When an apple falls from a tree, Earth exerts a gravitational pull on the apple that amounts to an acceleration of around $9.81\,m/s^2$. But as the apple falls, it gets closer to Earth and thereby the gravitational pull as well as the acceleration increase.
When the apple orbits Earth, the gravitational pull is (nearly) constant, but it moves perpendicular to the pull. Can we have both: follow the direction of the pull while having constant acceleration for a non-trivial time and path length?
Put another way: Is it possible to form a mass such that its gravitational pull on other objects is constant along the path these objects follow when moving in the direction of the pull? Can the path be straight or does it have to be straight?
(No, not a homework question. Just curious.)