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Actually, now that I think about it, both of these descriptions seem to be just different ways of phrasing exactly the same thing. Is this what you mean by "not accelerating" or have I gone awry somewhere? Also, why does this only apply to objects that are "small enough"? I'm afraid you lost me there.
It only happens to objects which are small enough because large objects will have enough volume so that different sections of them are significantly closer or further from the gravitating body so that they have different accelerations.
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Yes, but isn't acceleration itself relative? I don't see how it can make any more sense than "motion" without another reference frame to be accelerating relative to.
The problem I think I'm having is that I can't see how acceleration can have any more meaning than motion without something to be accelerating relative to.
Acceleration is basically moving between reference frames, going from one velocity relative to a given observer to another.
So any observer will see you change speed, in a sense it is observable to all observers including yourself, where as velocity isn't.