I am trying to study the motion of a falling body in the earth’s gravitational field however not assuming a constant acceleration. I want to work out the distance travelled in a given time.
We know that 
[tex]a = \frac{{GM}}{{{r^2}}}[/tex]
Likewise, we can calculate that
[tex]\begin{array}{l}
\frac{{da}}{{dr}} = \frac{{ - 2GM}}{{{r^3}}}\\
da = \frac{{ - 2GM}}{{{r^3}}}dr
\end{array}[/tex]
We also know that [tex]s = \frac{1}{2}a{t^2}[/tex]
. Therefore I’m guessing we can say that
.[tex]s = \frac{{GM}}{{{r^3}}}{t^2}dr[/tex]
I’m thinking we have to do some kind of an integral. How would one tackle this problem?
Thank you
We know that 
[tex]a = \frac{{GM}}{{{r^2}}}[/tex]
Likewise, we can calculate that
[tex]\begin{array}{l}
\frac{{da}}{{dr}} = \frac{{ - 2GM}}{{{r^3}}}\\
da = \frac{{ - 2GM}}{{{r^3}}}dr
\end{array}[/tex]
We also know that [tex]s = \frac{1}{2}a{t^2}[/tex]
. Therefore I’m guessing we can say that
.[tex]s = \frac{{GM}}{{{r^3}}}{t^2}dr[/tex]
I’m thinking we have to do some kind of an integral. How would one tackle this problem?
Thank you
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