A Sorrowful Shooting Star

I'm currently reading a book suggested by my brother called House of Suns.  It's about an interstellar civilization divided into familial factions with an uneasy peace.  A recently-read portion concerned the funeral rites of a character from one of the families.  The deceased is raised into the air by a platform,

Not long after, [redacted] reached space and the platform tilted to release [them] for [their] long fall back to Neume's atmosphere.  We watched as [they] scratched a line of glorious fire across the sky...

 This passage gave me pause, because I thought I recalled that Felix Baumgartner's record-setting 2012 skydive was technically from space.  It turns out his dive was from 39 km above the surface, while space is defined to begin at the Kármán line, 100 km up.

Aerodynamic heating is caused by the friction between an object and the air it passes though, and is proportional to the object's kinetic energy, given by

where m is the object's mass, and v its velocity.  We can consider how much extra energy something would have after falling from 100 km to 39 km from the gravitational potential energy

where g is the acceleration due to gravity, and h is the distance fallen.  Using the average human mass of 62 kg, the extra energy picked up is 37 megajoules.  In the absence of atmosphere, that would produce a speed of about 2,400 mph, exceeding Mach 3 (once there was enough air for the speed of sound to be meaningful).

The density of the atmosphere drops off quite rapidly, so this may not be such a bad approximation:

It certainly seems that those extra 61 km make all the difference.  I suppose I was taken in by the marketing of Baumgartner's "space jump" that, while impressive, was nothing of the sort.