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## Main Question or Discussion Point

Let's say an object is falling towards earth from a long distance away. As it gets closer and closer, the acceleration would increase, inversely proportional to the distance squared.

Is there any way I can graph this on an acceleration/time graph, or a distance/time graph?

The challenge is that the acceleration is dependent on distance from the centre of gravity, but to be able to find that distance at any given time, I first need to know the acceleration, so that I can double-integrate it.

Here's what I've already got:

If I know the acceleration is mG/D

D ' ' = mG/D

To keep things simple, I'm going to assume mG to be 1:

D ' ' = 1/D

But I'm not sure where to go from there, or if I'm even on the right track.

Is there any way I can graph this on an acceleration/time graph, or a distance/time graph?

The challenge is that the acceleration is dependent on distance from the centre of gravity, but to be able to find that distance at any given time, I first need to know the acceleration, so that I can double-integrate it.

Here's what I've already got:

If I know the acceleration is mG/D

^{2}(assuming D to be distance), and I know that acceleration is the double-differential of distance, I can get:D ' ' = mG/D

^{2}To keep things simple, I'm going to assume mG to be 1:

D ' ' = 1/D

^{2}But I'm not sure where to go from there, or if I'm even on the right track.