Say the acceleration and velocity are described using acceleration time and velocity time graphs, I have no idea whether these graphs would look the same or different to the same graphs but made for the real earth. I'm not talking exact numbers but the shape of the graph. A large distance is just far enough away that g≠9.8. I think the value of g with respect to r follows a 1/r curve but i don't know how to translate that into an acceleration vs time graph.
1 Answer
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The value of $g$ varies with $\frac{1}{r^2}$. For constant $g$, the shapes of the curves are a parabola for height and a linear increase for velocity. The parabola will get "elongated" somewhat, and the straight line for velocity will get curved. There is no neat functional form.