Question

Any way to Find the Position Function of a body under gravitational force?

Answer 1

Let's say we have a planet with a mass of m. We also have an object of relatively small mass (so small that its gravitational field would not affect the planet), and we know that at time 0 it is at position h.

If we know the acceleration due to gravity (g), we can calculate the position y at time t:

y=h−gt22y=h−gt22

And we know that the acceleration due to gravity could be calculated:

g=Gmy2

Answer 2

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know the acceleration due to gravity (g), we can calculate the position y at time t:

y=h−gt22

And we know that the acceleration due to gravity could be calculated:

g=Gmy2

But since the acceleration depends on the position of the object relative to the planet, and the position of the object is dependent on the acceleration, this would obviously mean that the first formula won't work when we are working with displacement so large that it would change the acceleration significantly.



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