if you were in a spaceship in the furthest depths of space, and you fired a cannonball into space, what force would you have to exert on the ball to keep it moving?

Answer 1

"furtherest" depths of space? Hmmmm.

So you are at the edge of the expanding universe, which you cannot be, as that is the beginning of time, because distances within the universe are always increasing, the only force required to move the ball would be a local force greater than the gravitaional attraction of the ball to cannon, after that is overcome, the ball keeps moving along space-time boundry, and eventually ends up where it started.
As I tried for years to explain the shape of the universe (all matter and light) to my physics students, if you look far enough, you can see the back of your head.

Answer: force greater than gravity attraction between the ball and cannon.

Answer 2

http://www.universetoday.com/37351/shape-of-the-universe/