I was trying to figure out the necessary weight and size an object has to be to become a black hole and this is what I did. But I have a small unit related problem that is blatantly obvious. I know where the problem is but I don't know how to solve it.

Lets start with equations...

F = (Gmamb) / r^2

where F = force

G = the gravitational constant... 6.67E-11 m^3/Kg*s^2

ma = mass of object a in kilograms

mb = mass of object b in kilograms

and r = the distance between object a's and object b's centers of gravities in meters

You can figure out the acceleration an object will cause ANY another object of any weight to experience...

a = acceleration

a = f/mb = (Gmamb) / mbr^2 = (Gma)/r^2

I then plugged the speed of light in for a because the black hole's gravity has to pull light in faster than the speed of light in order to be a black hole.

300 000 = 6.67E-11m/r^2

2.68E+8 = m/r^2

m is in kilograms

r is in meters

So if an object is more than 2.68E+8Kg/m^2 then the object is a black hole.

Too me it seems that it should be 2.68Kg/m^3 instead... I know the problem lies with my putting in the speed of light for acceleration because the speed of light is a velocity, so that causes me to lose a second unit on the left side of my equation but I also think there is something else wrong with my units... But I am fairly sure my number is right. How should I go about solving this? Is there something else I should put in instead of the speed of light? Thanks.