# What is a geocentric satellite

## Geosynchronous orbit

A **geosynchronous orbit** is a satellite orbit in which the orbital time around the earth corresponds exactly to the period of rotation of the earth (sidereal day), so the satellite moves synchronously with the earth. In the special case of the **geostationary orbit** a satellite is always at the same point in the sky for an observer on the earth's surface.

Because the earth's gravitational field *Not* is rotationally symmetrical, orbit disturbances are particularly noticeable in geosynchronous orbits. Satellites positioned there need fuel to correct this. Therefore, they only have a limited lifespan.

Geostationary satellites are mainly used for communication, but weather satellites also take advantage of this orbit.

### Orbit classes

Geosynchronous orbits have inclination angles from 0 ° (geostationary) through 90 ° (polar orbit) to 180 ° (retrograde, i.e. counter-rotation to the rotation of the earth).

### Inclined orbit

If the inclination is different from 0 °, it is called the orbit *more inclined* geosynchronous orbit, English *inclined geosynchronous orbit (IGSO)*.

Depending on the orbit inclination or angle of inclination, one differentiates

- Low inclination orbits are known as Inclined Orbit and are used by former geostationary communications satellites to extend their lifespan when their fuel reserves are almost exhausted. However, because their position in the sky then fluctuates, such satellites can only be received with professional antennas with antenna tracking.
- The Quasi-Zenith Satellite System (QZSS) is a four-satellite system used to improve satellite navigation systems in Japan. The satellites stand on a 45 ° inclined orbit with an eccentricity of 0.09 and a perigee angle (argument of perigee) of 270 ° for eight hours, almost vertically above the island.
- Highly elliptical orbits of large inclination are also called tundra orbits.

### Geostationary orbit

The special case of a circular orbit with an easterly direction of rotation and an orbit inclination of 0 ° is called geostationary. The orbit speed is always 3.075 kilometers per second (km / s) (= 11,070 km / h), and the orbit radius is 42,157 km. This corresponds to a distance of about 35,786 km to the earth's surface.

When viewed from Earth, a geostationary satellite appears to stand still in the sky (it is "stationary") because it moves at the same angular velocity as the observer on Earth. Because of this, this orbit is widely used for television and communications satellites. The antennas on the ground can be fixed to a specific point, and each satellite always covers the same area of the earth. However, these satellites usually focus their antennas on individual regions (coverage zones), so that the signals can usually only be received in the broadcast areas.

### Formulas

In order to keep a body of mass $ m $ with angular velocity $ \ omega $ on a circular path with radius $ r $, there is a centripetal force of strength

- $ \! \ F_1 = m \ omega ^ 2 r $

required. On a circular orbit around a planet, gravity is approximately the only effective force. At a distance $ r $ - starting from the center of the planet - you can use the formula

- $ F_2 = \ frac {G M m} {r ^ 2} $

be calculated. $ G $ denotes the gravitational constant and $ M $ the mass of the planet.

Since gravity is the only force that keeps the body on the circular path, its value must correspond to the centripetal force. So the following applies:

- $ \! \ F_1 = F_2 $

By inserting it results:

- $ m \ omega ^ 2 r = \ frac {G M m} {r ^ 2} $

Solving for $ r $ gives:

- $ r = \ sqrt [3] {G \ frac {M} {\ omega ^ 2}} $

The angular frequency $ \ omega $ results from the period of rotation $ t $ as:

- $ \ omega = \ frac {2 \ pi} {t} $

Inserting it into the formula for $ r $ gives:

- $ r = \ sqrt [3] {\ frac {G} {4 \ pi ^ 2} M t ^ 2} $

This formula now determines the radius of the geostationary orbit of a center of mass starting from the center of the planet under consideration.

In order to get the distance of the orbit from the surface of the planet - for example the height of a geostationary satellite above the earth's surface - its radius has to be subtracted from the result. So we have:

- $ h = \ sqrt [3] {\ frac {G} {4 \ pi ^ 2} M t ^ 2} - R_P $

where $ R_P $ denotes the radius of the planet.

If the planet has a satellite (e.g. the moon) with known orbit data, the third law of Kepler can also be used as an alternative

- $ \ frac {T_ {Sat} ^ 2} {T_ {Moon} ^ 2} = \ frac {r_ {Sat} ^ 3} {r_ {Moon} ^ 3} $

apply to satellite and geostationary satellite.

In the example of an earthly satellite, the orbit data of the earth's moon can be used (orbital period *T*_{moon} ≈ 655 h, semi-major axis of the lunar orbit *r*_{moon} ≈ 384,000 km, *T*_{Sat} = 23 h 56 min). Solved for the orbit radius of the geostationary satellite, which is equal to the orbit radius because of the circular orbit, this results in:

- $ \ qquad r_ {Sat} = \ sqrt [3] {\ frac {r_ {Moon} ^ 3 \ cdot T_ {Sat} ^ 2} {T_ {Moon} ^ 2}} \ approx 42,000 \, km $

The height above the surface of the planet, here the earth, is again obtained by subtracting the planet's radius.

### history

The idea of a geostationary satellite was first suggested by Herman Potočnik in his 1928 book *The problem of navigating space - the rocket engine* released.

In 1945, science fiction writer Arthur C. Clarke proposed placing satellites in geostationary orbit. Worldwide radio communication would be possible with three satellites, each offset by 120 °. He assumed that satellites could be positioned there within the next 25 years. With Syncom 2 in geosynchronous orbit in 1963 and Syncom 3 in geostationary orbit in 1964, his idea was realized much more quickly, after about 19 years.

The picture on the right shows the diagram in which Clarke wrote his thoughts in the magazine *Wireless World* presented to the public for the first time.^{[1]}

### See also

### Web links

### Individual evidence

- ^ The 1945 Proposal by Arthur C. Clarke for Geostationary Satellite Communications

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