Artemis II crew splashes down near San Diego after historic moon mission

NASA's Artemis II astronauts returned to Earth with a splashdown landing in the Pacific Ocean after making a high-speed reentry through the atmosphere.

Glad that they're safe and sound.

It's worth pointing out that this is the first extremely public, widely acknowledged high risk mission NASA has done in over 50 years. The Shuttle was risky, but it wasn't thought of or acknowledged by NASA as being risky until very late in its lifecycle.

According to NASA's OIG, Artemis acceptable crew mortality rate is 1 in 30. Roughly 3x riskier than the shuttle. There genuinely is a world where they don't make it back home.

I am grateful that they did. And I'm grateful that we're going to go even further. I can't wait to see what Jared's cooking up (for those who don't know, he made his own version of the Gemini program in Polaris and funded it out of pocket).

An error in any of the orbital math may have seen them flung out into space with no chance of recovery.
Orbits do not work that way

The craft has aerodynamics and speed. It might be figuratively true "unrecoverable" but if it takes e.g. 2 weeks to complete a return, their oxygen and food and batteries ran out. Alternatively if it enters too fast they return ... in pieces.

I think you're being a pedant, if your point is a grazing entry causing rebound skip ultimately returns to some orbital path downward.

You seem to intentionally be ignoring the original quote that any error may have caused them to be flung into space. This is patently false unless the one math error is pumping in hundreds of pounds more propellant and burning far longer than the scheduled burns. NASA would need to make a significant series of mistakes beyond orbital math for the "flung out into space" statement to be true.

They certainly could've gotten the return wrong but with a perigee of 119 miles they arent even in a stable orbit and likely could deorbit themselves using only rcs thrusters at apogee, or by just waiting a few orbits.

This is underselling the risks. On top of the many trajectories which push them into unrecoverable situations, leaving them stranded in orbit, there can be trajectories where the moon gives a gravity assist strong enough to fling the spacecraft into escape velocity, fulfilling the OP.

In fact, the trajectory they chose for this mission exploited the opposite effect to yield a free return without propellant expense.

In the modern day, the chance of a math error being the root cause behind this failure mode are vanishingly small, but minor burn execution mistakes that do not require hundreds of extra pounds of propellant are definitely plausible. They were extremely common in the early days of spaceflight and plagued most of the very first moon exploration attempts. Again, with modern RCS this is unlikely. But reentry is still incredibly tight and dangerous. Apollo famously had a +-1° safe entry corridor, and Orion is way heavier and coming in even faster. If their perigee was off they could’ve easily burned up or doubled their mission time, which they may not have been able to survive.