Two lines of numbers that describe an orbit.

What a two-line element set (TLE) contains, how the SGP4 model turns it into a satellite position, what the epoch means, and why predictions become less reliable as the data ages.

Every dot in Orbit Atlas starts life as a short block of text. For decades, the standard way to share the orbit of a satellite has been the two-line element set, or TLE: two lines of 69 characters each, packed with numbers. Feed those numbers into the right mathematical model and you can estimate where the satellite is at any moment. This guide explains what is in those two lines, how they become a position, and why you should always look at how old they are.

Who produces the numbers

Objects in orbit are tracked by networks of radars and optical telescopes, such as the GEODSS site in the photograph above. ESA estimates that space surveillance networks now track about 40,000 objects, of which about 11,000 are active satellites. The rest are old satellites, spent rocket stages and fragments.

The United States Space Force maintains a public catalog of these objects and publishes orbital elements for them. CelesTrak, a long-running service created by Dr T.S. Kelso, redistributes much of that data in convenient form. Orbit Atlas uses a dated subset retrieved from CelesTrak, credited on the about page.

What the two lines contain

CelesTrak's format guide describes each field in detail. You do not need to memorize them, but a few are worth recognising.

Line 1

• Catalog number: a unique identifier for each object, often called the NORAD number. The International Space Station is 25544.
• International designator: the launch year, the launch number of that year, and a letter for each piece from that launch.
• Epoch: the moment the elements describe, written as a two-digit year followed by the day of the year with a fractional part. For example, 98001.00000000 means midnight UT at the start of 1 January 1998.
• BSTAR: a drag term describing how strongly the object is slowed by the thin upper atmosphere.
• Checksum: the last digit of each line is a simple error check.

Line 2

• Inclination: the tilt of the orbit relative to the equator, in degrees.
• Right ascension of the ascending node: where the orbit crosses the equator heading north, which fixes the orientation of the orbital plane in space.
• Eccentricity: how far the orbit is from a perfect circle.
• Argument of perigee and mean anomaly: where the lowest point of the orbit is, and where the object is along its orbit at the epoch.
• Mean motion: how many orbits it completes per day. The space station is close to 16.

Together, these describe the shape of the orbit, its orientation and the satellite's place on it at one instant.

From numbers to a position: SGP4

A TLE is not a direct measurement of position. It is a set of mean elements, fitted for use with a specific model called SGP4 (and its deep-space variant SDP4 for higher orbits). CelesTrak's guide notes that all distributed element sets are generated using the SGP4/SDP4 model, so they are meant to be used with it rather than plugged into a different orbit model.

SGP4 takes the elements and a target time and calculates where the satellite should be, accounting in a simplified way for Earth's uneven gravity and atmospheric drag. Orbit Atlas runs SGP4 in your browser through the open-source satellite.js library, which is why it can show predicted paths without contacting a server.

Why predictions get worse with time

The epoch is the most important number for anyone using a TLE. Predictions are best close to that moment and become less reliable the further you move away from it, forward or backward.

There are several reasons.

• Drag changes. The density of the upper atmosphere rises and falls with solar activity. A burst of activity can increase drag on low satellites, so they descend faster than the elements assumed.
• Manoeuvres. Operators fire thrusters to raise orbits, avoid debris or keep stations. A TLE published before a burn knows nothing about it.
• Model simplifications. SGP4 is designed to be fast and general, not perfect.

The International Space Station shows how much this matters. NASA's Spot the Station explains that the thin atmosphere at the station's altitude causes the projected trajectory to accumulate small errors, so flight controllers update the trajectory data about three times a week.

For this reason, Orbit Atlas shows the age of each element set. When the median epoch in its catalog is more than seven days old, the globe switches to explicitly historical time, and pass predictions exclude stale elements. A position estimate is only as fresh as its data.

Reading a TLE yourself

You can find a current TLE for most public satellites on CelesTrak. Try reading one:

1. Check the catalog number on both lines matches. If not, the lines belong to different objects.
2. Decode the epoch to see how old the data is.
3. Look at the inclination on line 2 and compare it with the inclination guide.
4. Divide 1,440 (minutes in a day) by the mean motion to get the orbital period in minutes.

For the space station, the result will be about 92 to 93 minutes, which matches NASA's figure of about 16 orbits a day.

A format with limits

The format dates from the early 1970s and shows its age. The two-digit year has to be interpreted: by convention, 57 to 99 mean 1957 to 1999 and 00 to 56 mean 2000 to 2056. The five-digit catalog number also runs out at 99,999. To deal with this, newer formats carry the same information in more flexible ways, including formats based on standards from the Consultative Committee for Space Data Systems. NASA, for example, publishes the space station's trajectory as an Orbit Ephemeris Message.

The principle is the same either way: a satellite position on a screen is a calculation from data captured at a specific time. Keep an eye on that time, and you will know how much to trust the dot. To see the effects of drag in action, read why GPS flies 20,000 km up and the ISS only 400.