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What formula could be used to describe the minimums required for an unprotected human body to burn up completely in reentry to Earth's gravity well?

As a hypothetical, a burial of the deceased in orbit, who's last wish was to be cremated in such a way, say from the ISS.

Second hypothetical; an Earth company that wanted to offer reentry cremation for the deceased. What would be the minimum requirements (the least expensive) to fulfill the contract?

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Build a 20-ton orbital corpse deployment pod carrying 75 bodies, able to eject them one at a time into a reentry trajectory. Each body is in an individual shroud, constructed and weighted in such a way to optimize incineration (e.g. streamlined to avoid decelerating too early in the reentry).

Launch it on a Falcon 9.

If you charge US\$2 million per body you bring in \$150M revenue per mission. Launch costs \$62M, deployment pod costs \$3M. Assume that permits, lawsuits, mission operations, recording the deployments and distributing videos to the families, etc. eat another \$10M, and you're left with \$75M profit.

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  • $\begingroup$ Much harder to launch them one at a time, as it would involve delta v. Much easier to put the bodies in a faring, lunch into a sub-orbital (non-circularized) trajectory, then separate the bodies using "decouplers". The result would be MIRV style reentry. $\endgroup$
    – Aron
    Jun 1, 2016 at 5:37
  • $\begingroup$ I think you can monetize the ceremonial aspect of doing them one at a time. $\endgroup$
    – Russell Borogove
    Jun 1, 2016 at 14:23
  • $\begingroup$ @RussellBorogove If you time the corpse-reentries right, you could have the ceremony end with the funeral-goers watching from below, which would be quite dramatic/memorable $\endgroup$
    – Dragongeek
    Nov 10, 2019 at 9:53
  • $\begingroup$ You may not need a falcon to do this because if you didn't want to hit orbit. Then you'd just need to exit the atmosphere sufficiently fast that on the way back down it burns up all debris, organic or otherwise. $\endgroup$
    – Magic Octopus Urn
    Nov 11, 2019 at 15:39
  • $\begingroup$ See if you can get a fairing on an F9 booster without second stage. Fully reusable = cheaper. Without second stage, the booster has higher Δv, might be enough. Not sure if watching reentry on land is feasible, but watching on a ship and also seeing the booster land on the drone ship is great, too. $\endgroup$
    – darsie
    May 7, 2020 at 10:17

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