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?

1 Answer
Aug 31, 2016

Answer:

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=(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#.