The Mathematics of Artemis II's Return

On April 10, 2026, Orion came home from the Moon with four people inside, hitting the top of the atmosphere at about 24,660 miles per hour. This paper works through the whole trip back: the free-return path around the Moon, the small burns that aimed it, the modified skip entry, the heat shield that had to survive it, and the parachutes that set the capsule down off San Diego.

It is built from first principles and a few rounded orbital values. The model’s entry speed lands within 0.3 percent of what NASA reported, and where the model and the mission disagree, the paper says so.

I wrote this in April 2026, before the series started, and corrected it in September 2026.