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. 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 preceding 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 latter saved on cards and produced smaller decks when updating the databases.