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I found the following "far out" spacecraft:

note: @BillGray's answer of XL8D89E is the highest and the correct answer!

I found the following "far out" spacecraft:

Here are there IDs:

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.

I've put a plot of TESS' calculated orbit from Horizons below. The green, tightly repeating orbit is the Moon's. The red orbit, inclined, evolving, changing orbit is for TESS only for a few years currently in the Horizon's simulation. It's almost a miracle that it can remain so close to it's orbit. Well, it's "just F=ma" (roughly), but it's still beautiful!

Here are their IDs:

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 over 500,000 km or about 81 Earth radii. However, according to the Japanese space agency's website (see also Wikipedia), the orbit is designed to cover the magnetotail over a wide range of distances: 8 Re to 210 Re from the earth. This is over 1,300,000 km from the Earth! In fact, some sections of that site and those of NASA/ESA suggest the maximum apogee may have been an even higher 220 Re, over 1,400,000 km distant!

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 its 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 of its time staring at nearby stars looking for exoplanets, then it makes a close pass by Earth to download data, once every two weeks.

I've put a plot of TESS' calculated orbit from Horizons below. The green, tightly repeating orbit is the Moon's. The red orbit, inclined, evolving, changing orbit is for TESS only for a few years currently in the Horizon's simulation. It's almost a miracle that it can remain so close to its orbit. Well, it's "just F=ma" (roughly), but it's still beautiful!

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 problem is that for such high orbits, the gravity of the Sun and the Moon can push them around significantly so their orbits change over time, sometimes by quite a bit!