Geostationary and Geosynchronous Orbits

The core principle of an orbit is that as a satellite or object moved tangentially, it falls toward the earth / other body, but it moved so quickly that earth / body will curve away beneath it. Thus we can understand that gravity pulls this object into a curved path as it attempts to fly off in a straight line. A satellite has enough tangential velocity to miss the orbited object, and will continue falling indefinitely.

In other words, when the satellite is moving in the orbits, it stays in position because the centripetal force on the satellite balances the gravitational attractive force of the earth. This balance depends on the following:

• Distance from the earth
• Tangential speed of the satellite
• Earth’s radius
• Gravitational force of the earth.
• But it does not depend upon:
• Mass of the satellite
• Size of the Satellite

Key Concepts

• An artificial satellite is always falling towards earth, but it has enough tangential velocity to continue fall indefinitely.
• Centripetal force on the satellite balances the gravitational attractive force of the earth. This balance does not depend upon the mass and size of the satellite.

Types of Orbits

There are three major types of orbits viz. Polar, Inclined and Equatorial.

The Polar Orbits cover the poles, Equatorial are above the equator and inclined orbits are inclined from the equatorial orbit. They are shown as below:

Geostationary Orbit (GEO)

If we need a satellite for the purpose which needs this satellites to remain at a particular distance from earth at all the time, then we need circular orbits so all the points on circular orbit are at equal distance from earth’s surface. The circular equatorial orbit is exactly in the plane of equator on the earth. If the satellite is moving in the circular-equatorial orbit and its angular velocity is equal to earth’s angular velocity, the satellite is said to be moving along with the earth. This satellite would appear stationary from the earth and this orbit would be called Geostationary Orbit.

Features of geostationary satellite

• The orbit is circular
• The orbit is in equatorial plane i.e. directly above the equator and thus inclination is zero.
• The angular velocity of the satellite is equal to angular velocity of earth
• Period of revolution is equal to period of rotation of earth.
• Finish one revolution around the earth in exactly one day i.e. 23 hours, 56 Minutes and 4.1 seconds
• There is ONLY one geostationary orbit.

Geosynchronous Orbit

There is a difference between the geostationary and geosynchronous orbits. We should note that while other orbits may be many, there is ONLY ONE Equatorial orbit, i.e. the orbit which is directly above the earth’s equator. Sometimes we send a satellite in the space which though has a period of revolution is equal to period of rotation of earth, but its orbit is neither equatorial nor Circular. So, this satellite will finish one revolution around the earth in exactly one day i.e. 23 hours, 56 Minutes and 4.1 seconds, yet it does NOT appear stationary from the earth. It looks oscillating but NOT stationary and that is why it is called Geosynchronous.

Features of a geosynchronous satellite

• The orbit is NOT circular
• The orbit is NOT in equatorial planee. directly above the equator, it’s in inclined orbit
• The angular velocity of the satellite is equal to angular velocity of earth
• Period of revolution is equal to period of rotation of earth.
• Finish one revolution around the earth in exactly one day i.e. 23 hours, 56 Minutes and 4.1 seconds
• There are many geosynchronous orbits.

Please note that it is practically NOT possible to achieve an absolute geostationary orbit. So, the terms geostationary and geosynchronous are used alternatively.

Advantages of GEO satellites

• Most communications satellites in use today for commercial purposes are placed in the geostationary orbit, because one satellite can cover almost 1/3 of Earth’s surface, offering a reach far more extensive than what any terrestrial network can achieve.
• The geosynchronous satellites remain stationary over the same orbital location, users can point their satellite dishes in the right direction, without costly tracking activities, making communications reliable and secure
• GEO satellites are proven, reliable and secure – with a lifespan of 10-15 years.
• GEO systems have significantly greater available bandwidth than the Low Earth Orbit -LEO and Medium Earth Orbit -MEO systems. This permits them to provide two-way data, voice and broadband services that may be unpractical for other types of systems.
• Because of their capacity and configuration, GEOs are often more cost-effective for carrying high-volume traffic, especially over long-term contract arrangements. For example, excess capacity on GEO systems often is reserved in the form of leased circuits for use as a backup to other communications methods.

