Newton's major work Principia included a substantial specific
disproof of Descartes' vortex theory of planetary motion, not
naming Cartes in this disproof though his was the only such vortex theory at the
time. Below you can read all of Principia book 2 section 9, devoted
to this disproof. Newton also argued strongly against Descartes'
physics more basic requirement that space is filled with a material
'ether' substance (also required by the physics of both Aristotle and Einstein).
He instead chiefly supported Gilbert's view that space must be largely really
empty, but also that knowing the experimental maths of nature was the limit of science.

In disproving Descartes' vortex theory of planetary motion, and some other aspects of Cartesian physics, Newton claimed to not conclude that he had completely disproved Descartes'
general theory of a mechanical push universe, some modified form of
which he took as one possible option beside Gilbert's signal
attraction theory in his own black-box 'cause unknown' physics. He just did not prove that his good maths
produced from Gilbertian attraction theory could also fit any actual valid Cartesian push physics theory - only that it might also fit some possible push physics. So the Newton maths evidence seemed to clearly favour attraction physics.
And Gilbert had claimed to have disproved Greek-Atomist or Cartesian push-physics if maybe somewhat less convincingly.

"Of the circular motion of fluids.

HYPOTHESIS.

The resistance arising from the want of lubricity in the parts of a
fluid, is, caeteris paribus, proportional to the velocity with
which the parts of the fluid are separated from each other.

PROPOSITION LI. THEOREM XXXIX.

If a solid cylinder infinitely long, in an uniform and infinite
fluid, revolve with an uniform motion about an axis given in
position, and the fluid be forced round by only this impulse of the
cylinder, and every part of the fluid persevere uniformly in its
motion ; I say, that the periodic times of the parts of the fluid
are as their distances from, the axis of the cylinder.

Let AFL be a cylinder turning uniformly about the axis S, and
let the concentric circles BGM, CHN, DIO, EKP, etc., divide the
fluid into innumerable concentric cylindric solid orbs of the same
thickness. Then, because the fluid is homogeneous, the impressions
which the contiguous orbs make upon each other mutually will be (by
the Hypothesis) as their translations from each other, and as the
contiguous superficies upon which the impressions are made. If the
impression made upon any orb be greater or less on its concave than
on its convex side, the stronger impression will prevail, and will
either accelerate or retard the motion of the orb, according as it
agrees with, or is contrary to, the motion of the same. Therefore,
that every orb may persevere uniformly in its motion, the
impressions made on both sides must be equal and their directions
contrary. Therefore since the impressions are as the contiguous
superficies, and as their translations from one another, the
translations will be inversely as the superficies, that is,
inversely u the distances of the superficies from the axis. But the
differences of the angular motions about the axis are as those
translations applied to the distances, or as the translations
directly and the distances inversely; that is, joining these ratios
together, as the squares of the distances inversely. Therefore if
there be erected the lines Aa, Bb, Cc, Dd, Ee, etc., perpendicular
to the several parts of (he infinite right line SABCDEQ, and
reciprocally proportional to the squares of SA, SB, SO, SD, SE,
etc., and through the extremities of those perpendiculars there be
supposed to pass an hyperbolic curve, the sums of the differences,
that is, the whole angular motions, will be as the correspondent
sums of the lines Aa, Bb, Cc, Dd, Ee, that is (if to constitute a
medium uniformly fluid the number of the orbs be increased and
their breadth diminished in inflnitum), as the hyperbolic areas
AaQ., BAQ, CcQ, DdQ, EeQ, etc., analogous to the sums; and the
times, reciprocally proportional to the angular motions, will be
also reciprocally proportional to those areas. Therefore the
periodic time of any particle as D, is reciprocally as the area
DdQ, that is (as appears from the known methods of quadratures of
curves), directly as the distance SD. Q.E.D.

COR. 1. Hence the angular motions of the particles of the fluid are
reciprocally as their distances from the axis of the cylinder, and
the absolute velocities are equal.

COR. 2. If a fluid be contained in a cylindric vessel of an
infinite length, and contain another cylinder within, and both the
cylinders revolve about one common axis, and the times of their
revolutions be as their semi-diameters, and every part of the fluid
perseveres in its motion, the periodic times of the several parts
will be as the distances from the axis of the cylinders.

