(adsbygoogle = window.adsbygoogle || []).push({}); 1-dimensional problem in newtonian gravity- HELP!!

The problem is this:

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# 1-dimensional problem in newtonian gravity- HELP

**Physics Forums | Science Articles, Homework Help, Discussion**