Disadvantages of GEO Satellites

• GEO systems, like all other satellite systems, require line-of-sight communication paths between terrestrial antennae and the satellites. But, because GEO systems have fewer satellites and these are in a fixed location over the Earth, the opportunities for line of sight communication are fewer than for systems in which the satellites “travel” across the sky. This is a significant disadvantage of GEO systems as compared to LEO and MEO systems, especially for mobile applications and in urban areas where tall buildings and other structures may block line-of-sight communication for hand-held mobile terminals.
• There are concerns with the transmission delays associated with GEO systems, particularly for high-speed data. However, sophisticated echo cancellation and other technologies have permitted GEOs to be used successfully for both voice and high-speed data applications.

Height of Geostationary Satellites

Key Points

• The height of the geostationary orbit is 35786 kilometers above earth
• In Geostationary Orbit, the satellite moves with an orbital speed of 11068 km per hours.
• A minimum of three satellites are needed to cover the entire earth
• Super synchronous orbit is a disposal / storage orbit above GSO. From earth, they would seem drifting in westerly direction.
• Sub synchronous orbit is a orbit close to but below GSO and is used for satellites undergoing station, changes in an eastern direction.

Calculation of Height

For circular motion of a planet, the condition is that:

F (Gravitational) = F (centripetal)

V is the speed. Now, we know that the speed v of the planet in its orbit is equal to the circumference of the orbit divided by the time required for one revolution T. so v=2πr/T. So, the above formula becomes as follows:

From the above formula, we can derive the value of T2 as follows

The above mathematical derivation is suitable for circular as well as elliptical orbits. Now we know that geostationary satellite follows a circular, equatorial, geostationary orbit, without any inclination, so we can apply the Kepler’s third law to determine the geostationary orbit. Since, the path is circle, its semi-major axis will be equal to the radius of the orbit.

Now, it has already been calculated that Earth completes one rotation on its polar axis in 23 hr 56 min and 4.09 sec, which comes out to be 86164.09 seconds. So, the period of rotation of the Geostationary satellite should be 86164.09 seconds.

This means that

T=86164.09 seconds

Now we use this formula:

The above derivation gives the height of the Geostationary orbit. Now, please note that the above height includes radius of Earth which is 6,384 km. When we deduct it from the calculated height we get 35916 Kilometers. The precise height is altitude of 35,786 km (22,236 mi) above ground.

Orbital speed (how fast the satellite is moving through space) is calculated by multiplying the angular speed by the orbital radius:

Orbiting at the height of 22,282 miles above the equator (35,786 km), the satellite travels in the same direction and at the same speed as the Earth’s rotation on its axis, taking 24 hours to complete a full trip around the globe. Thus, as long as a satellite is positioned over the equator in an assigned orbital location, it will appear to be “stationary” with respect to a specific location on the Earth.

Inclined Orbit

An inclined orbit is used to cover the Polar Regions. It’s not a very popular orbit and used not very frequently. The height of the inclined orbit is kept such that it covers the required area of the region of interest. The time for which the satellite is visible to the point on the earth is also controlled. Satellite cannot remain in continuous contact with the point on the earth if rotating in inclined orbit. Sometimes the inclined orbit is also called elliptical inclined orbit.

Clarke Orbit

Please note that a single geostationary satellite can view approximately one third of the Earth’s surface. If three satellites are placed at the proper longitude, the height of this orbit allows almost the Earth’s entire surface to be covered by the satellites. It was first of all conceptualized by world famous science fiction writer Arthur C. Clarke. The arrangement which was suggested by Clarke is shown in the following figure:

The stations would be arranged approximately equidistantly around the earth and the following longitudes appear suitable:

• 30°E – Africa & Europe
• 150°E – China & Oceania
• 90° W- The Americas

The station chain would be linked by radio or optical beams and thus any broadcast service could be provided. The geostationary orbit is now sometimes referred as the Clarke Orbit or the Clarke Belt in his honor.