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 fahnen/7.jpg Keplerian Elements Tutorial

The Keplerian Elements Short Tutorial
provided by Miguel Menendez Vazquez, EA1BCU

### What are the Keplerian Elements?

The Keplerian Elements are a set of numbers which allow satellite tracking programs to calculate a satellite's position in space. The keplerian elements come in two formats - either the NASA 2-line elements (TLE) or the AMSAT verbose format elements.

Keps, as they are sometimes called, give us specific information about a satellite's orbit at a specific moment. Once these elements are known for a specific time, the satellite's position in space can be predicted using complex mathematical calculations. There is, however, one problem. Keps are given for a specific time. The accuracy of the position prediction degrades as time goes by. The predicted postion of a satellite using 7 days old keps is more accurate than a prediction using 3 months old keps.

Another factor to take into consideration is the height of the satellite's orbit. High orbiting satellites, such as Oscar 40, suffer much less from the effect of the earth's atmosphere and gravity than lower orbiting satellites, as the International Space Station and the Low Earth Orbiting (LEO) satellites. Thus the age of keps has a lower influence on predictions for high orbiting satellites than for the low orbiting ones. Also, the ISS can be maneuvered in space to avoid collisions with other objects in space, so the keps for it should be updated more frequently

We suggest updating the keps every 2 weeks, depending on the height of the satellite you're interesed in. Update every couple of weeks for low orbiting satellites, and every 4-5 weeks for high orbiting ones.

Keplerian Elements For the International Space Station
6 May, 2004

`ISS1 25544U 98067A   04127.92349537  .00017095  00000-0  14786-3 0  72322 25544  51.6276 176.0525 0011067 106.0444 249.6038 15.69246258311835`

#### 2-Line Element Definition (use key to decode)

`1 AAAAAU YYLLLPPP  BBBBB.BBBBBBBB  .CCCCCCCC  DDDDD-D  EEEEE-E F GGGGZ2 AAAAA  HHH.HHHH III.IIII JJJJJJJ KKK.KKKK MMM.MMMM NN.NNNNNNNNRRRRRZ`

### Key

• [1] - Line #1 label
• [2] - Line #2 label
• [AAAAA] - Catalog Number assigned sequentially (5-digit integer from 1 to 99999)
• [U] - Security Classification (U = Unclassified)
• [YYLLLPPP] - International Designator (YY = 2-digit Launch Year; LLL = 3-digit Sequential Launch of the Year; PPP = up to 3 letter Sequential Piece ID for that launch)
• [BBBBB.BBBBBBBB] - Epoch Time -- 2-digit year, followed by 3-digit sequential day of the year, followed by the time represented as the fractional portion of one day
• [.CCCCCCCC] - ndot/2 Drag Parameter (rev/day2) -- one half the first time derivative of the mean motion. This drag term is used by the SGP orbit propagator.
• [DDDDD-D] - n double dot/6 Drag Parameter (rev/day3) -- one sixth the second time derivative of the mean motion. The "-D" is the tens exponent (10-D). This drag term is used by the SGP orbit propagator.
• [EEEEE-E] - Bstar Drag Parameter (1/Earth Radii) -- Pseudo Ballistic Coefficient. The "-E" is the tens exponent (10-E). This drag term is used by the SGP4 orbit propagator.
• [F] - Ephemeris Type -- 1-digit integer (zero value uses SGP or SGP4 as provided in the Project Spacetrack report.
• [GGGG] - Element Set Number assigned sequentially (up to a 4-digit integer from 1 to 9999). This number recycles back to "1" on the update following element set number "9999."
• [HHH.HHHH] - Orbital Inclination (from 0 to 180 degrees).
• [III.IIII] - Right Ascension of the Ascending Node (from 0 to 360 degrees).
• [JJJJJJJ] - Orbital Eccentricity -- there is an implied leading decimal point (between 0.0 and 1.0).
• [KKK.KKKK] - Argument of Perigee (from 0 to 360 degrees).
• [MMM.MMMM] - Mean Anomaly (from 0 to 360 degrees).
• [NN.NNNNNNNN] - Mean Motion (revolutions per day).
• [RRRRR] - Revolution Number (up to a 5-digit integer from 1 to 99999). This number recycles following revolution nymber 99999.
• [Z] - Check Sum (1-digit integer). Both lines have a check sum that is computed from the sum of all integer characters on that line plus a "1" for each negative (-) sign on that line. The check sum is the modulo-10 (or ones digit) of the sum of the digits and negative signs.

### Orbital Elements and Nomenclature

 a - Semi-major Axis (meters, feet)a constant defining the size of the orbit (meters) E0 - Eccentricity: a constant defining the shape of the orbit (0.0 = circular, greater than 0 and less than 1 = elliptical) I0 - Inclination (degrees) : The angle betwen the equator and the orbit plane O0 - Right Ascension of the Ascending Node (degrees): the angle between vernal equinox and the point where the orbit crosses the equatorial plane (going north) W0 - Argument of Perigee (degrees): the angle between the ascending node and the orbit's point of closest approach to the earth (perigee) "True Anomaly" - True Anomaly (degrees) The angle between perigee and the vehicle (in the orbit plane) M0 - Mean Anomaly (degrees) An imaginary angle, like True Anomaly but averaged out to vary at a constant rate. Apogee - In the orbit, The more distant point between satellite and the Earth Perigee - In the orbit, The nearer point between satellite and the Earth Ra - distance from the center of the Earth to the apogee point Line of Nodes - The point where the vehicle crosses the equator

## Satellite Attitude Control (ALON/ALAT)

To calculate the squint angle:

1. Attitude Longitude - ALON (refer to the picture) Relates the satellite's Z-axis to the orbit's major axis. It is equal to the TWIST angle + 180 degrees.
2. Attitude Latitude - ALAT If the satellite's Z-axis lies in the plane of the orbit (this page) then ALAT=0, otherwise the Z-axis looks above or below the orbit's plane and ALAT indicates this quantity.