This excellent answer to the question Why has no TLE been published for the DSCOVR satellite and the Falcon 9 R/B? suggests that to the best of the writer's knowledge TLEs are only issued for spacecraft in Earth orbit, presumably meaning a gravitationally bound orbit (rather than a hyperbolic one).

However, I'm thinking that it is certainly conceivable that one might be issued for a spacecraft executing a flyby maneuver of Earth if it is low enough and could potentially interact with other satellites as a precaution.

Then again, I'm thinking that this might be useless/meaningless since the format of a TLE requires a value for mean motion (revolutions/day) and there is no way the other parameters have enough information to describe an orbit without some way to communicate the semi-major axis, which would be negative for a hyperbolic fly-by.

Since Two-Line Element sets actually contain a blank space at column 52 (see Wikipedia and Celestrak) where a minus sign could potentially be inserted, in some universe it might be possible to actually do this. Also, Three-Line Element sets are at least defined (see Celestrak PDF) though I am not sure how often they are used, and columns 11 and 12 of card 3 are explicitly labeled "orbit type".

Question: So I'd like to know if a Two-Line or Three-Line Element set has ever been issued for a spacecraft trajectory not bound to Earth orbit, or if in fact none have, then in that case if one could be issued if necessary. Looking for a well-supported, factual answer, not just a "not to my knowledge" response.


Unfortunately, you can't generate a TLE for a parabolic or hyperbolic flyby. The eccentricity must be between 0 and 1, and the semimajor axis must be positive. In some cases, you can't even find a TLE that fits a very high (week or longer) period orbit, though that limitation can vanish if you explicitly use the SGP4 propagator (i.e., set the "ephemeris type" byte to 2). I do exactly that when computing TLEs for some very high earth orbiting objects :


Space-Track, with rare exceptions, does not provide TLEs for objects in this sort of high orbit. In the cases they've done so, the TLEs have either been for an object where SDP4 did fit, or the TLEs were rubbish.

It would be a lot more convenient for me and the people I work with (astronomers looking for and tracking near-earth asteroids) if TLEs had a greater degree of flexibility. But they don't.

The lack of a sign for eccentricity isn't a problem. An orbit with a negative eccentricity is equivalent to one with the sign flipped, 180 degrees added to/subtracted from the longitude of periapsis, and 180 degrees added to/subtracted from the mean anomaly. The fact that you can't store a parabolic or hyperbolic orbit in a TLE is a little more problematic, but just means you have to use some other format. See, for example, the elements for Cassini during its "encounter at Earth" :


But there's no "standard" format for orbital elements capable of handling any eccentricity or central object. I've tried to push one through, which has gotten zero acceptance, but the discussion should illustrate the general problems involved :


  • $\begingroup$ This is an interesting answer! I see what you mean, of four high-fliers I know of (Geotail, IBEX, Spektr-R and TESS) only Geotail shows a TLE in Celestrak (the other three a "lost" which I'll ask about separately). When you say "must be between 0 and 1, and ...must be positive" do you mean it is constrained by the TLE format, or by SGP4, or by decree? Can you clarify and support with a link? Thank you very much! $\endgroup$ – uhoh Apr 16 at 0:47
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    $\begingroup$ The eccentricity is constrained both by the TLE format (eccentricity is stored as seven digits with an implied leading decimal point) and the SDP4/SGP4 format. For example, at various points, quantities such as sqrt(1-e^2) are computed which would get you imaginary/complex values. Kepler's equation is solved in a manner that assumes elliptical orbits. And so on... format explanation is at projectpluto.com/tle_info.htm (and I'd recommend the Wikipædia and Celestrak columns linked therefrom.) $\endgroup$ – Bill Gray 2 days ago
  • $\begingroup$ A minus sign for eccentricity could be flagged using one of the unoccupied columns, as I pointed out in the question. It could direct a future SGP4 implementation to go to a negative eccentricity algorithm, the same way that periods longer than 225 minutes go to SDP4 instead of "SGP4 classic". But I have to agree that the chances of this ever having happened are getting lower by the minute ;-) So even though (as you said here) that it is hard to prove a negative, I'm going to accept your excellent answer and move on with my life ;-) $\endgroup$ – uhoh 2 days ago
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    $\begingroup$ Added a comment explaining that you can turn every negative eccentricity case into a positive eccentricity case. There would also be ways to 'extend' TLEs to handle parabolic/hyperbolic orbits, and in fact, I do just that in some of my software... but with zero expectation that anyone else would adopt the scheme, useful though it is for my particular purposes. $\endgroup$ – Bill Gray 2 days ago

No — TLEs are meant for a particular family of algorithms that are designed for trajectory propagation of Earth-orbiting spacecraft (the Simplified Perturbation Models).

What you can find instead, are state fixes (t, r, v) in a given frame, relative to a given center, issued as some kind of ephemerides. For example, JPL produces SPK files for all of its spacecraft.

You can propagate any point-mass trajectory as long as you know the initial state (six variables) and time, and an “appropriate” algorithm. “Appropriate” can be as easy as a two-body problem, or as complex as a proprietary algorithm that considers all known forces and attitude dynamics.

  • $\begingroup$ Can you support this with some supporting information, for example, a document that states this explicitly re TLE generation? I understand that two and three-line element sets are generally used for items orbiting the Earth, but that does not a priori show that they are fundamentally incapable of doing this. Remember SGP4 did not used to be able to apply the "deep-space" corrections (Moon and Earth effects) until it was later merged with SDP4, even though the TLEs were already being generated for both! See this question for example. $\endgroup$ – uhoh Jan 6 '18 at 15:40
  • $\begingroup$ As you can see in the link celestrak.com/NORAD/documentation/spacetrk.pdf, the SGP/SDP models are Earth-specific. $\endgroup$ – Escualo Jan 6 '18 at 15:44
  • $\begingroup$ OK grab the appropriate section and include it as a block-quote in your answer, rather than as a comment. Remember, that's a description of some of the algorithms for propagation (and not necessarily an absolutely complete one), not primarily a specification for their generation. $\endgroup$ – uhoh Jan 6 '18 at 15:46
  • $\begingroup$ It's possible that something in this discussion of project pluto projectpluto.com/sat_code.htm might (or might not) be helpful. $\endgroup$ – uhoh Jan 6 '18 at 16:23

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