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## Homework Statement

The radius

*Rh*of a black hole is the radius of a mathematical sphere, called the event horizon, that is centered on the black hole. Information from events inside the event horizon cannot reach the outside world. According to Einstein's general theory of relativity,

*Rh*= 2

*GM/c*2, where

*M*is the mass of the black hole and

*c*is the speed of light.

Suppose that you wish to study a black hole near it, at a radial distance of 43

*Rh*. However, you do not want the difference in gravitational acceleration between your feet and your head to exceed 10 m/s2 when you are feet down (or head down) toward the black hole.

**(a)**Take your height to be 2.0 m. What is the limit to the mass of the black hole you can tolerate at the given radial distance? Give the ratio of this mass to the mass

*MS*of our Sun.

**(b)**Is the ratio an upper limit estimate or a lower limit estimate?

## Homework Equations

*Rh*= 2

*GM/c^*2

Fg=GmM/R^2

Fg=m*a

## The Attempt at a Solution

Using the two expressions of the gravitational attraction: a=GM/(R+∂R)^2=10

and we have R=43*Rh=86GM/c^2

and my height is ∂R=2 metres

now sub the expression for R in, and do the massive calculation I got M=1.0125*10^32 kg

the sun has mass Msun=1.99*10^30 kg

thus the ratios is M/Msun=50.879...

This is not however the correct answer

Please let me know where I might have gone wrong