I received the following yesterday from my son the philosopher.
I will look forward to his visit at Christmas for the promised
explanation:
To: Leigh Palmer <palmer@sfu.ca>
From: Eric Palmer <epalmer@pellns.alleg.edu>
Subject: Re: F=ma
Hi Pa,
Well, sort of. Like Newton, Descartes held to the idea that bodies would
continue in their rectilinear paths unless a force was applied: 'a body in
[rectilinear] motion remains in motion' could apply to Descartes as well,
but this wasn't quite Newtonian momentum (he was only almost successful
with elastic/inelastic collision rules). Descartes thought that a
centripetal (in the current sense) force was indeed necessary to keep
planets in curved motion, so he had a fluid carrying the planets in their
circles (or ovals; which Newton would take him to task on -- Newton showed
that Descartes' scenario yielded ovals, rather than ellipses). The scenario
is very very roughly that of a continuously flushing toilet carrying
'foreign matter' in smooth orbits, rather than down the drain. Very rough
because there is no drain in Cartesian whirlpools; just a circular motion
of the pool that doesn't dissipate (i.e., become rectilinear motion)
because it is bounded on all sides by other whirlpools that for unexplained
reasons don't mix with it. The planets (and their own whirlpool
atmospheres around them) should move smoothly in their orbits, provided
they have the same fluid properties (anachronistic 'density' and
'fluidity') as the surrounding whirlpool.
Fine historical point: I might be overstating it to claim that Descartes
identified the force to keep bodies in orbits as centripetal in the current
sense (Descartes didn't use that word either).
In working through to the insights about the centripetal force necessary to
keep planets in motion, Newton generalized from the aforementioned elastic
collision laws, thinking about the energy required in infinitely many
collisions with other billiard balls that would make another billiard ball
follow a smooth curve. That story is an absolute beaute, if you don't know
it I should show you at Xmas.
Sorry for the wait; been out of town to chat with the historians...
yr son.