Keplerian Elements

Epoch [“Epoch Time” or “T0”]

The first Keplerian orbital element specifying the time at which the other orbital elements were taken. Expressed in most formats as YYDDD.FFFFFFFF (YearDay.Fractionalday).

 

Orbital Inclination [“Inclination” or “I0”]

The orbit ellipse lies in a plane known as the orbital plane. The orbital plane always goes through the center of the earth, but may be tilted any angle relative to the equator. The equatorial plane is the plane perpendicular to the axis of rotation of the central body.

Inclination is the angle between the orbital plane and the equatorial plane. By convention, inclination is a number between 0 and 180 degrees.

An inclination of 0 degrees means the orbiting body orbits the planet in its equatorial plane, in the same direction as the planet rotates;
An inclination of 90 degrees indicates a polar orbit, in which the spacecraft passes over the north and south poles of the planet; and
An inclination of 180 degrees indicates a retrograde equatorial orbit.

Inclination expressed in most formats as DDD.FFFF, (Degrees.Fractionaldegrees).

 

 

 

Right Ascension of Ascending Node [“RAAN” or “RA of Node”, “O0” or “Longitude of Ascending Node”]

Right Ascension of Ascending Node is an angle, measured at the center of the earth, from the vernal equinox to the ascending node. It is a number in the range 0 to 360 degrees.
The term “vernal equinox” above refers to the ascending node of the Sun’s orbit.

We can also use Aries (this is also the same location as the vernal equinox). So, the angle, from the center of the Earth, between Aries and the ascending node is called the RAAN. RAAN expressed in most formats as DDD.FFFF, (Degrees.Fractionaldegrees).

 

 

Argument of Perigee [“ARGP” or “W0”]

The point where the satellite is closest to the earth is called perigee, although it’s sometimes called periapsis or perifocus. We’ll call it perigee. The point where the satellite is farthest from earth is called apogee (apoapsis, or apifocus).

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. The angle range from 0° to 360° and expressed in most formats as DDD.FFFF, (Degrees.Fractional degrees).

Eccentricity [“ecce” or “E0” or “e”]

 

 

In the Keplerian orbit model, the satellite orbit is an ellipse. Eccentricity tells us the “shape” of the ellipse. Eccentricity is computed as the linear eccentricity (the distance from the center of the ellipse to the center of the Earth) divided by the semi major axis. The semi major axis describes the size of the ellipse. Semi-major axis is one half the longest distance across the ellipse (or one half the distance between apogee and perigee).

When e=0, the ellipse is a circle. When e is very near 1, the ellipse is very long and skinny. Eccentricity must be in the range 0 <= e < 1 and expressed in most formats as RRRRRRR, (dimensionless, leading “0.” implied).

Mean Motion [“N0”]

Kepler’s third law of orbital motion gives us a precise relationship between the speed of the satellite and its distance from the earth. Satellites that are close to the earth orbit very quickly. Satellites far away orbit slowly. This means that we could accomplish the same thing by specifying either the speed at which the satellite is moving, or its distance from the earth!

Mean Motion specifying the average orbital speed, (in revolutions/day) of the satellite’s. Expressed in most formats as RR.FFFFFFFFF, (Revolutions.Fractionrevolutions). Typically, satellites have Mean Motions in the range of 1 rev/day to about 16 rev/day.

 

 

Mean Anomaly [“M0” or “MA” or “Phase”]

Mean anomaly is simply an angle between the perigee and the position of the satellite, measured in the orbital plane, at the epoch. It is defined to be 0 degrees at perigee, and therefore is 180 degrees at apogee. Expressed in most formats as DDD.FFFF, (Degrees.Fractionaldegrees).

It has become common practice with radio amateur satellites to use Mean Anomaly to schedule satellite operations. Satellites commonly change modes or turn on or off at specific places in their orbits, specified by Mean Anomaly. Unfortunately, when used this way, it is common to specify MA in units of 256ths of a circle instead of degrees! Some tracking programs use the term “phase” when they display Mean Anomaly in these units. It is still specified in degrees, between 0 and 360, when entered as an orbital element.

Example: Suppose satelite has a period of 12 hours, and is turned off from Phase 240 to 16. That means it’s off for 32 ticks of phase. There are 256 of these ticks in the entire 12 hour orbit, so it’s off for (32/256)x12hrs = 1.5 hours. Note that the off time is centered on perigee. Satellites in highly eccentric orbits are often turned off near perigee when they’re moving the fastest, and therefore difficult to use.

 

 

Drag [“N1”]

Drag caused by the earth’s atmosphere causes satellites to spiral downward. As they spiral downward, they speed up. The Drag orbital element simply tells us the rate at which Mean Motion is changing due to drag or other related effects. Precisely, Drag is one half the first time derivative of Mean Motion and is measured at the epoch.
Its units are revolutions per day per day. It is typically a very small number. Common values for low-earth-orbiting satellites are on the order of 10^-4. Common values for high-orbiting satellites are on the order of 10^-7 or smaller. Negative values can indicate tidal forces on higher satellites or observational error. A high drag, (> 10-4) indicates the need for frequent observation.

 

 

Epoch Rev [“Revolution Number at Epoch”]

This tells the tracking program how many times the satellite has orbited from the time it was launched until the time specified by “Epoch”. Expressed in most formats as RRRR (Revolutions). This figure is sometimes ambiguous or in error. It has no effect on most tracking calculations.

 

 

Attitude [“Bahn Coordinates”]

The spacecraft attitude is a measure of how the satellite is oriented in space. Hopefully, it is oriented so that its antennas point toward you! There are several orientation schemes used in satellites. The Bahn coordinates apply only to spacecraft which are spin-stablized. Spin-stabilized satellites maintain a constant inertial orientation, i.e., its antennas point a fixed direction in space.
The Bahn coordinates consist of two angles, often called Bahn Latitude and Bahn Longitude. These are published from time to time for the elliptical-orbit amateur radio satellites in various amateur satellite publications. Ideally, these numbers remain constant except when the spacecraft controllers are re-orienting the spacecraft. In practice, they drift slowly.
For highly elliptical orbits these numbers are usually in the vicinity of: 0,180. This means that the antennas point directly toward earth when the satellite is at apogee.
These two numbers describe a direction in a spherical coordinate system, just as geographic latitude and longitude describe a direction from the center of the earth. In this case, however, the primary axis is along the vector from the satellite to the center of the earth when the satellite is at perigee.
This element is not expressed in most formats.

 

 

Sources:
1. http://everything2.com
2. http://en.wikipedia.org
3. http://www.marine.rutgers.edu
4. http://www.mindspring.com
5. http://www.amsat.org