NASA finds 'new earth'

Think about it for a bit.

Ignoring all other matter, if planet A was really far away, it's a no-brainer to say that the direction of gravity from your perspective is towards planet A. Now throw planet B into the mix, which has the same mass and size (for simplicity's sake). If you were equidistant between these two planets, the net gravitational pull on you is zero. Throw planet C into the mix, which is just as far away from you, and all other planets are the same distance away from each other as well as being identical in mass and size. Net gravitational pull is still zero. We can keep on doing this for a however many planets.

Now imagine that you are in the center of a planet, ignoring all other matter. How will gravity pull at you? Because there's an equal amount of matter at any given distance away from you in all directions, the net gravitational pull is zero.

The thing about reality is, with the exception of black holes, it's not really accurate to treat bodies as a point mass. The way the educational system teaches it gets you "good enough" results (negligible difference) if you're sufficiently far away from something, just like how we don't factor in time distortion if we're moving at 200mph across Utah's salt flats.

Actually, not ENTIRELY true. Yes, you would assume that when you enter a planet the gravitational force gets greater because the radius shrinks, and what you said was correct, but not quite the true reason. If you go to the center of mass of an object (the core of the Earth, for instance), all of the mass of the object is pulling you equally. So, if you are for instance at the core, the north hemisphere is pulling you equally as strong as the south hemisphere. If you were on the surface, however, all of the Earth's mass is pulling you towards it (which happens to be towards the center). Pretty much a sum of all masses at different radii, or a triple integral.