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{{Short description|Orbital data format}}
A '''two-line element set''' ('''TLE''', or more rarely '''2LE''') or '''three-line element set''' ('''3LE''') is a [[file format|data format]] encoding a list of [[orbital elements]] of an Earth-orbiting object for a given point in time, the ''epoch''. Using a suitable prediction formula, the [[Orbital state vectors|state]] (position and velocity) at any point in the past or future can be estimated to some accuracy. The TLE data representation is specific to the [[simplified perturbations models]] (SGP, [[SGP4]], [[SDP4]], SGP8 and SDP8), so any algorithm using a TLE as a data source must implement one of the SGP models to correctly compute the state at a time of interest. TLEs can describe the trajectories only of Earth-orbiting objects. TLEs are widely used as input for projecting the future orbital tracks of [[space debris]] for purposes of characterizing "future debris events to support [[risk analysis]], close approach analysis, [[Collision avoidance (spacecraft)|collision avoidance]] maneuvering" and [[forensic analysis]].<ref name=aiaa2008>
{{cite journal |last1=Carrico |first1=Timothy |last2=Carrico |first2=John |last3=Policastri |first3=Lisa |last4=Loucks |first4=Mike |title=Investigating Orbital Debris Events using Numerical Methods with Full Force Model Orbit Propagation |journal=American Institute of Aeronautics and Astronautics |date=2008 |issue=AAS 08–126 |url=http://www.applieddefense.com/wp-content/uploads/2012/12/2008-Carrico-Policastri-Investigating_Orbital_Debris_Events.pdf |url-status=dead |archive-url=https://web.archive.org/web/20141204122502/http://www.applieddefense.com/wp-content/uploads/2012/12/2008-Carrico-Policastri-Investigating_Orbital_Debris_Events.pdf |archive-date=2014-12-04 }}</ref><ref name=":0">{{cite web |title=Space-Track.org Basic Description of the Two Line Element (TLE) Format |url=https://www.space-track.org/documentation#/tle |access-date=18 June 2025 |website=www.space-track.org |publisher=[[Combined Force Space Component Command]] |ref=spacetracktle}}</ref>
The format was originally intended for [[punch card|punched card]]s, encoding a set of elements on two [[punched card#IBM 80-column format and character codes|standard 80-column cards]]. This format was eventually replaced by [[text file]]s as punch card systems became obsolete, with each set of elements written to two 69-column [[ASCII]] lines preceded by a title line. The [[United States Space Force]] tracks all detectable objects in Earth orbit, creating a corresponding TLE for each object, and makes publicly available TLEs for many of the space objects on the
A TLE set may include a title line preceding the element data, so each listing may take up three lines in the file, in which case the TLE is referred to as a three-line element set (''3LE''), instead of a two-line element set (''2LE''). The title is not required, as each data line includes a unique object identifier code.
==History==
In the early 1960s, Max Lane developed mathematical models for predicting the locations of satellites based on a minimal set of data elements. His first paper on the topic, published in 1965, introduced the Analytical Drag Theory, which concerned itself primarily with the effects of drag caused by a spherically symmetric non-rotating atmosphere.<ref name=revisit>{{cite journal |first1=David |last1=Vallado |first2=Paul |last2=Crawford |first3=Richard |last3=Hujsak |first4=T.S. |last4=Kelso |title=Revisiting Spacetrack Report #3 |url=http://celestrak.com/publications/AIAA/2006-6753/AIAA-2006-6753.pdf |journal=American Institute of Aeronautics and Astronautics |year=2006}}</ref> Joined by K. Cranford, the two published an improved model in 1969 that added various harmonic effects due to Earth-Moon-Sun interactions and various other inputs.<ref name=improved>{{cite journal |first1=Max |last1=Lane |first2=Kenneth |last2=Cranford |journal=AIAA |title=An improved analytical drag theory for the artificial satellite problem |year=1969|oclc=122930989 }}</ref>
Lane's models were widely used by the military and NASA starting in the late 1960s. The improved version became the standard model for [[NORAD]] in the early 1970s, which ultimately led to the creation of the TLE format. At the time there were two formats designed for [[punch card]]s, an "internal format" that used three cards encoding complete details for the satellite (including name and other data), and the two card "transmission format" that listed only those elements that were subject to change.<ref name=format>{{cite
Cranford continued to work on the modelling, eventually leading Lane to publish ''Spacetrack Report #2'' detailing the Air Force General Perturbation theory, or AFGP4. The paper also described two simplified versions of the system, IGP4 which used a simplified drag model, and SGP4 (Simplified General Perturbations) which used IGP4's drag model along with a simplified gravity model.<ref name=spacetrack2>{{cite
Shortly after the publication of ''Report #3'', NASA began posting elements for a variety of visible and other well known objects in their periodic ''NASA Prediction Bulletins'', which consisted of the transmission format data in printed form. After trying for some time to convince NASA to release these in electronic form, T.S. Kelso took matters into his own hands and began manually copying the listings into text files which he distributed through his [https://celestrak.com CelesTrak] [[bulletin board system]]. This revealed a problem in NASA's [[checksum]] system, which
The SGP4 model was later extended with corrections for deep space objects, creating SDP4, which used the same TLE input data. Over the years a number of more advanced prediction models have been created, but these have not seen widespread use. This is due to the TLE not containing the additional information needed by some of these formats, which makes it difficult to find the elements needed to take advantages of the improved model. More subtly, the TLE data is massaged in a fashion to improve the results when used with the SGP series models, which may cause the predictions of other models to be less accurate than SGP when used with common TLEs. The only new model to see widespread use is SGP8/SDP8, which were designed to use the same data inputs and are relatively minor corrections to the SGP4 model.
