Butch

Sorry, folks... tired brain, will work more on question than solution.

I am only looking for a vector statement to show that the gravitational influence of the 2 point system on the single point reduces as the distance between the 2 constituents of the 2 point system increases... I understand the vector math, but lost on the proper formula syntax. I could draw it and deduce it, but a singular mathematical statement eludes me.

It would do to consider the 2 point system to be static except for them receding from one another tangent to the single point.

BTW Thank you Swan.

2 hours ago, mathematic said:

Use inverse squarer relationship.  Your description doesn't describe the motion of the first two relative to the third.

I am using that relationship, however showing that the 2 point system influence diminishes with the distance between the 2 is what is eluding me... I suppose I need to reference the point equidistant from the 2 and apply the 1/x^2 there. Sorry people, probably making this more complex than need be.

And thank you mathematic.

Perhaps I can restate...

The resultant of 2 vectors with a common origin decreases as theta increases. I need a simple proof.

That is not exactly correct.

Given 2 gravitational points in a close oscillatory relationship and a 3rd at a relativly greater distance, how would I demonstrate mathematically that the influence of the first 2 upon the 3rd decreases as the distance between the first 2 increases?

Assume the oscillatory relationship to be circular, or an average.