Okay, so gravity and acceleration are the same?

Well then, riddle me this Batman.

If you're a person on a planet, gravity pulls you "down", because the source of the geodesics is the center of the planet ("center of mass").

But when you're in an accelerating spaceship, "down" is the direction opposite the acceleration, so if you're accelerating forward, down is behind you in the direction of the engine.

So now, imagine the spaceship standing vertically on the surface of the earth prior to takeoff. The gravitational force at the tip of the rocket is slightly less than the gravitational force at its base, because the tip is slightly farther away from the earth.

Here's the question: in an accelerating spaceship, is the "force of gravity" the same throughout the ship, or is it slightly smaller at the tip?