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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]]
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 websites Space Track and Celestrak,<ref>{{cite web|url=https://www.space-track.org/|title=Introduction and sign in to Space-Track.Org|publisher=Space-track.org|access-date=28 November 2014}}</ref><ref>{{cite web|url=http://celestrak.com/|title=Celestrak homepage|publisher=Celestrak.com|access-date=28 November 2014}}</ref> holding back or obfuscating data on many military or [[Classified information|classified objects]]. The TLE format is a ''de facto'' standard for distribution of an Earth-orbiting object's orbital elements.
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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 tech report |url=http://celestrak.com/NORAD/documentation/ADCOM%20DO%20Form%2012.pdf |title=ADCOM Form 2012}}</ref> The latter saved on cards and produced smaller decks when updating the databases.
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 tech report |first1=Max |last=Lane |first2=Felix |last2=Hoots |title=General Perturbations Theories Derived from the 1965 Lane Drag Theory |publisher=Project Space Track, Aerospace Defense Command |date=December 1979 |url=http://apps.dtic.mil/dtic/tr/fulltext/u2/a081264.pdf |archive-url=https://web.archive.org/web/20150709125624/http://www.dtic.mil/dtic/tr/fulltext/u2/a081264.pdf |url-status=live |archive-date=July 9, 2015 }}</ref> The differences between the three models were slight for most objects. One year later, ''Spacetrack Report #3'' was released,
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]]:
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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)===
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||2||03–07||[[Satellite Catalog Number|Satellite catalog number]]||25544
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||3|| 08 ||Classification (U: unclassified, C: classified, S: secret)
|-
||4||10–11||[[International Designator]] (last two digits of launch year)||98
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||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)
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||12||
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||13||65–68||Element set number. Incremented when a new TLE is generated for this object.<ref name="nasahelp"/>||292
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||3||09–16||[[Orbital inclination|Inclination]] (degrees)||51.6416
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||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
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||5||27–33||[[Orbital eccentricity|Eccentricity]] (unitless, decimal point assumed)||0006703
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||6||35–42||[[Argument of perigee]] (degrees)||130.5360
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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
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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