Blackhole spaghettification and maximum body tension

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SUMMARY

The discussion centers on calculating the maximum distance Celeste åפֿאל ۻ. .54 can approach a black hole with a mass of 10 MSun without being torn apart by tidal forces. The key equation used is F = GmM/R², which relates gravitational force to mass and distance. The athlete's body can withstand a force of 500,000 Newtons, and the challenge is to determine the distance from the singularity where the gravitational difference between her head and feet equals this force. The professor advises that the specific mass of the athlete is not critical for the calculation, as the focus is on the difference in gravitational forces.

PREREQUISITES
  • Understanding of gravitational force equations, specifically F = GmM/R²
  • Familiarity with black hole physics, particularly Schwarzschild radius calculations
  • Basic knowledge of tidal forces and their effects on bodies in strong gravitational fields
  • Ability to perform algebraic manipulations to solve for variables in equations
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  • Research the Schwarzschild radius and its implications for objects near black holes
  • Study tidal forces and their effects on human bodies in varying gravitational fields
  • Explore gravitational force calculations involving different masses and distances
  • Learn about the physical limits of human endurance in extreme environments
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Astronomy students, physicists, and anyone interested in the effects of extreme gravitational forces on the human body.

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Homework Statement


In the Schwarzschild Slalom, brave athletes dive from a platform orbiting at a distance of 1 AU from the singularity at the centre of a black hole with a mass of 10 MSun. The competitor who can get closest to the singularity, and survive, wins the event. (The rules state the athlete must point the length of her body toward the black hole at closest approach.) The winner in 20010 was (I mean, will be) Celeste åפֿאל ۻ. .54, whose height is 1.5 metres.

(a) If the force holding together the flesh, muscle and bones in the human body is about 500,000 Newtons†, how closely (in AU and km) could Celeste åפֿאל ۻ. .54 approach the singularity without being ripped apart by the tidal force? (In other words, at what distance from the black hole would the difference in gravity between the top of her head and the bottom of her feet just equal the force holding together her body?

Homework Equations


F = GmM/R2
RSch = 2GM/c2

The Attempt at a Solution


I tried setting the difference between the two gravitational forces at her head and feet equal to the maximum force that holds together the human body:

500 000 N = GmM/R2 - GmM/(R + 1.5)2

But the problem is that I don't know little m and I'm stuck about how to move forward.
 
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Little m in this case would be the mass of the athlete. If this is not given, you could make a reasonable assumption about what somebody weighs (or technically, how massive they are).
 
I can't make an assumption on the mass. I emailed my prof:

"Think of small masses at Celeste's feet and head and what would be the forces on them.

The difference in the forces is the same even if the points are not
attached. You're calculating a difference, so the exact masses you
use for m will not make a big difference to the answer. (No pun
intended.)"
 

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