Keplerian elements provide a mathematical description of a Satellite's orbit. Satellite tracking software reads the Keplerian elements and provides graphical and/or tabular orbital predictions. Keplerian data are most commonly provided in the AMSAT and the Space Command / NASA Two-Line Element (TLE) format. Johann Kepler determined three laws characterizing orbital motion, using Tycho Brahe's planetary observation data. These laws can be proven mathematically using Newton's law of gravitation. Kepler's laws are paraphrased below along with the corresponding physical implications. These laws apply directly to satellite orbital motion, thus the laws are from the point of view of an Earth-orbiting satellite.

Johannes Kepler (1571-1630)
Kepler had studied astronomy long before he met Tycho: he favored the Copernican world-view and corresponded with Galileo.
Tycho's observations included some very accurate measurements of the position of the planet Mars, which did not agree with either Ptolemy or Copernicus. When Tycho died, Kepler got hold of those observations and tried to puzzle them out. In 1609, the same magic year when Galileo first turned his telescope towards the heavens, Kepler caught a glimpse of what he thought might be the answer. That was when he published his three laws of planetary (satellite) motion:

Kepler's First Law:

Satellite orbits are elliptical Paths with the Earth at one focus of
the ellipse.

Kepler's Second Law:

A line between the center of the Earth and the satellite sweeps out
equal areas in equal intervals of time.

Kepler's Third Law:

The square of the orbital period is proportional to the cube of the
the orbit's semi major axis.

Johannes Kepler

Father of Keplerian Elements

Current Keplerian Elements

(Thanks to John Corby of Hearsat.org for maintaining this list)

***NOTE: January 24, 2005: HearSat TLE distribution suspended due to Space Track Homeland Security regulations

Date (DD-MM-YYYY): 07/03/2005

Download Latest Keplerian Text File: ===> Kepler.txt
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NASA Format
This is the format used by NASA to distribute satellite elements in their "NASA Prediction Bulletin".
The origin of the format is unknown. Some old NORAD reports refer to this as T-card format. NASA
documents often call it the "2-line" format.
Most satellite tracking programs expect a file which contains groups of 3 lines: One line containing
the satellite's name, followed by the NASA 2 lines of numbers.
NASA leaves some fields out of some element sets. The "international designators" for example are of-ten
missing.

NASA Two-line format files look like this...
OSCAR 10
1 14129U 88230.56274695 0.00000042 10000-3 0 3478
2 14129 27.2218 308.9614 6028281 329.3891 6.4794 2.05877164 10960
GPS-0008
1 14189U 88230.24001475 0.00000013 0 5423
2 14189 63.0801 108.8864 0128028 212.9347 146.3600 2.00555575 37348
Each number is in a specified fixed column. Spaces are significant. The last digit on each line is a
mod-10 check digit, which is checked by the program. The program also checks the sequence numbers
(first column), and checks each orbital element for reasonable range. This is a very good set of checks,
so this format is very safe, and robust.
I have noticed recently files of "almost NASA format" elements on some BBSs. Specifically, some peo-ple
have been leaving off the check digits, and adding commentary to the first line. There is no excuse
for this. We can only exchange data if we adhere to standards. An almost NASA format file is no
better than a diskette that's "almost" the right size to fit in that little slot in the front of your
computer.
The following description, which I obtained from T.S.Kelso, describes the NASA format in detail:
Data for each satellite consists of three lines in the following format:
AAAAAAAAAAA
1 NNNNNU NNNNNAAA NNNNN.NNNNNNNN +.NNNNNNNN +NNNNN-N +NNNNN-N N NNNNN
2 NNNNN NNN.NNNN NNN.NNNN NNNNNNN NNN.NNNN NNN.NNNN NN.NNNNNNNNNNNNNN
Line 1 is a eleven-character name.
Lines 2 and 3 are the standard Two-Line Orbital Element Set Format identical to that used by NASA
and NORAD. The format description is:

Line 2

Column Description
01-01 Line Number of Element Data
03-07 Satellite Number
10-11 International Designator (Last two digits of launch year)
12-14 International Designator (Launch number of the year)
15-17 International Designator (Piece of launch)
19-20 Epoch Year (Last two digits of year)
21-32 Epoch (Julian Day and fractional portion of the day)
34-43 First Time Derivative of the Mean Motion divided by 2., or Ballistic Coefficient (Depending of ephemeris type)
45-52 Second Time Derivative of Mean Motion divided by 6. (Blank if N/A)
54-61 BSTAR drag term if GP4 general perturbation theory was used. Otherwise, radiation pressure coefficient.
63-63 Ephemeris type
65-68 Element number
69-69 Check Sum (Modulo 10)
(Letters, blanks, periods = 0; minus sign = 1; plus sign = 2)

Line 3

Column Description
01-01 Line Number of Element Data
03-07 Satellite Number
09-16 Inclination [Degrees]
18-25 Right Ascension of the Ascending Node [Degrees]
27-33 Eccentricity (decimal point assumed)
35-42 Argument of Perigee [Degrees]
44-51 Mean Anomaly [Degrees]
53-63 Mean Motion [Revs per day]
64-68 Revolution number at epoch [Revs]
69-69 Check Sum (Modulo 10)
All other columns are blank or fixed. Note that the International Designator fields are usually blank,
as issued in the NASA Prediction Bulletins.

AMSAT Format
There are several very similar formats generated by several different people that seem to be called
"AMSAT" format. This format is very user-friendly, and can be easily read and/or edited by humans.
Spaces are not significant. Each orbital element must appear on a separate line. The order in which
orbital elements appear is not significant, except that each element set should begin with a line
containing the word "satellite".

First example AMSAT format, as distributed by Conrad Kirksey W5BWF:
Satellite: AO-10
Int'l Object Number: 14129
NASA Designation: 1983-058B
Epoch Time, T0: 88239.30510271
Fri Aug 26, 1988.
Epoch Rev, K0: 1114
Mean Anomaly, M0: 6.0030 deg
Mean Motion, N0: 2.05882335 rev/day
Inclination, I0: 27.1492 deg
Eccentricity, E0: 0.6027104
Arg Perigee, W0: 331.5568 deg
RAAN, O0: 307.6972 deg
Period: 699.428632 min/rev
Increment: 174.857158 deg/rev
Beacon, F1: 145.8100 MHz
Decay, N1: -1.38E-06 rev/day^2
Element Set: 352

Second example AMSATish format, as distributed in an ARRL bulletin..KEPLERIAN BULLETIN 77 ARLK077
FROM ARRL HEADQUARTERS
NEWINGTON CT SEPTEMBER 24, 1988
TO ALL RADIO AMATEURS
Satellite: oscar-10
Catalog number: 14129
Epoch time: 88248.53312992
Element set: 353
Inclination: 27.1605 deg
RA of node: 306.2255 deg
Eccentricity: 0.6029797
Arg of perigee: 333.9978 deg
Mean anomaly: 5.4273 deg
Mean motion: 2.05877131 rev/day
Decay rate: 4.4e-07 rev/day sq
Epoch rev: 3933