### Subject: Solution for motion of two masses under gravity

Date: **Sun Dec 19 14:45:33 2004**

Posted by **Brock**

Grade level: **grad (science)**
School: **Private Citizen**

City: **Bogalusa** State/Province: **Louisiana**
Country: **USA**

Area of science: **Physics**

ID: **1103489133.Ph**

**Message:**

I know I found this similar question and answer:
http://www.madsci.org/posts/archives/1999-03/922410914.As.r.html
However I would like to know the exact equation / function that describes the
motion of the two masses.
Two masses M1 and M2 are released at rest in a vacuum, and the only force acting
on them is their own gravity. Using only F=ma and F=Gm1m2/r^2 solve for the
function x1=f1(t) and x2=f2(t) ... position of mass 1, x1, as a function, f1, of
time, and position of mass 2, x2, as a function, f2, of time.
I start out with: F=m1a2, F=m2a2, F=Gm1m2/(x2-x1)^2 ... Then notice that
a1=v1'=x1" and a2=v2'=x2" ... so you get a set of differential equations:
x1"(x2-x1)^2=Gm2 and x2"(x2-x1)^2=Gm1
But I don't know where to go from there, mathematically.
Thanks.

Re: Solution for motion of two masses under gravity

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