# Can someone explain to me the TEME reference frame in defining orbital coordinates?

I am undertaking a project of developing a "surface station" for my desktop, which will track the position of different satellites as they fly overhead. I have zero background in astrophysics and the such, but I have learned a ton so far.

I understand the importance of defining orbits to an ECI (earth-centered inertial) reference frame. From this, I can either translate my position on Earth to the ECI reference frame, or translate the satellites position from the ECI, to my ECEF (earth-centered, earth-fixed) reference frame.

I followed this article here, where we determine my local sidereal time, by determining the Greenwich sidereal time, which from what I understand, is the conversion between the x-axis in the ECI reference frame, to the ECEF reference frame (with the prime meridian as the x-axis). This Greenwich sidereal time, we use (what I assume to be) an empirical formula to determine the angle, with some time from the J2000 epoch.

Where I am getting confused now, is that apparently TLE (two-line element) data from satellites use a TEME (true equator, mean equinox) ECI reference frame, which a given epoch time with the TLE data.

My question then is, how do I determine the Greenwich sidereal time from a given TEME reference time - it makes sense to me when we have a well defined J2000 epoch - but doesn't make sense to me if this epoch time is changing every time TLE data is published.

Sorry if some of this doesn't make sense, I am trying to learn and any help would be greatly appreciated.

• Welcome to Astronomy SE! Could you please add some details regarding what some of your acronyms are? Also, congrats on posting our 11,000th question! (as of 6/2/2021) Jun 2 at 22:05
• Thanks, I think I have now defined all acronyms. Jun 2 at 23:34

WARNING: This is an attempt to answer. The reason is that I thought I understood the TEME concept until, trying to answer your question leads me to be more cautious. Especially, when I discovered that "TEME" may have different definitions, interpretations, in various implementations of SGP4 (cf ).

My answer will be based largely on this paper .

First, we all know that TEME is in the class of ECI (non-rotating) reference systems, with the prime direction (X) pointing along the Vernal Equinox and the Z direction is the CEP (Celestial Ephemeris Pole). That's good so far, provided that this Z direction doesn't move wrt to the stars (Celestial Sphere). Yet it does! Wrt to the Celestial Sphere, Earth orbital trajectories have a nutation and a precession. With this in mind, we must understand first the difference between "true" and "mean" used in TEME. Wiki (https://en.wikipedia.org/wiki/Equatorial_coordinate_system) gives a clear definition: "true" is when all variations are accounted for and "mean" is when oscillating variations are ignored (eg "small periodic oscillations of nutation").

What does "true Equator" mean? According to my reading, it means the plane perpendicular to the CEP at a given specified time. The mean Equator is the plane perpendicular to an axis computed from the CEP from which the nutation terms are excluded.

What does "mean Equinox" refer to? It means the Equinox located on the "mean Equator". This is better explained in , page 4, just before Fig.1, which I also reproduce here. In this Fig. we can see that the "Mean Equinox", in the TEME sense, is on the "True Equator" plane, but it is not the intersection of this True Equator with the (true) Ecliptic (so not really an Equinox in its classical sense!). As implied by Fig. 1, you have to take the intersection between the Ecliptic and the "Mean Equator" (Equator computed with precession equation, but ignoring nutation), then project it to the "True Equator". The "of date" term means that the precession is taken into account. The precession is a slow motion of the CEP with a perod of 25700 years.

I feel that my answer is correct. But I apologize in advance if my interpretations are wrong!