3 ms·
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
by TrainedMonkey 5y ago
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
- spfzero 5y agoBefore you got very far into this it would be really hard to stay curled up in a ball.
- tinco 5y agoVery 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.
- TeMPOraL 5y agoWorth 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.
- vladTheInhaler 5y agoWell the ISS orbits at R_earth + 400 km. So it wouldn't be nearly as bad as that number makes it sound.
- 7373737373 5y agoDoes anyone know how fast one would fall in from a 100km initial distance? This answer: https://physics.stackexchange.com/a/332510/236187 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.