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title	summary	tags
The two-line element format	The fixed width columns of a two-line element set, the checksum rule, and the two conventions that are easy to misread.	tle, elements, format, checksum

The two-line element format

A two-line element set, or TLE, is a fixed width text record that describes the mean orbit of a catalogued satellite. It is what a catalogue publishes and it is the input the SGP4 propagator is fitted to. This document gives the layout, the checksum rule, and the units.

Definition

A two-line element set has one optional name line followed by two data lines, conventionally called line 1 and line 2. Every field occupies a fixed range of columns, numbered from one. Each data line ends with a single checksum digit.

ISS (ZARYA)
1 25544U 98067A   08264.51782528 -.00002182  00000-0 -11606-4 0  2927
2 25544  51.6416 247.4627 0006703 130.5360 325.0288 15.72125391563537

Field layout

Line 1:

Columns	Field	Unit
1	Line number, always `1`
3-7	Satellite catalog number
8	Classification, `U`, `C`, or `S`
10-17	International designator
19-32	Epoch, two digit year and fractional day	year, day of year
34-43	First derivative of mean motion divided by two	rev/day^2
45-52	Second derivative of mean motion divided by six	rev/day^3
54-61	`BSTAR` drag term	1 / Earth radius
63	Ephemeris type
65-68	Element set number
69	Checksum

Line 2:

Columns	Field	Unit
1	Line number, always `2`
3-7	Satellite catalog number
9-16	Inclination	deg
18-25	Right ascension of the ascending node	deg
27-33	Eccentricity, assumed decimal point	dimensionless
35-42	Argument of perigee	deg
44-51	Mean anomaly	deg
53-63	Mean motion	rev/day
64-68	Revolution number at epoch
69	Checksum

Two conventions that are easy to misread

The exponent fields carry an assumed decimal point. An exponent field is written as a sign, a mantissa without a decimal point, a sign for the exponent, and a single exponent digit. The mantissa is read with a decimal point in front of its first digit. So

Written in the element set	Means
`12345-3`	`0.12345e-3`
`-11606-4`	`-0.11606e-4`

The eccentricity has an assumed decimal point. The field 0006703 means 0.0006703, not 6703.

A field that is entirely blank is zero, which is how the format writes an absent term.

Mathematical meaning

The checksum of a line is the sum of the decimal digits on the line, plus one for each minus sign, reduced modulo ten:


\text{checksum} = \left( \text{sum of digits} + \text{number of minus signs} \right) \bmod 10

Only the first 68 columns contribute; the checksum occupies column 69 and is not part of its own sum. For the example line 1 the sum is 167 and the checksum is 7.

The epoch is written as a two digit year and a fractional day of that year. The two digit year is expanded with the convention that years 57 through 99 are in the twentieth century and years 00 through 56 are in the twenty-first, which places the boundary before the start of the satellite catalogue.

Unit convention

The format is not self describing and its units are fixed:

Orientation angles are in degrees.
Mean motion is in revolutions per day.
Derivatives of mean motion are per day to the matching power.
BSTAR is in units of inverse Earth radii, the Earth radius being the equatorial radius in kilometers used by the propagator.
Eccentricity is dimensionless.
The epoch is a UTC instant.

The parser keeps the units of the format. The conversion to radians and to radians per minute happens in the propagator, not in the parser, so a value read from a parsed element set is exactly what the file says.

Applicability

A two-line element set describes mean elements, not instantaneous ones. The numbers are the input to the SGP4 model and are only meaningful together with it. Feeding them to a two-body propagator gives a different and wrong answer.

The format has no field for the accuracy of the element set and no field for the propagation model to use. The convention that SGP4 is the model is external to the format. Both facts are reasons to keep the element set together with its source and the model that was used.

A two-line element set is valid for a limited interval around its epoch. The propagator includes a drag term that models the decay of the orbit over that interval, and the interval over which the model is useful is measured in days to weeks depending on the altitude and the activity of the Sun.

Comparison of element formats

Format	Content	Model it is fitted to	Precision	Used here
Two-line element set	Mean elements, drag term	SGP4 and SDP4	Kilometers over days	Yes
CCSDS OEM	Position and velocity or elements at a time grid	Any	Meters	No
CCSDS OPM	Position and velocity at one epoch	Any	Meters	No
SP3	Satellite position at a regular grid	Any	Centimeters to meters	No
Broadcast ephemeris	Keplerian elements plus corrections	A GNSS orbit model	Meters	No
Precise ephemeris	Position and clock at a grid	Post-processed	Centimeters	No

The two-line format is the least precise of these and the most widely available, which is why it matters.

Source

The field layout follows the format description published by CelesTrak, FAQs: Two-Line Element Set Format, which documents the columns defined by the original NORAD specification. The checksum rule is the one stated there and used by Space-Track.

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