Tracking Objects in Space: The Rise and Reign of Two-Line Elements

Brief History of TLEs

Keeping track of objects in space is no easy task. The first real concerted effort to systematically track earth orbiting satellites started back in 1957, with the launch of Sputnik 1. The US government quickly realized they needed a way to keep track of all the objects in space and thus, Project Space Track was born. In the early days, tracking was done through a combination of radar, telescopes, radio, and even citizen observations. These observations were then manually reduced, and corrections were determined in order to generate orbital elements that could be used for predictions.

The goal was to develop a method that would provide a fast-updating situational report of objects in space using the computing power that was available at the time for “large-scale space applications and simulations” (Hujsak, 1979). In pursuit of a concise data format for efficient data processing, Two-Line Elements (TLEs) were created to describe the orbits of objects in space. This ultimately led to the creation of SpaceTrack Report 2 (Lane and Hoots, 1979) and the adoption of the TLE format by the North American Aerospace Defense Command (NORAD). The model used to generate this data, Simplified General Perturbations 4 (SGP4), is an analytical model that eventually became the go-to model for commercial and scientific spacecraft operators.

What are TLEs? How are they made today?

But what exactly are TLEs? A single TLE is a two-line, 69-character description of a satellite’s identity, orbital geometry (using Keplerian elements), the orbit epoch for which this information was generated, and a term related to the ballistic coefficient (B-star). The TLE format is described in more detail in Vallado (2006). However, it’s important to note that the B-star term is widely understood to be somewhat problematic as the simplified force modelling and the way in which the data is processed means that this term ends up serving as a catch-all term for model errors (Vallado, 2006).

Today, TLEs are generated from a variety of data sources, such as radars, optical sensors, and in-orbit sensors. All these sources fall under the United States Space Surveillance Network (USSSN), as seen in the image below.

Since March 1998, T.S. Kelso has been pioneering the dissemination of TLEs through his website Celestrak.org. TLEs are now generated by the 18th Space Control Squadron (18th SpCS) and shared through their website (space-track.org). Spacetrack serves as the de-facto source of data for a multitude of SSA products the community relies on. These include but are not limited to conjunction (collision) data messages, decay and re-entry predictions.

More recently, Celestrak has also started sharing Operator TLEs for certain spacecraft. Operator TLEs (also referred to as Supplemental TLEs or SupTLEs) are TLEs that are “derived directly from owner/operator-supplied orbital data” instead of 18th SPCS measurements. This type of TLE is valuable as the operator-supplied orbital data used to generate them is typically derived from on-board GNSS receivers (Murley, 1982a), or operator ephemerides (Johnson, 2022), both of which are usually orders of magnitude more accurate than TLE data. When fit to high-accuracy ephemerides (e.g.GPS SEM Almanac orbits), these TLEs can be orders of magnitude more accurate than a run-of-the-mill NORAD TLE (Supplemental TLE Link). In practice, this means going from multi-kilometre error (~5-10 Km) to sub-kilometre error (~0.85 Km)

The graph below illustrates the performance of NORAD TLEs against supplemental TLEs on GPS spacecraft (work by T.S.Kelso. See https://celestrak.org for more information).

Limitations of TLEs

Whilst TLEs are the current bedrock of many SSA products, one should be aware of their (many) limitations. For example, TLEs are generated by fitting tracking data to the SGP4 force model (using batch-least squares), which while widely used, remains relatively inaccurate compared to state-of-the-art propagators. This saves on computational cost but also on accuracy.

TLEs are provided without any information pertaining to their accuracy (covariance matrices). This is done purposefully by the 18th Space Control Squadron to limit the ability of external parties to infer information about the sensors the USSSN disposes of. Furthermore, utilizing TLEs fitted to SGP4 with other force models will result in degraded performance. This means that, unfortunately any TLE is “stuck” with the SGP4 force model. Additionally, the accuracy of TLEs is known to degrade rapidly over time. They must be updated frequently with new tracking data to keep providing a representative picture of reality.

Despite these limitations, TLEs remain a valuable tool to provide a quick and efficient way to track and predict the orbits of objects in space and are widely used by spacecraft operators and other organizations involved in space activities. The recent addition of Operator TLEs, which are derived from more accurate operator-supplied data, adds an extra level of precision to TLE predictions.

TLEs have played a crucial role in the development of space monitoring and traffic management since the launch of Sputnik 1. The TLE format, while not without its limitations, provides a concise and efficient way to track and predict the orbits of objects in space. As space traffic continues to increase, it’s essential that the valid use cases of TLE continue to be monitored and that the space traffic management community continues to build tools that meet their ever-evolving needs. The recent addition of a public facing repository of Operator TLEs is an example of a tool that helps to improve the safety of space operations.