A two-line element set (TLE) is a data format encoding a list of orbital elements of an Earth-orbiting object for a given point in time, the ''epoch''. Using suitable prediction formula, the 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.
The format uses two lines of 80-column ASCII text to store the data, having originated as punch card format with one line per card. The United States Air Force tracks all detectable objects in Earth orbit, creating a corresponding TLE for each object, and makes available TLEs for non-classified objects on the website Space Track.〔(【引用サイトリンク】title=Introduction and sign in to Space-Track.Org )〕〔(【引用サイトリンク】title=Celestrak homepage )〕 The TLE format is a ''de facto'' standard for distribution of an Earth-orbiting object's orbital elements. TLEs can describe the trajectories only of earth orbiting objects.
A TLE set may include a title line proceeding the element data, so each listing may take up three lines in the file. The title is not required, as each data line includes a unique object identifier code.
The two-line format traces its history to seminal work by Max Lane in the early 1960s to develop 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. Joined by K. Cranford, the two published a greatly improved model in 1969 that added various harmonic effects due to Earth-Moon-Sun interactions and various other inputs.
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 cards, 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. The later 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. The differences between the three models were slight for most objects. One year later, ''Spacetrack Report #3'' was released, included full FORTRAN source code for the SGP4 model. This quickly became the ''de facto'' standard model, both in the industry as well as the astronomy field.
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, Ted Kelso took matters into his own hands and began manually copying the listings into text files which he distributed through his CelesTrak bulletin board system. This revealed a problem in NASA's checksum system, which traced back to the lack of the plus character (+) on the teletype machines used at NASA, which ultimately turned out to be a problem from the punch card era that occurred when NORAD updated from the BCD to EBCDIC character set on the computer sending out the updates. This problem went away when Kelso began to receive data directly from NORAD in 1989.
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 that 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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