After the big-bang, tiny black holes may have formed. If one with a mass of $1 x 10^11 kg$ (and a radius of only $1 x 10^-16 m$ ) 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.

The acceleration you would experience is:

$a=(GM)/r^2$

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

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

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

$r^2=(GM)/a=6.67/9.81$

This gives $r=0.82m$ .

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

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

$r=(GM)/c^2$

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

After the big-bang, tiny black holes may have formed. If one with a mass of 1 x 10^11 kg1 x 10^11 kg (and a radius of only 1 x 10^-16 m1 x 10^-16 m) reached Earth, at what distance from your head would its gravitational pull on you match that of the Earth's?