Weighty questions

This post over at Bronze Dog’s place got me thinking about issues in gravity and space station destruction (read the link for some explanation). I’m going to go back to my Physics textbooks soon enough to see if I can answer some of these questions myself, but I’d like to hear what others have to think.

So, here’s the scenario: you’re in your starfighter on the surface of a space station roughly the size (1737 km) and mass (7.3477×1022 kg) of Earth’s moon (assume that any artificial gravity works inside the station only). The space station is set to self-destruct. Which is the better course of action, escape velocity-wise?

  1. Leave now, hit escape velocity, and be home free.
  2. Wait until the detonation and ride along the edge of the explosion/shockwave.

It occurs to me that we might need to know the speed of the expanding shockwave in order to do this completely.

Anyway, assuming the explosion is spherically symmetrical, the center of mass of the space station would remain in the same place. So, if you’re riding along the edge of the shockwave, you’re essentially still on the surface, except that the station is expanding, and so the distance between you and the center of mass is increasing, thus causing the gravitational force to approach zero.

What this really got me thinking about, though, is what would happen if you left after the explosion, so you were starting inside the expanding sphere. Or, more simply, what’s gravity like when you’re 20 km underground? Since we traditionally model gravity as radiating out from the center of mass (FG=Gm1m2/R2, it should get stronger as you get closer to the canter (R -> 0). And at the center? While I would have assumed that you’d be weightless, the equation would suggest to me that the gravitational force is infinite, or at least undefined. It’s an asymptote, to be sure, and it seems like the graph would show an increase toward infinity as you approach the center. And this should be true of the center of any mass.

And that seems like it can’t possibly work. So, what am I missing? Do you disregard the mass above you when you’re beneath the surface? That doesn’t seem right. Is this just one of those kinks that’ll get ironed out when we have a GUT?

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