COR. 3. If there be added or taken away any common quantity of
angular motion from the cylinder and fluid moving in this manner;
yet because this new motion will not alter the mutual attrition of
the parts of the fluid, the motion of the parts among themselves
will not be changed; for the translations of the parts from one
another depend upon the attrition. Any part will persevere in that
motion, which, by the attrition made on both sides with contrary
directions, is no more accelerated than it is retarded.

COR. 4. Therefore if there be taken away from this whole system of
the cylinders and the fluid all the angular motion of the outward
cylinder, we shall have the motion of the fluid in a quiescent
cylinder.

COR. 5. Therefore if the fluid and outward cylinder are at rest,
and the inward cylinder revolve uniformly, there will be
communicated a circular motion to the fluid, which will be
propagated by degrees through the whole fluid; and will go on
continually increasing, till such time as the several parts of the
fluid acquire the motion determined in Cor. 4.

COR. 6. And because the fluid endeavours to propagate its motion
still farther, its impulse will carry the outmost cylinder also
about with it, unless the cylinder be violently detained; and
accelerate its motion till the periodic times of both cylinders
become equal among themselves. But if the outward cylinder be
violently detained, it will make an effort to retard the motion of
the fluid; and unless the inward cylinder preserve that motion bv
means of some external force impressed thereon, it will make it
cease by degrees.

All these things will be found true by making the experiment in
deep standing water.

PROPOSITION LII. THEOREM XL.

If a solid sphere, in an uniform and infinite fluid, revolves about
an axis given in position with an uniform motion, and the fluid be
forced round by only this impulse of the sphere ; and every part of
the fluid perseveres- uniformly in its motion ; I say, that the
periodic times of the parts of the fluid are as the squares of
their distances from the centre of the sphere.

CASE 1. Let AFL be a sphere turning uniformly about the axis S,
and let the concentric circles BGM, CHN, DIO, EKP, etc., divide the
fluid into innumerable concentric orbs of the same thickness.
Suppose those orbs to be solid ; and, because the fluid is
homogeneous, the impressions which the contiguous orbs make one
upon another will be (by the supposition) as their translations
from one another, and the contiguous superficies upon which the
impressions are made. If the impression upon any orb be greater or
less upon its concave than upon its convex side, the more forcible
impression will prevail, and will either accelerate or retard the
velocity of the orb, ac cording as it is directed with a conspiring
or contrary motion to that of the orb. Therefore that every orb may
persevere uniformly in its motion, it is necessary that the
impressions made upon both sides of the orb should be equal, and
have contrary directions. Therefore since the impressions are as
the contiguous superficies, and as their translations from one
another, the translations will be inversely as the superficies,
that is, inversely as the squares of the distances of the
superficies from the centre. But the differences of the angular
motions about the axis are as those translations applied to the
distances, or as the translations directly and the distances
inversely; that is by compounding those ratios, as the cubes of the
distances inversely. Therefore if upon the several parts of the
infinite right line SABCDEQ there be erected the perpendiculars Aa,
Bb, Cc, Dd, Ee, etc., reciprocally proportional to the cubes of SA,
SB, SO, SD. SE, etc., the sums of the differences, that is, the
whole angular motions will be as the corresponding sums of the
lines Aa, Bb, Cc, Dd, Ee, etc., that is (if to constitute an
uniformly fluid medium the number of the orbs be increased and
their thickness diminished in inflnitum), as the hyperbolic areas
AaQ, BbQ, CcQ, DdQ., EeQ, etc., analogous to the sums; and the
periodic times being reciprocally proportional to the angular
motions, will be also reciprocally proportional to those areas.
Therefore the periodic time of any orb DIO is reciprocally as the
area DdQ,, that is (by the known methods of quadratures), directly
as the square of the distance SD. Which was first to be
demonstrated.