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The internal format used three 80-column punch cards. Each card started with a card number, 1, 2 or 3, and ended with the letter "G". For this reason, the system was often known as the "G-card format". In addition to the orbital elements, the G-card included various flags like the launching country and orbit type (geostationary, etc.), calculated values like the [[perigee]] altitude and visual magnitude, and a 38-character comments field.
The transmission format is essentially a cut-down version of the G-card format to make, removing any data that is not subject to change on a regular basis, or data that can be calculated using other values. For instance, the perigee altitude from the G-card is not included as this can be calculated from the other elements. What remains is the set of data needed to update the original G-card data as additional measurements are made. The data is fit into 69 columns and does not include a trailing character. TLEs are simply the transmission format data rendered as ASCII text.
An example TLE for the [[International Space Station]]:
Line 30:
2 25544 51.6416 247.4627 0006703 130.5360 325.0288 15.72125391563537
The meaning of this data is as follows:<ref
===Title line (optional)===
[[File:Tle title.jpg|top|TLE title]]
{| class="wikitable"
Line 44:
|-
|}
If present, the TLE is a three-line element set (''3LE'').
If not, the TLE is a two-line element set (''2LE'').
===Line 1===
Line 58 ⟶ 62:
||2||03–07||[[Satellite Catalog Number|Satellite catalog number]]||25544
|-
||3|| 08 ||Classification (U: unclassified, C: classified, S: secret)
|-
||4||10–11||[[International Designator]] (last two digits of launch year)||98
Line 70 ⟶ 74:
||8||21–32||[[Epoch (astronomy)|Epoch]] (day of the year and fractional portion of the day)||264.51782528
|-
||9||34–43||First derivative of [[mean motion]]; the ballistic coefficient (rev/day, per day)<ref name="nasahelp">{{cite web|url=http://spaceflight.nasa.gov/realdata/sightings/SSapplications/Post/JavaSSOP/SSOP_Help/tle_def.html|archive-url=https://web.archive.org/web/20000301052035/http://spaceflight.nasa.gov/realdata/sightings/SSapplications/Post/JavaSSOP/SSOP_Help/tle_def.html|url-status=dead|archive-date=1 March 2000|title=NASA, ''Definition of Two-line Element Set Coordinate System''|publisher=Spaceflight.nasa.gov|access-date=28 November 2014}}</ref>||-.00002182
|-
||10||45–52||Second derivative of [[mean motion]] (rev/day³, decimal point assumed)
|-
||11||54–61||[[BSTAR|''B''*]], the drag term, or radiation pressure coefficient (units of 1/(Earth radii), decimal point assumed)
|-
||12||
|-
||13||65–68||Element set number. Incremented when a new TLE is generated for this object.<ref name="nasahelp"/>||292
Line 99 ⟶ 103:
||3||09–16||[[Orbital inclination|Inclination]] (degrees)||51.6416
|-
||4||18–25||[[Right ascension of the ascending node]] (degrees), in the [[Earth-centered inertial|ECI reference frame]], measured from the [[vernal point]]||247.4627
|-
||5||27–33||[[Orbital eccentricity|Eccentricity]] (unitless, decimal point assumed)||0006703
|-
||6||35–42||[[Argument of perigee]] (degrees)||130.5360
Line 118 ⟶ 122:
The checksums for each line are calculated by adding all numerical digits on that line, including the line number. One is added to the checksum for each negative sign (-) on that line. All other non-digit characters are ignored.
For a body in a typical [[low Earth orbit]], the accuracy that can be obtained with the SGP4 orbit model is on the order of 1 km within a few days of the epoch of the element set.<ref>{{cite web|
The activation of the [[Space Fence]] in 2020 resulted in a great increase in the number of objects being tracked as the Space Fence's [[S-band]] RADAR is more sensitive than the radars used by the [[Air Force Space Surveillance System]] that previously had generated the raw data used for TLEs.<ref name="CelesTrak"/> The increase in the number of objects tracked meant that [[Satellite Catalog Number]]s may no longer fit in the five-digit field available in traditional TLEs. A secondary cause for the increase in Satellite Catalog Numbers was the commercialization of space and break-up events and collisions that have created debris objects.<ref name="CelesTrak"/> Adaptations of the TLE were considered to extend the number of encodable Satellites within the TLE but instead a new format, the [[CCSDS]] OMM (Orbit Mean-Elements Message), started being used in 2020 that supports nine-digit Satellite Catalog Numbers. The legacy TLE format will continue to use five-digit Satellite Catalog Numbers.<ref name="CelesTrak">{{Cite web|title=CelesTrak: A New Way to Obtain GP Data|url=https://celestrak.com/NORAD/documentation/gp-data-formats.php|access-date=2020-07-29|website=celestrak.com}}</ref>
▲Two-digit Epoch Years from 57 to 99 correspond to 1957-1999 and those from 00 to 56 correspond to 2000–2056.<ref>{{cite web |title=Frequently Asked Questions: Two-Line Element Set Format |publisher=CelesTrak |url=https://celestrak.com/columns/v04n03/}}</ref>
As a stop-gap measure for systems which can only take in five characters for the Satellite Catalog number, the Space Force developed the "Alpha-5" numbering scheme, where the highest digit can be replaced with an alphabetical character to represent higher numbers from 100000–339999. The letters "I" and "O" are skipped to avoid confusion with the numbers "1" and "0". For example, the number 100000 can be represented as "A0000" in the Alpha-5 format, 110000 is represented by "B0000", up to the highest number 339999 which is represented as "Z9999". However, using the nine-digit Satellite Catalog number is preferred.<ref name=":0" />
==References==
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