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I'm not sure I follow your desire to calling g a "gravitational variable".
The way I see it, I perform a number of experiments of objects in free fall
near the earth, and I measure their accelerations. If I can eliminate
and/or account for air, I find that all the objects fall with an
acceleration of 9.8 m/s^2. For convenience I give that acceleration a
symbol, g, and a name, "acceleration due to gravity". What else it that
but an acceleration?