CASE 2. From the centre of the sphere let there be drawn a great
number of indefinite right lines, making given angles with the
axis, exceeding one another by equal differences; and, by these
lines revolving about the axis, conceive the orbs to be cut into
innumerable annuli; then will every annulus have four annuli
contiguous to it, that is, one on its inside, one on its outside,
and two on each hand. Now each of these annuli cannot be impelled
equally and with contrary directions by the attrition of the
interior and exterior annuli, unless the motion be communicated
according to the law which we demonstrated in Case 1. This appears
from that demonstration. And therefore any series of annuli, taken
in any right line extending itself in inflnitum from the globe,
will move according to the law of Case 1, except we should imagine
it hindered by the attrition of the annuli on each side of it. But
now in a motion, according to this law, no such is, and therefore
cannot be, any obstacle to the motions persevering according to
that law. If annuli at equal distances from the centre revolve
either more swiftly or more slowly near the poles than near the
ecliptic, they will be accelerated if slow, and retarded if swift,
by their mutual attrition; and so the periodic times will
continually approach to equality, according to the law of Case 1.
Therefore this attrition will not at all hinder the motion from
going on according to the law of Case 1, and therefore that law
will take place; that is, the periodic times of the several annuli
will be as the squares of their distances from the centre of the
globe. Which was to be demonstrated in the second place.

CASE 3. Let now every annulus be divided by transverse sections
into innumerable particles constituting a substance absolutely and
uniformly fluid; and because these sections do not at all respect
the law of circular motion, but only serve to produce a fluid
substance, the law of circular motion will continue the same as
before. All the very small annuli will either not at all change
their asperity and force of mutual attrition upon account of these
sections, or else they will change the same equally. Therefore the
proportion of the causes remaining the same, the proportion of the
effects will remain the same also; that is, the proportion of the
motions and the periodic times. Q.E.D. But now as the circular
motion, and the centrifugal force thence arising, is greater at the
ecliptic than at the poles, there must be some cause operating to
retain the several particles in their circles; otherwise the matter
that is at the ecliptic will always recede from the centre, and
come round about to the poles by the outside of the vortex, and
from thence return by the axis to the ecliptic with a perpetual
circulation.

COR. 1. Hence the angular motions of the parts of the fluid about
the axis of the globe are reciprocally as the squares of the
distances from the centre of the globe, and the absolute velocities
are reciprocally as the same squares applied to the distances from
the axis.

COR. 2. If a globe revolve with a uniform motion about an axis of a
given position in a similar and infinite quiescent fluid with an
uniform motion, it will communicate a whirling motion to the fluid
like that of a vortex, and that motion will by degrees be
propagated onward in infinitum ; and this motion will be increased
continually in every part of the fluid, till the periodical times
of the several parts become as the squares of the distances from
the centre of the globe.

COR. 3. Because the inward parts of the vortex are by reason of
their greater velocity continually pressing upon and driving
forward the external parts, and by that action are perpetually
communicating motion to them, and at the same time those exterior
parts communicate the same quantity of motion to those that lie
still beyond them, and by this action preserve the quantity of
their motion continually unchanged, it is plain that the motion is
perpetually transferred from the centre to the circumference of the
vortex, till it is quite swallowed up and lost in the boundless
extent of that circumference. The matter between any two spherical
superficies concentrical to the vortex will never be accelerated;
because that matter will be always transferring the motion it
receives from the matter nearer the centre to that matter which
lies nearer the circumference.

COR. 4. Therefore, in order to continue a vortex in the same state
of motion, some active principle is required from which the globe
may receive continually the same quantity of motion which it is
always communicating to the matter of the vortex. Without such a
principle it will undoubtedly come to pass that the globe and the
inward parts of the vortex, being always propagating their motion
to the outward parts, and not receiving any new motion, will
gradually move slower and slower, and at last be carried round no
longer.

COR. 5. If another globe should be swimming in the same vortex at a
certain distance from its centre, and in the mean time by some fore
e revolve constantly about an axis of a given inclination, the
motion of this globe will drive the fluid round after the manner of
a vortex; and at first this new and small vortex will revolve with
its globe about the centre of the other; and in the mean time its
motion will creep on farther and farther, and by degrees be
propagated in infinitum, after the manner of the first vortex. And
for the same reason that the globe of the new vortex was carried
about before by the motion of the other vortex, the globe of this
other will be carried about by the motion of this new vortex, so
that the two globes will revolve about some intermediate point, and
by reason of that circular motion mutually fly from each other,
unless some force restrains them. Afterward, if the constantly
impressed forces, by which the globes persevere in their motions,
should cease, and every thing be left to act according to the laws
of mechanics, the motion of the globes will languish by degrees
(for the reason assigned in Cor. 3 and 4), and the vortices at last
will quite stand still.

