Update 2022-02-14: It now turns out that it's not a Falcon 9 upper stage, it's a Chang'e 5-T1 booster ( 2014-065B).
The misidentification came from the coincidence that the tracked object passed by the moon a few days after the DSCOVR launch and thus was circumstantially assumed to be the DSCOVR second stage.
This is (almost) entirely based on Bill Gray's fantastic webpage covering this event (he is the only reason that this is an event). I have very little to add so I apologize if this is 'link-only-eqsue'
Bill Gray has been doing the tracking of 2015-007B (40391). There are TLE's, but there was a 5 year gap in data and the most recent TLE is from Sept-2021 (mean elements, use with caution):
Bill Gray provides pseudo TLEs:
Can you provide TLEs for it?
Unfortunately, no. The orbit goes well past the moon and has an
eccentricity of about 0.89. The 'usual' SGP4/SDP4 model for two-line
elements (TLEs) fails in such cases. I have posted "TLEs" for this
object; I use these to generate ephemerides and to identify the object
from observations... and they work with my code and (probably) nobody
As Bill Gray puts it his involvement is:
My "day work" is for the asteroid hunting community. The big surveys (Catalina Sky
Survey, ATLAS, Pan-STARRS, and ZTF) observe on most clear, moonless
nights, imaging the sky for slowly moving objects. [...] But there are about a dozen
"high-flying" objects that can move slowly enough to look like a rock,
at least briefly.
For about fifteen or twenty years now, I've taken these observations
and computed orbits. Then, when the surveys find such objects, they
can fairly quickly say "never mind; it's not a rock; it's just another
nuisance artificial object", and go back to looking for actual rocks.
If it wasn't for that, these objects would go untracked. Objects in
lower orbits are very carefully tracked, [...] High-altitude payloads are carefully tracked; these are all scientific missions, and you need to know where
they're going. For example, NASA can tell you where the James Webb
Space Telescope is quite precisely, but they lost interest in its
booster once it separated from JWST. (I did not; the JWST booster is
being tracked as it goes into orbit around the sun and its orbit
Generally speaking, high-altitude junk goes ignored. (Except, it
appears, by me.)
A detailed rundown of the tracking timeline since 2015 is given on the website. Essentially, (professional?) telescopes reported observations for a provisional "WE0913A" near Earth object. Bill Gray used these observations (and subsequent ones) to refine the object's orbit and "back-predict" it to a lunar flyby in 2015 that matches the one the DSCOVR spacecraft (and thus rocket body) did. He has tracked it ever since.
Recent observations were specifically targeted (professional or amateur: I've no grounds to judge):
Bill Gray uses these observations with his custom software find_orb (on Github) to propagate the object's orbit and thus found the lunar impact date, time, and position.
The propagator appears to use a Runge-Kutta-Fehlberg 7(8) integrator.