How high above the Moon are Artemis' Orion spacecraft going to orbit, in comparison to the Apollo spacecraft? Will their flights surpass or be able to surpass humanity's current record of the farthest voyage from Earth set by Jim Lovell, Jack Swigert and Fred Haise? Artemis 2 is going to perform a similar circumlunar flight pattern, after all.
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Apollo 13 took the record mainly because the moon was near the apogee of its orbit at the time they passed it - the distance to the moon can vary by up to 50,000 km over the course of a month.
(The "maximum possible altitude above Earth's surface" for an Apollo mission orbiting at ~150 km would be I think 402,220 km - the maximum distance between the two centres, less the Earth's radius to count it from the surface, plus the Moon's radius to count it from the back side, plus orbital distance. This is only about 2050 km higher than Apollo 13 managed.)
This summary of the flight plan for Artemis II (dated 2018, so caveat emptor - it may have been developed since then) quotes a mean altitude of 4000 nmi over the Lunar farside - 7400 km.
This would equate to a maximum "distance from the surface of Earth" of 409,740 km at the Moon's apogee, but only 359,250 at perigee. So it will very heavily depend on where the Moon is at the time. They have a decent chance of breaking the record - eyeballing the graph I would say at a wild guess maybe one in four or five? - but I don't think we can say for sure without having the exact date to work with.
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$\begingroup$ The currently planned date is May 2024 but I guess we need to know the day more precisely. $\endgroup$– user46063Jan 4, 2022 at 18:19