What is/was legacy TLE ephemeris type 2? (TLE, line 1, column 63)

Question

Wikipedia's Two-Line Element Set entry for line 1, column 63 (1.12) says:

Ephemeris type (internal use only - always zero in distributed TLE data)¹³

¹³Celestrak Frequently Asked Questions: Two-Line Element Set Format

And that says:

Field 1.12 represents the ephemeris type (i.e., orbital model) used to generate the data. Spacetrack Report Number 3 suggests the following assignments: 1=SGP, 2=SGP4, 3=SDP4, 4=SGP8, 5=SDP8. However, this value is used for internal analysis only—all distributed element sets have a value of zero and are generated using the SGP4/SDP4 orbital model (as appropriate).

However, this answer to Will the new “TLE format” be orbitally-mechanically better than traditional TLEs? links to https://www.space-track.org/documentation#/sgp4 (requires login to read content) which is said to say (double block quote because I'm quoting a quote):

To ensure backward compatibility, there is a new Ephemeris Type 4 (XP) now accommodated by the TLE that allows users to use legacy SGP4 Ephemeris Types 0 or 2, or SGP4-XP Ephemeris Type 4 TLEs without changing inputs to the SGP4prop library. This keeps interfaces from changing due to the XP upgrade.

Question: What ephemeris type does the "2" refer to in "legacy SGP4 Ephemeris Types 0 or 2"? Have TLEs ever been released specifying this type? And no matter yes or now, what type does the "2" correspond to?

Answer 1

This has to do with ambiguities in the definitions used for certain terms, and software doing strange contortions to avoid breaking backwards compatibility. The USAF's family of Simplified General Perturbations propagators are based on mean element theories of orbital motion. However, there are multiple ways to define and compute mean motion, and historically the Air Force used two of them mixed together.

In the words of Walter, "by mean elements we understand osculating elements from which short-periodic and long-periodic perturbations of the earth’s potential have been subtracted." Brouwer and Kozai both published their formulas for mean elements in 1959, and they had the same goal, but their implementations selected different perturbations to subtract. They were working so simultaneously that their articles appeared in the same issue of the same journal on successive pages. What exactly the differences between them are is very complicated to state, since both papers are mainly just lists of equations, some of which run to 7 or 8 lines each.

The difference that concerns us here is simply that SGP, the original one without the 4 on the end, uses Kozai mean elements; but SGP4, the one used operationally for the last more than 40 years, uses Brouwer mean elements. When that change was made, however, the USAF decided not to change the TLE format at all, so they are still specified in Kozai form even though that means they need to be converted to Brouwer before use. This topic is treated by Vallado, who also discusses ambiguities in the definition of the coordinate system used for TLEs. Furthermore, it points out that conversions between elements, such as mean motion to or from semi-major axis, need to be done using the WGS-72 model that SGP4 used internally; attempting to use numbers from a newer theory produces worse answers, because inconsistency magnifies inaccuracy. The new SGP4-XP, however, uses EGM-96, which is a nice upgrade, but introduces additional differences between the old Type 0 and new Type 4 TLE.

Type 0 TLE contains Kozai elements, as originally used by SGP not 4, is the one in which data has always been distributed. Type 2 TLE contains Brouwer mean elements, as used internally by SGP4, but Type 2 is never broadcast. It exists during calculation, as transformation from Kozai to Brouwer elements is the first thing SGP4 has to do, but it is not retained in that form, unless you save the intermediate result yourself. If you do that, they should be stored as Type 2, which tells the official US government SGP4 not to duplicate the conversion step it would otherwise have started with. If you are using some other implementation not obtained directly from the US Air Force, it may introduce significant error by double-counting.

Answer 2

I find Ryan C's answer interesting... but I've never actually interpreted the documentation that way. It's difficult to be certain, since all official TLEs have had ephem type 0. But I (and others with whom I've discussed the matter) have assumed that ephem type 0 means "use SGP4 if you've got 6.4 or more revolutions/day; otherwise, use SDP4", and that ephem type 2 means "use SGP4 even if this is a higher object."

In some of my TLEs for cislunar/very high objects, I actually do set ephem type 2, for the simple reason that SDP4 is not able (as best I can tell) to support certain long-period and/or high-eccentricity orbits without diverging. As far as I know, I'm the only one to actually make use of this (and I do it as rarely as possible, i.e., only if the TLE would fail to converge otherwise.)

Be warned, though, that because officially distributed TLEs have only used type 0, much software will probably just ignore the ephemeris type. Mine certainly did, before I ran into the issues with high-altitude artsats.