# Geosynchronous vs geo-stable orbit?

1. Jul 14, 2010

### jnorman

simple question - can someone please clarify the difference between these two orbits? i recall arthur c clarke's original concept for communication satellites in what i believe he called geosynchronous orbit such that the satellite(s) would remain over a single fixed point on earth's surface, which in his discussion indicated an orbital height of 22,000 miles.

yesterday, i looked up geosynchronous orbit, and found that it was at an orbital height of 26,000 miles and was apparently some type of elliptical orbit. the article then went on to differentiate geosynchronous from geo-stable, which was a circular orbit at 22,000 miles.

now i am a tad confused - can you please clarify? thanks.

2. Jul 14, 2010

### D H

Staff Emeritus
About the 22,000 versus 26,000 miles (or more precisely, 22,236 versus 26,199 miles): They are really the same number. The first is altitude, which is the distance above the surface of the Earth. The second is orbital radius, which is the distance from the center of the Earth. The Earth's equatorial radius is 3,963 miles, so the orbital altitude will be 3,963 miles smaller than the orbital radius.

Any satellite's orbit whose period is one sidereal day is in a geosynchronous orbit. The will orbit the equator if the orbital inclination is zero. In that case, the satellite will appear to be stationary from the perspective of an Earth-based observer. These are geostationary orbits. A satellite that is in a geosynchronous orbit with a non-zero inclination will appear to move in a figure-8 pattern when viewed from the surface of the Earth.

A huge advantage results from satellites that are in a geostationary orbit. All that is needed to receive a transmission from that satellite is a very simple antenna pointed at the right fixed direction. There is also a huge disadvantage to those geostationary orbits. There aren't stable. Perturbations due to gravity from the Sun and Moon, the Earth's non-spherical shape, and radiation pressure from sunlight act to push the vehicle into a different orbit. Satellites in a geostationary orbit must occasionally fire thrusters to put themselves back into the right geostationary orbit.

There is one set of geosynchronous (but not geostationary) orbits that are stable. A geosynchronous orbit that is inclined by 7.3° will have the perturbations due to Earth J2 (the first term that describes Earth's non-spherical shape) cancel the perturbations to solar gravity, lunar gravity, and solar radiation pressure. This is the GEO (all caps, do note) stable plane. (GEO here means geostationary equatorial orbit. Calling this orbital plane that is not equatorial the GEO stable plane is a bit of a misnomer, but that's what it is called; were stuck with it.)

Even in that supposedly stable plane orbits are not necessarily stable. There are two points that are: above 75°E and 105°W longitude. The stable plane only accounts for Earth J2. There are a lot more terms than J2 that describe the Earth's non-spherical shape. J2 is just the biggest of these; it describes how an oblate spheroid model of the Earth differs from a spherical model. Orbits with an inclication of 7.3° degrees and a location of 75°E or 105°W longitude are stable, even after accounting for those higher order terms. Dead geostationary satellites tend to accumulate at those two spots in the GEO stable plane.

3. Jul 14, 2010

danke.