Question

You’re studying black holes and are planning an expedition to view one up close and in person. You want to get as close as possible to get good measurements, but you know that you’ll have to worry about tidal forces causing “spaghettification.” So, you need to calculate a minimum safe distance to avoid being ripped apart. Assume you will approach along a radial line, with your feet toward the black hole and your head away. You know that the tidal force will act on each end of your body with the same magnitude, but in opposite directions, causing you to be pulled apart. The limiting factor in being ripped apart is the tensile strength of bone; you figure your body can withstand about 105 N of force before being pulled apart. The mass of the black hole you are studying is about 10²⁰ kg.

a. Estimate the minimum safe distance.

b. Compare your minimum safe distance to the “size” of the black hole, given by the Schwarzchild radius, Rs = 2GM/c² ; where G is Newton’s gravitational constant, M is the mass of the black hole and c is the speed of light.

Answer 1

My mass is 65 kg and my height is 170 cm = 1.7 meters.

(a) Let us say that the feet is at a distance of r from the black hole. Then we can write the forces on the feet vs head as, (here we are just considering magnitudes of forces, therefore not taking the negative sign)

Now the limit of difference between these two forces is 105 N. Hence we can write,

Taking positive solution we get, the value of r as,

(b) The Schwarzchild radius is given by,

The minimum safe distance is about 20 orrders of magnitude greater than the Schwarzchild radius.