From previously, if earth were to shrink to a radius of \({r}_{o}=0.00886\)m then it is dense enough to be a black hole. Since,
\(\cfrac { { r }_{ e }^{ 3 } }{ { r }_{ o }^{ 3 } } =\cfrac { { d }_{ o } }{ { d }_{ e } }\) , earth density, \({d}_{e}\) = 5.52 g/cm³, earth radius, \({r}_{e}\)=6371 km
We have mass density of this black hole, \({d}_{o}\)
\({ d }_{ o }=\cfrac { { r }_{ e }^{ 3 } }{ { r }_{ o }^{ 3 } } { d }_{ e }\)=(6371000/0.00886)^3*5.52= 2.0524*10^27 g/cm³
Space permeates through all matter. This density may be the limit beyond which space cannot penetrate.
