It doesn't necessarily have to increase the gravity...

by roland , Thursday, August 29, 2013, 13:49 (3890 days ago) @ ZackDark

In mathematical terms, the gravitational pull outside of the body in question is a function of the mass/(distance from mass center^2), so the smaller the radius, the smaller the distance from the center of mass, the greater the pull.

ZackDark speaks the truth.

A few minor clarifications... the amount of gravitational force exerted by a given point of mass is proportional to (the mass) / (the distance from that point)^2. For real objects (i.e. not point masses), the gravitational force is a combination of the forces exerted by a bunch of points distributed about you. For example, if a mountain were massive enough and you were standing near it, it could exert a non-negligible gravitational force on you that pulled you slightly sideways.

So, if the radius gets really small then unless the object is spherical (often not the case for things like asteroids) the gravitational force may not necessarily go up in the direction you might expect.