Using a 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 TLE format is a de facto standard for distribution of an Earth-orbiting object's orbital elements.
The title is not required, as each data line includes a unique object identifier code.
In the early 1960s, Max Lane developed mathematical models for predicting the locations of satellites based on a minimal set of data elements.
[5] 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.
The improved version became the standard model for NORAD in the early 1970s, which ultimately led to the creation of the TLE format.
Cranford continued to work on the modelling, eventually leading Lane to publish Spacetrack Report #2 detailing the Air Force General Perturbation theory, or AFGP4.
One year later, Spacetrack Report #3 was released, included full FORTRAN source code for the SGP4 model.
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.
[10] The SGP4 model was later extended with corrections for deep space objects, creating SDP4, which used the same TLE input data.
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.