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straight line, ellipse, telos, momentum, fiction

When we hear of the law of momentum, we think of movement in a straight line.  But perhaps the same movement could be thought of as an extremely small section of elliptical movement.  For if you were to set two very small and dense rocks in movement in relation to each other with nothing else around, one or both would move in an elliptical orbit with respect to the other rather than in a straight line.

But in any case, imagine a projectile rock moving toward three rocks that form a perfect triangle and are stationary with respect to each other.  It's heading toward the middle of the triangle and at a right angle to the plain defined by the three non-projectile rocks.  Since there are three rather than one, the path of the projectile rock will be the average of the three elliptical paths that it would have travelled around each of the other three.  The resultant path would look a lot more like a straight line.

Perhaps the straight line movement that we imagine when we hear of the law of momentum is really the result of averaging of all of the would-be elliptical paths that the projectile would travel if it were relating to any one part of the physical surroundings.    


Doesn't the straight-line-as-average capture the interrelatedness of movement better?  Isn't the law of momentum, as typically understood, more of a useful fiction than a genuine understanding of what is going on in nature?  Finally, isn't there something teleological about elliptical movement?  After all, in the Summa contra gentiles Aquinas -- following Aristotle and others -- spoke of circular movement as teleological.  Isn't the ellpsis just a Keplerian correction of the circle?  So: if the straight line mentioned in the law of momentum is in some sense derived from many elliptical movements, then isn't that straight line in some derivative sense teleological as well?

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