Earth = Black hole?

The solution to a gravitational well of given mass is the Schwarzchild Radius $\frac{2GM}{{c}^{2}}$ . Substituting the given values, we get 8.893E-3 m or 8.893 mm.

We know that the expression for escape velocity (which can be derived from Energy conservation quite simply) is as follows :

${ v }_{ e }\quad =\quad \sqrt { \frac { 2GM }{ r } }$

where ${ v }_{ e }$ is the escape velocity, $G$ is the Universal Gravitational Constant, $M$ is the mass of the spherically symmetric body and $r$ is the radius of the same.

Now, for a black hole, the escape velocity is the speed of light since the gravitational field is so strong.

Hence,

$c\quad=\quad \sqrt { \frac { 2GM }{ r } }$

Squaring both sides, we get :

${ c }^{ 2 }\quad=\quad \frac { 2GM }{ r }$

Rearranging terms we get:

$r\quad=\quad \frac { 2GM }{ { c }^{ 2 } }$

Plugging in the given values, we get $r= \boxed {8.89 mm}$