and that is the gravitational force exerted on the satellite by the Earth. This force is constantly pulling the satellite towards the centre of the Earth.

A satellite doesn't fall straight down to the Earth because of its velocity. Throughout a satellites orbit there is a perfect balance between the gravitational force due to the Earth, and the centripetal force necessary to maintain the orbit of the satellite.

The formula for centripetal force is: F = (mv²)/r
The formula for the gravitational force between two bodies of mass M and m is (GMm)/r²

The most common type of satellite orbit is the geostationary orbit. This is described in more detail below, but is a type of orbit where the satellite is over the same point of Earth always. It moves around the Earth at the same angular speed that the Earth rotates on its axis.

We can use our formulae above to work out characteristics of the orbit.

(mv²/r) = (GMm)/r²
=> v²/r = (GM)/r²

Now, v = (2πr)/T.

=> (((2πr)/T)²)/r = (GM)/r²
=> (4π²r)/T² = (GM)/r²
=> r³ = (GMT²)/4π²

We know that T is one day, since this is the period of the Earth. This is 8.64 x 10⁴ seconds.
We also know that M is the mass of the Earth, which is 6 x 10²⁴ kg.
Lastly, we know that G (Newton's Gravitational Constant) is 6.67 x 10^-11 m³/kg.s²

So we can work out r.

r³ = 7.57 x 10²²

Therefore, r = 4.23 x 10⁷ = 42,300 km.

So the orbital radius required for a geostationary, or geosynchronous orbit is 42,300km. Since the radius of the Earth is 6378 km the height of the geostationary orbit above the Earth's surface is ~36000 km.

There are many different types of orbits used for satellite telecommunications, the geostationary orbit described above is just one of them. Outlined below are the most commonly used satellite orbits. The orbits are sometimes described by their inclination - this is the angle between the orbital plane and the equatorial plane.

The most common orbit used for satellite communications is the geostationary orbit (GEO). This is the orbit described above – the rotational period is equal to that of the Earth. The orbit has zero inclination so is an equatorial orbit (located directly above the equator). The satellite and the Earth move together so a GEO satellite appears as a fixed point in the sky from the Earth.

The advantages of such an orbit are that no tracking is required from the ground station since the satellite appears at a fixed position in the sky. The satellite can also provide continuous operation in the area of visibility of the satellite. Many communications satellites travel in geostationary orbits, including those that relay TV signals into our homes.

However, due to their distance from Earth GEO satellites have a signal delay of around 0.24 seconds for the complete send and receive path. This can be a problem with telephony or data transmission. Also, since they are in an equatorial orbit, the angle of elevation decreases as the latitude or longitude difference increases between the satellite and earth station. Low elevation angles can be a particular problem to mobile communications.

A special type of LEO is the Polar Orbit. This is a LEO with a high inclination angle (close to 90degrees). This means the satellite travels over the poles.

LEO Orbit		Polar Orbit

    
Satellites that observe our planet such as remote sensing and weather satellites often travel in a highly inclined LEO so they can capture detailed images of the Earth’s surface due to their closeness to Earth. A satellite in a Polar orbit will pass over every region of Earth so can provide global coverage. Also a satellite in such an orbit will sometimes appear overhead (unlike a GEO which is only overhead to ground stations on the equator). This can enable communication in urban areas where obstacles such as tall buildings can block the path to a satellite. Lastly, the transmission delay is very small.

Any LEO or MEO system however, for continuous operation, requires a constellation of satellites. The satellites also move relative to the Earth so widebeam or tracking narrowbeam antennas are needed.

A satellite in elliptical orbit follows an oval-shaped path. One part of the orbit is closest to the centre of Earth (perigee) and another part is farthest away (apogee). A satellite in this type of orbit generally has an inclination angle of 64 degrees and takes about 12 hours to circle the planet. This type of orbit covers regions of high latitude for a large fraction of its orbital period.