Given a system of arbitrarily many mass points that attract each converges uniformly.
2.
One of the solutions suggested was a system of rotating discs with mass points positioned along their circumferences.
3.
By symmetry, the net gravitational force attracting a mass point towards a homogeneous sphere must be directed towards its centre.
4.
In other words do particles occupy a volume in space or are they only energy / mass points that have spatial relations to each other?
5.
The gravitational field of a spherically symmetric mass distribution like a mass point, a spherical shell or a homogenous sphere must also be spherically symmetric.
6.
What we were looking for was the critical-mass point where communication was cheap enough and the tools good enough that people wanted to publish electronically and you'd get positive feedback.
7.
But the discrete formulation ( ) of the equation of state with a finite number of mass point is just the suitable one for a numerical propagation of the string motion.
8.
If the string is approximated with 100 discrete mass points one gets the 100 coupled second order differential equations ( ), ( ) and ( ) or equivalently 200 coupled first order differential equations.
9.
A second approach is to introduce explicit forces that work to maintain the constraint; for example, one could introduce strong spring forces that enforce the distances among mass points within a " rigid " body.
10.
To get the total work done by the gravitational force from infinity to the final distance R ( for example the radius of Earth ) of the two mass points, the force is integrated with respect to displacement:
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