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?
To keep an object moving in space, you would need to exert a force equal to zero if you want the cannonball to continue moving with a constant velocity. This is due to Newton's First Law of Motion, which states that an object at rest or in motion will continue to remain in that state unless acted upon by an external force. In the vacuum of space, there is no atmospheric resistance or gravity to slow down the cannonball, so once it is set in motion, it will continue moving indefinitely.
Now, if you want to accelerate or change the velocity of the cannonball, you would need to exert a force on it. This force can be calculated using Newton's Second Law of Motion, which states that the force (F) applied to an object is equal to its mass (m) multiplied by its acceleration (a), or F = m * a.
In space, the amount of force needed to accelerate the cannonball depends on the desired acceleration and the mass of the cannonball itself. The more massive the cannonball, the more force you need to apply to achieve the same acceleration. Similarly, the greater the desired acceleration, the more force you need to exert.
Therefore, the force required to keep the cannonball moving with a constant velocity in space is zero, but if you want to change its velocity, the force required will depend on the desired acceleration and the mass of the cannonball.
"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.