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Quote by D_L
 Quote by TurtleMeister It just seems unintuitive to have to set my frame of reference to one or the other objects. Lets take the following example: An object in Earth free-fall will accelerate at the same rate regardless of it's mass. That is true.
As perceived by whom?
A = M2 * G / r2 where M2 = mass of Earth
The objects mass has no affect.

 Quote by D_L Let's ignore the Earth's rotation. Suppose we have two observers with infinitely accurate means of assessing acceleration. One is fixed with respect to this non-rotating Earth and the other is fixed with respect to some inertial frame. Both measure the acceleration of an object falling toward their Earth at the same time with their infinitely accurate sensors. The two will measure different accelerations. Now suppose we use a different test object whose mass is orders of magnitude greater than that of the first test object. Both observers measure the acceleration of this new test object after placing it at exactly the same position with respect to the Earth as the first test object. While the Earth-based observer will measure a different acceleration than measured for the first test object, the inertial observer will see this new object as undergoing exactly the same acceleration as the first test object.
I'm not sure how to comment on this because I don't know what "some inertial frame" is. If this observer who is at "some inertial frame" measures the acceleration relative to himself then what he measures will depend on what his velocity and acceleration is relative to the objects being measured. However, I can use this to illustrate my point where I say that using A = M2 * G / r2 is unintuitive. If your observer at "some inertial frame" and the Earth observer measured the time lapse of the objects free-falls, wouldn't their results be the same - regardless of the frame of reference of the observer at "some inertial frame"? Your post seems bolster my argument!