156 lines
5.8 KiB
Markdown
156 lines
5.8 KiB
Markdown
---
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title: The two-line element format
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summary: The fixed width columns of a two-line element set, the checksum rule, and the two conventions that are easy to misread.
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tags: tle, elements, format, checksum
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---
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# The two-line element format
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A two-line element set, or TLE, is a fixed width text record that describes
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the mean orbit of a catalogued satellite. It is what a catalogue publishes
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and it is the input the SGP4 propagator is fitted to. This document gives
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the layout, the checksum rule, and the units.
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## Definition
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A two-line element set has one optional name line followed by two data
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lines, conventionally called line 1 and line 2. Every field occupies a fixed
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range of columns, numbered from one. Each data line ends with a single
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checksum digit.
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```text
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ISS (ZARYA)
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1 25544U 98067A 08264.51782528 -.00002182 00000-0 -11606-4 0 2927
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2 25544 51.6416 247.4627 0006703 130.5360 325.0288 15.72125391563537
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```
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## Field layout
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Line 1:
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| Columns | Field | Unit |
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|---------|-------|------|
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| 1 | Line number, always `1` | |
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| 3-7 | Satellite catalog number | |
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| 8 | Classification, `U`, `C`, or `S` | |
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| 10-17 | International designator | |
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| 19-32 | Epoch, two digit year and fractional day | year, day of year |
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| 34-43 | First derivative of mean motion divided by two | rev/day^2 |
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| 45-52 | Second derivative of mean motion divided by six | rev/day^3 |
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| 54-61 | `BSTAR` drag term | 1 / Earth radius |
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| 63 | Ephemeris type | |
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| 65-68 | Element set number | |
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| 69 | Checksum | |
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Line 2:
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| Columns | Field | Unit |
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|---------|-------|------|
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| 1 | Line number, always `2` | |
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| 3-7 | Satellite catalog number | |
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| 9-16 | Inclination | deg |
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| 18-25 | Right ascension of the ascending node | deg |
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| 27-33 | Eccentricity, assumed decimal point | dimensionless |
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| 35-42 | Argument of perigee | deg |
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| 44-51 | Mean anomaly | deg |
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| 53-63 | Mean motion | rev/day |
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| 64-68 | Revolution number at epoch | |
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| 69 | Checksum | |
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## Two conventions that are easy to misread
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**The exponent fields carry an assumed decimal point.** An exponent field is
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written as a sign, a mantissa without a decimal point, a sign for the
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exponent, and a single exponent digit. The mantissa is read with a decimal
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point in front of its first digit. So
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```text
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12345-3 means 0.12345e-3
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-11606-4 means -0.11606e-4
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```
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**The eccentricity has an assumed decimal point.** The field `0006703` means
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`0.0006703`, not `6703`.
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A field that is entirely blank is zero, which is how the format writes an
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absent term.
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## Mathematical meaning
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The checksum of a line is the sum of the decimal digits on the line, plus
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one for each minus sign, reduced modulo ten:
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```text
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checksum = (sum of digits + number of minus signs) mod 10
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```
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Only the first 68 columns contribute; the checksum occupies column 69 and is
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not part of its own sum. For the example line 1 the sum is 167 and the
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checksum is 7.
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The epoch is written as a two digit year and a fractional day of that year.
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The two digit year is expanded with the convention that years `57` through
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`99` are in the twentieth century and years `00` through `56` are in the
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twenty-first, which places the boundary before the start of the satellite
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catalogue.
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## Unit convention
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The format is not self describing and its units are fixed:
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- Orientation angles are in **degrees**.
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- Mean motion is in **revolutions per day**.
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- Derivatives of mean motion are per **day** to the matching power.
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- `BSTAR` is in units of **inverse Earth radii**, the Earth radius being the
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equatorial radius in kilometers used by the propagator.
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- Eccentricity is **dimensionless**.
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- The epoch is a **UTC** instant.
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The parser keeps the units of the format. The conversion to radians and to
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radians per minute happens in the propagator, not in the parser, so a value
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read from a parsed element set is exactly what the file says.
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## Applicability
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A two-line element set describes **mean** elements, not instantaneous ones.
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The numbers are the input to the SGP4 model and are only meaningful together
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with it. Feeding them to a two-body propagator gives a different and wrong
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answer.
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The format has no field for the accuracy of the element set and no field for
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the propagation model to use. The convention that SGP4 is the model is
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external to the format. Both facts are reasons to keep the element set
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together with its source and the model that was used.
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A two-line element set is valid for a limited interval around its epoch. The
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propagator includes a drag term that models the decay of the orbit over that
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interval, and the interval over which the model is useful is measured in
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days to weeks depending on the altitude and the activity of the Sun.
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## Comparison of element formats
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| Format | Content | Model it is fitted to | Precision | Used here |
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|--------|---------|-----------------------|-----------|-----------|
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| Two-line element set | Mean elements, drag term | SGP4 and SDP4 | Kilometers over days | Yes |
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| CCSDS OEM | Position and velocity or elements at a time grid | Any | Meters | No |
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| CCSDS OPM | Position and velocity at one epoch | Any | Meters | No |
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| SP3 | Satellite position at a regular grid | Any | Centimeters to meters | No |
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| Broadcast ephemeris | Keplerian elements plus corrections | A GNSS orbit model | Meters | No |
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| Precise ephemeris | Position and clock at a grid | Post-processed | Centimeters | No |
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The two-line format is the least precise of these and the most widely
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available, which is why it matters.
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## Source
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- The field layout follows the format description published by CelesTrak,
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*FAQs: Two-Line Element Set Format*, which documents the columns defined
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by the original NORAD specification. The checksum rule is the one stated
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there and used by Space-Track.
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## See also
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- [[sgp4]] for the propagator the elements are fitted to
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- [[keplerian-elements]] for the elements of the orbit itself
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- Try the parser in the online tool: *Parse a two-line element set*
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