COR. 6. If several globes in given places should constantly revolve
with determined velocities about axes given in position, there
would arise from them as many vortices going on in infinitum. For
upon the same account that any one globe propagates its motion in
infinitum, each globe apart will propagate its own motion in
infinitum also; so that every part of the infinite fluid will be
agitated with a motion resulting from the actions of all the
globes. Therefore the vortices will not be confined by any certain
limits, but by degrees run mutually into each other; and by the
mutual actions of the vortices on each other, the globes will be
perpetually moved from their places, as was shewn in the last
Corollary; neither can they possibly keep any certain position
among themselves, unless some force restrains them. But if those
forces, which are constantly impressed upon the globes to continue
these motions, should cease, the matter (for the reason assigned in
Cor. 3 and 4) will gradually stop, and cease to move in
vortices.

COR. 7. If a similar fluid be inclosed in a spherical vessel, and,
by the uniform rotation of a globe in its centre, is driven round
in a. vortex; and the globe and vessel revolve the same way about
the same axis, and their periodical times be as the squares of the
semi-diameters; the parts of the fluid will not go on in their
motions without acceleration or retardation, till their periodical
times are as the squares of their distances from the centre of the
vortex. No constitution of a vortex can be permanent but
this.

COR. 8. If the vessel, the inclosed fluid, and the globe, retain
this motion, and revolve besides with a common angular motion about
any given axis, because the mutual attrition of the parts of the
fluid is not changed by this motion, the motions of the parts among
each other will not be changed; for the translations of the parts
among themselves depend upon this attrition. Any part will
persevere in that motion in which its attrition on one side retards
it just as much as its attrition on the other side accelerates
it.

COR. 9. Therefore if the vessel be quiescent, and the motion of the
globe be given, the motion of the fluid will be given. For conceive
a plane to pass through the axis of the globe, and to revolve with
a contrary motion ; and suppose the sum of the time of this
revolution and of the revolution of the globe to be to the time of
the revolution of the globe as the square of the semi-diameter of
the vessel, to the square of the semi-diameter of the globe; and
the periodic times of the parts of the fluid in respect of this
plane will be as the squares of their distances from the centre of
the globe. COR. 10. Therefore if the vessel move about the same
axis with the globe, or with a given velocity about a different
one, the motion of the fluid will be given. For if from the whole
system we take away the angular motion of the vessel, all the
motions will remain the same among themselves as before, by Cor. 8,
and those motions will be given by Cor. 9.

COR. 11. If the vessel and the fluid are quiescent, and the globe
revolves with an uniform motion, that motion will be propagated by
degrees through the whole fluid to the vessel, and the vessel will
be carried round by it, unless violently detained; and the fluid
and the vessel will be continually accelerated till their periodic
times become equal to the periodic times of the globe. If the
vessel be either withheld by some force, or revolve with any
constant and uniform motion, the medium will come by little and
little to the state of motion defined in Cor. 8, 9, 10, nor will it
ever persevere in any other state. But if then the forces, by which
the globe and vessel revolve with certain motions, should cease,
and the whole system be left to act according to the mechanical
laws, the vessel and globe, by means of the intervening fluid, will
act upon each other, and will continue to propagate their motions
through the fluid to each other, till their periodic times become
equal among themselves, and the whole system revolves together like
one solid body.

SCHOLIUM.

