[7373737373]

In 1957, two months before the Sputnik 1 launch, a steel cap covering an underground nuclear explosion test, although unlikely, may have been the first object reaching greater then orbital, in fact escape velocity from earth: https://en.wikipedia.org/wiki/Operation_Plumbbob#Missing_ste...

[david_draco]

Does it really count if it is vaporized before leaving the atmosphere?

[7373737373]

These calculations suggest that it indeed probably vaporized within a few meters due to the insane amount of heat: https://physics.stackexchange.com/questions/488151/could-the...

[beerandt]

That meteor equation isn't the right one to use. It's based on assumptions that don't apply here. It has to be re-derived, at a minimum, if it can even be repurposed.

Any dt equation like that should have some value of X_final-X_initial for any constants that change.

For rho, he plugs in rho_initial for rho_final. And rho_initial in space is zero, so it likely got dropped from the equation when it was derived.

That said, if it even survived the initial xray ablation, yeah, it probably burnt up before reaching space, or at least slowed down enough that it came back down.