Bruce McCandless and Robert Stewart, mission specialists on the Space Shuttle Challenger during STS-41-B, used nitrogen-propelled maneuvering units to perform the first untethered spacewalks #OTD in 1984.

Images: NASA
https://www.flickr.com/photos/nasacommons/9449352571/in/photolist-fq3fDN-fp1oz4-fpfDTJ-fp1piV-8PHqJi-pa383r-wzDSb8/

This photo shows Bruce McCandless a football field away from the shuttle, with no tether.

No astronaut had ever been that far from their ship while in space.
Image: NASA

There’s trusting the laws of orbital mechanics on paper, and then there is strapping yourself into a maneuvering unit and wandering off from your ship while moving at 7 km/s more than 300 km above the surface of the Earth.

When you are a human satellite.

Image: NASA

Bruce McCandless’s spent about two hours untethered during this EVA, and the orbital period of the shuttle was just over 90 minutes. So unless I’m missing something, McCandless completed a full orbit of Earth disconnected from the shuttle.

I believe this record still stands. No one since has ventured further away from their ship. https://twitter.com/mcnees/status/1358444500578930699