I did not know that "vortical theory" had a history until reading Neal Stephenson's Baroque Cycle trilogy. Those books include among their many subplots the professional feud between Newton and Leibniz -- centered, of course, on which had primacy in the invention of the calculus.

They also mention, more than once, the effect publication of Newton's Principia had on Rene Descartes' vortex theory of gravity and orbital motion, which is recapitulated in brief here (which I found by Googling "Descartes + vortex") :

Now once everything was filled with ethereal matter one had to consider what happened when a solid body, such as a planet, moved through the ether. Clearly the ether must be forced away from the front of the object and it will then flow round it in a circular motion. As bodies were in motion, the universe must consist of eddies, vortices and whirlpools. If, Descartes argued, the ether was perpetually in vortex motions caused by bodies passing through it, then the ether in turn would cause motion in bodies situated in it. These vortices were the cause of gravity; they held the planets in their orbits round the Sun. The Earth was surrounded by ethereal material which circulated rapidly round the Earth. This light, rapidly moving material would flow away from the Earth, and heavy, slow moving bodies like a stone would fall towards the centre of the Earth to replace it.

Followed by this, after a discussion of Huygens' and Leibniz's and Malebranche's attempts to adjust Descarte's theory to more closely follow observation:

The Principia also gives arguments against Descartes' theory of gravitation. Newton showed that Kepler's first and second law could not both hold under Descartes' theory. He also asked how comets were able to cross vortices strong enough to keep the planets in their orbits without any effect on their own orbits. It was a devastating attack on Descartes' vortex theory of gravitation and put forward a brilliantly simple theory from which so much could be explained.

The remainder of the paragraph, and those that follow, address what Einstein much later called "spooky action at a distance."