I found the following "far out" spacecraft:
- TESS (Transiting Exoplanet Survey Satellite) recently launched, not in final orbit yet
- Spektr-R
- IBEX or Interstellar Boundary Explorer
- Geotail
Here are there IDs:
TESS 43435 2018-038A
Spektr-R 37755 2011-037A
IBEX 33401 2008-051A
Geotail 22049 1992-044A
I downloaded both TLEs and orbit data from JPL Horizons in order to piece together this qualitative data.
The problem is that for such high orbits, the gravity of the Sun and the Moon can push them around significantly so their obits change over time, sometimes by quite a bit!
The all-time winner (of the four that I found) seems to be Geotail. Using historical TLEs shows Geotail's maximum semi-major axis of about 280,000 km or about 44 Earth radii, and a maximum apoapsis of orver 500,000 km or about 81 Earth radii. However, according to Wikipedia, Geotail's maximum distance from the Earth reached 210 earth radii, or over 1,300,000 km from the Earth! This would not likely have been long term stable, and so after sampling the tail of the magnetosphere out there it was ramped down closer to Earth.
I have two plots for TESS, both current data from TLEs and future data (the big DOT) after it will use a close swing-by maneuver with the Moon and then another propulsive maneuver in order to reach it's half lunar month orbit. Once that happens, TESS will be the longest period artificial satellite around the Earth, at least one with a fairly stable orbit and whose information is available publicly.
TESS has this orbit in order to spend most if its time staring at nearby stars looking for exoplanets, then it makes a close pass by Earth to download data, once every two weeks.
You can read more about how TESS' orbit works in this answer to the question TESS orbit and moon resonance.
I've put a plot of TESS' calculated orbit from Horizons below. The green, tightly repeating orbit is the Moon's the red, inclined, evolving, changing orbit is for TESS only for a few years. It's alamost a miracle that it can remain so close to it's orbit. Well, it's "just F=ma" (roughly), but it's still beautiful!
TESS might represent the highest non-Lagrangian Geocentric orbit that is stable over decades. It was carefully designed to have half the period of the Moon in order to cancel out perturbing effects. It is called a 2:1 resonant orbit. For orbits higher than that, lunar perturbations may become problematic.
Earth-Moon Lagrange orbits are Geocentric orbits that are in 1:1 resonance with the Moon (they are not lunar orbits). They will have their own stability issues and require station keeping. A particularly stable Geocentric orbit which is associated with the Earth-Moon Lagrange points is the Near Rectilinear Halo Orbit. Read more about it in the questions and their answers:
The Halo orbit associated with the Earth-Moon Lagrange L1 and L2 points are probably the highest Geocentric orbits that are also usefully stable. Instead of being perturbed by the Moon's gravity, they remain in resonance with it and use it to provide additional stability. However, they still require station keeping.
- Why is a near rectilinear halo orbit proposed for LOP-G (formerly known as Deep Space Gateway?)
- What is a near rectilinear halo orbit?
- LOPG/Deep Space Gateway - What is a cislunar orbit?
