- #1

Romeo

- 13

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Given sun of mass M and a body of mass m (M>>m) a distance r from the sun, find the time for the body to 'fall' into the sun (initially ignoring the radius of the sun).

Our first equation is therefore [tex] \frac {d^2r}{dt^2} = \ddot{r} = \frac {GM}{r^2} [/tex].

I am able to integrate this, giving:

[tex] \dot{r} = - {\sqrt{2GM}}{\sqrt{1/r - 1/R}} [/tex],

where R is the inital distance of the body from the sun. However, I am unable to integrate this again. I have shoved it into wolfram's integrator for an indicator of what to aim for, but cannot come close.

Any thoughts would be greatly appreciated.

Regards

Romeo