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Comment by tinco | Hacker News Reader

At what range would the gravity differential kill you? Would you be able to see it before it kills you? If it was close to the sun we should be seeing some kind of halo around it due to gravitational lensing right?

edit: ok maybe we'd need it to be between us and the sun for that to work, the lensing would be that of other stars I guess. I suppose the important question is, since it's relatively close to us, would it deform space hard enough for the gravitational lensing to be noticeable at such close proximity.

edit2: more train of thought, just because it's fun, I suppose since it's so small and the gravity relatively weak (i.e. not as strong as some huge stars or galaxies) any halo or distortion would not extend more than a couple meter, which wouldn't be noticeable from our distance, right?

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As usual the answer is - it depends, but we could estimate forces in question. Assuming my math is correct, at 67 kilometers getting 1 meter closer will results in gravitational pull difference of 137kg. At 40 kilometers, this number increases to ~623kg. I am assuming bad things will happen somewhere between those two ranges.

F = G * (m1 * m2) / r^2 . G = 6.674 / 10^11 (m^3 / (kg * s^2)) | m1 = 5 * 5.972 * 10^24 kg | m2 = 100 kg

Only r in the equation above is not a constant, so we can compute F(r) - F(r+1) to get a difference in force that being 1 meter closer to the black hole would make at a distance r. Basically, this is the difference between how hard your toes would be pulled down vs your heard if you curl into a ball.

  Distance Force          Force + 1      Diff in kg
  1        1.99286E+17    4.98214E+16    1.49464E+16
  1000     1.99286E+11    1.98888E+11    39797421.92
  10000    1992856400     1992457888     39851.15023
  20000    498214100      498164282.3    4981.767364
  30000    221428488.9    221413727.7    1476.11612
  40000    124553525      124547297.6    622.744272
  50000    79714256       79711067.53    318.8474585
  60000    55357122.22    55355277.03    184.5191277
  70000    40670538.78    40669376.79    116.1990494

Before you got very far into this it would be really hard to stay curled up in a ball.

Very cool, thanks! It's closer than I thought, yet just too far to see it unless it's causing things to happen around it. I suppose if it would crash (slowly :p) into the earth and you were at 67 kilometers you'd see some crazy things.

Worth remember for comparison that the Kármán line is at 100 kilometers. ISS orbits at ~400 kilometers. So, if such a hole were to appear on the surface of the planet, even the crew of the ISS would have a very bad day.

Well the ISS orbits at R_earth + 400 km. So it wouldn't be nearly as bad as that number makes it sound.

Does anyone know how fast one would fall in from a 100km initial distance?

This answer: https://physics.stackexchange.com/a/332510/236187 seems to suggest that it takes mere milliseconds once one is within three times the Schwarzschild radius of the black hole. And that dozens of radii outward, one already moves at a significant fraction of the speed of light.

I believe that the Roche limit would be roughly the same as it is on earth. However, the gravity constant would be the same. So for something as massive as a person, you should not experience any destructive forces until you reached extremely close to the object. Probably measured in a handful of miles or less.

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