If you had an object in an empty sphere with a radius of a few miles, surrounded by equally distributed and very concentrated mass, what effects of gravity would the object feel?
As long as the mass isn’t so concentrated that the laws of general relativity become important, the object won’t feel any gravity at all. The forces from opposite sides of the surrounding mass will cancel exactly. For example, if you were at the center of the earth in a large spherical opening, you would be perfectly weightless. The force from the north side of the earth would balance the force from the south side. This effect is quite remarkable and depends on the fact that gravity becomes weaker as the inverse square of the distance separating two objects. That way, even if you aren’t in the exact center of the earth, the forces still cancel.