# Keplerian Elements

There are several reasons why you want to study the orbits of satellites:

• Sample Design: You want to match an orbit with the type of study you want to conduct.
• Predict Orbit: You want to know where a satellite will be at any particular time.
• Orbital Accuracy: You want to know what will influence the orbit of a satellite for instruments such as altimeters.

## Things You Need to Know in Order to Calculate a Satellite's Orbit

There are 8 elements that you need to define an orbit. These elements are also called Keplerian Elements after the German astronomer Johannes Kepler (1571-1630). Kepler discovered that planets moved in elliptical orbits rather than circular orbits. The following are Keplerian Elements:

1. Epoch Time
2. Orbital Inclination
3. Right Ascension of Ascending Node
4. Eccentricity
5. Argument of Perigee
6. Mean Motion
7. Mean Anomaly
8. Drag

## Epoch Time

The first thing you need to define an orbit is the time at which the Keplerian Elements were defined. You need a snapshot of where and how fast the satellite was going.

## Orbital Inclination

This element tells you what the angle is between the equator and the orbit when looking from the center of the Earth. If the orbit went exactly around the equator from left to right, then the inclination would be 0. The inclination ranges from 0 to 180 degrees. ## Right Ascension of Ascending Node

This is probably one of the most difficult of the elements to describe. The ascending node is the place where the satellite crosses the equator while going from the Southern Hemisphere to the Northern Hemisphere. Now since the Earth rotates, you need to specify a fixed object in space. We use Aries (this is also the same location as the vernal equinox). The angle, from the center of the Earth, between Aries and the ascending node is called the right ascension of ascending node. ## Eccentricity

The eccentricity tells you how flat the orbit is. If the orbit is a perfect circle, then the eccentricity is 0. When the eccentricity is close to 1, then the orbit is very flat. ## Argument of Perigee

Since an orbit usually has an elliptical shape, the satellite will be closer to the Earth at one point than at another. The point where the satellite is the closest to the Earth is called the perigee. The point where the satellite is the furthest from the Earth is called the apogee. The argument of perigee is the angle formed between the perigee and the ascending node. If the perigee would occur at the ascending node, the argument of perigee would be 0. ## Mean Motion

The mean motion tells you how fast the satellite is going. According to Kepler's Law: as the satellite gets closer to the Earth, its velocity increases. If we know how fast the satellite is going, we also know the altitude of the satellite.

## Mean Anomaly

The mean anomaly tells you where the satellite is in its orbital path. The mean anomaly ranges from 0 to 360 degrees. The mean anomaly is referenced to the perigee. If the satellite were at the perigee, the mean anomaly would be 0.

## Drag (optional)

Several factors can affect the velocity of a satellite. If the satellite were in a low orbit, then the atmosphere would produce drag. This would cause the satellite to come closer to the Earth therefore speeding up (Kepler's Law). Another factor that can affect satellite orbits is gravitational pull from stellar bodies such as the sun or the moon. These bodies could pull the satellite away from the Earth causing it to slow down.

## Other Links on Keplerian Elements

http://www.amsat.org/amsat/keps/kepmodel.html

http://www-leland.stanford.edu/~iburrell/sat/kepler.html