After the big-bang, tiny black holes may have formed. If one with a mass of $1 x 10^{11} k g$ $1 x 10^11 kg$ (and a radius of only $1 x 10^{- 16} m$ $1 x 10^-16 m$ ) reached Earth, at what distance from your head would its gravitational pull on you match that of the Earth's?

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After the big-bang, tiny black holes may have formed. If one with a mass of $1 x 10^{11} k g$ $1 x 10^11 kg$ (and a radius of only $1 x 10^{- 16} m$ $1 x 10^-16 m$ ) reached Earth, at what distance from your head would its gravitational pull on you match that of the Earth's?

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Answer 1 · 2016-08-31T10:16:44

Your head would need to be about 0.82 metres from the black hole to experience 1g.

Explanation:

The acceleration you would experience is:

$a = \frac{G M}{r^{2}}$ $a=(GM)/r^2$

Where $M = 10^{11} k g$ $M=10^11kg$ is the mass of the black hole, $G = 6.674 m^{2} k g^{- 1} s^{- 2}$ $G=6.674m^2kg^(-1)s^(-2)$ is the gravitational constant and $r$ $r$ is the distance from the black hole.

The acceleration due to gravity on Earth is $a = 9.81 m s^{- 2}$ $a=9.81ms^(-2)$ .

So, to experience 1g of acceleration, thee distance is:

$r^{2} = \frac{G M}{a} = \frac{6.67}{9.81}$ $r^2=(GM)/a=6.67/9.81$

This gives $r = 0.82 m$ $r=0.82m$ .

Being so close to a black hole puts you in the region where tidal effects can occur. At $r = 0.6 m$ $r=0.6m$ , $a = 18.5 m s^{- 2}$ $a=18.5ms^(-2)$ . At $r = 0.4 m$ $r=0.4m$ , $a = 41.7 m s^{- 2}$ $a=41.7ms^(-2)$ .

Incidentally, the Schwarzschild radius for a black hole is given by:

$r = \frac{G M}{c^{2}}$ $r=(GM)/c^2$

Where $c$ $c$ is the speed of light. A black hole with a mass of $10^{11} k g$ $10^11kg$ has a radius of $7.4 \cdot 10^{- 17} m$ $7.4*10^(-17)m$ , which is slightly smaller than $10^{- 16} m$ $10^-16m$ .

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After the big-bang, tiny black holes may have formed. If one with a mass of $1 x 10^{11} k g$ $1 x 10^11 kg$ (and a radius of only $1 x 10^{- 16} m$ $1 x 10^-16 m$ ) reached Earth, at what distance from your head would its gravitational pull on you match that of the Earth's?

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Explanation:

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1 Answer

Explanation:

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Impact of this question

After the big-bang, tiny black holes may have formed. If one with a mass of $1 x 10^{11} k g$ $1 x 10^11 kg$ (and a radius of only $1 x 10^{- 16} m$ $1 x 10^-16 m$ ) reached Earth, at what distance from your head would its gravitational pull on you match that of the Earth's?