In all these reasonings I suppose the fluid to consist of matter of
uniform density and fluidity ; I mean, that the fluid is such, that
a globe placed any where therein may propagate with the same motion
of its own, at distances from itself continually equal, similar and
equal motions in the fluid in the same interval of time. The matter
by its circular motion endeavours to recede from the axis of the
vortex, and therefore presses all the matter that lies beyond. This
pressure makes the attrition greater, and the separation of the
parts more difficult; and by consequence diminishes the fluidity of
the matter. Again; if the parts of the fluid are in any one place
denser or larger than in the others, the fluidity will be less in
that place, because there are fewer superficies where the parts can
be separated from each other. In these cases I suppose the defect
of the fluidity to be supplied by the smoothness or softness of the
parts, or some other condition ; otherwise the matter where it is
less fluid will cohere more, and be more sluggish, and therefore
will receive the motion more slowly, and propagate it farther than
agrees with the ratio above assigned. If the vessel be not
spherical, the particles will move in lines not circular, but
answering to the figure of the vessel; and the periodic times will
be nearly as the squares of the mean distances from the centre. In
the parts between the centre and the circumference the motions will
be slower where the spaces are wide, and swifter where narrow; but
yet the particles will not tend to the circumference at all the
more for their greater swiftness; for they then describe arcs of
less curvity, and the conatus of receding from the centre is as
much diminished by the diminution of this curvature as it is
augmented by the increase of the velocity. As they go out of narrow
into wide spaces, they recede a little farther from the centre, but
in doing so are retarded ; and when they come out of wide into
narrow spaces, they are again accelerated; and so each particle is
retarded and accelerated by turns for ever. These things will come
to pass in a rigid vessel; for the state of vortices in an infinite
fluid is known by Cor. 6 of this Proposition.

I have endeavoured in this Proposition to investigate the
properties of vortices, that I might find whether the celestial
phenomena can be explained by them; for the phenomenon is this,
that the periodic times of the planets revolving about Jupiter are
in the sesquiplicate ratio of their distances from Jupiter's
centre; and the same rule obtains also among the planets that
revolve about the sun. And these rules obtain also with the
greatest accuracy, as far as has been yet discovered by
astronomical observation. Therefore if those planets are carried
round in vortices revolving about Jupiter and the sun, the vortices
must revolve according to that law. But here we found the periodic
times of the parts of the vortex to be in the duplicate ratio of
the distances from the centre of motion; and this ratio cannot be
diminished and reduced to the sesquiplicate, unless either the
matter of the vortex be more fluid the farther it is from the
centre, or the resistance arising from the want of lubricity in the
parts of the fluid should, as the velocity with which the parts of
the fluid are separated goes on increasing, be augmented with it in
a greater ratio than that in which the velocity increases. But
neither of these suppositions seem reasonable. The more gross and
less fluid parts will tend to the circumference, unless they are
heavy towards the centre. And though, for the sake of
demonstration, I proposed, at the beginning of this Section, an
Hypothesis that the resistance is proportional to the velocity,
nevertheless, it is in truth probable that the resistance is in a
less ratio than that of the velocity ; which granted, the periodic
times of the parts of the vortex will be in a greater than the
duplicate ratio of the distances from its centre. If, as some
think, the vortices move more swiftly near the centre, then slower
to a certain limit, then again swifter near the circumference,
certainly neither the sesquiplicate, nor any other certain and
determinate ratio, can obtain in them. Let philosophers then see
how that phenomenon of the sesquiplicate ratio can be accounted for
by vortices.

PROPOSITION LIII. THEOREM XLI.

Bodies carried about in a vortex, and returning in the same orb,
are of the same density with the vortex, and are moved according to
the same law with the parts of the vortex, as to velocity and
direction of motion.

For if any small part of the vortex, whose particles or physical
points preserve a given situation among each other, be supposed to
be congealed, this particle will move according to the same law as
before, since no change is made either in its density, vis insita,
or figure. And again; if a congealed or solid part of the vortex be
of the same density with the rest of the vortex, and be resolved
into a fluid, this will move according to the same law as before,
except in so far as its particles, now become fluid, may be moved
among themselves. Neglect, therefore, the motion of the particles
among themselves as not at all concerning the progressive motion of
the whole, and the motion of the whole will be the same as before.
But this motion will be the same with the motion of other parts of
the vortex at equal distances from the centre; because the solid,
now resolved into a fluid, is become perfectly like to the other
parts of the vortex. Therefore a solid, if it be of the same
density with the matter of the vortex, will move with the same
motion as the parts thereof, being relatively at rest in the matter
that surrounds it. If it be more dense, it will endeavour more than
before to recede from the centre; and therefore overcoming that
force of the vortex, by which, being, as it were, kept in
equilibrio, it was retained in its orbit, it will recede from the
centre, and in its revolution describe a spiral, returning no
longer into the same orbit. And, by the same argument, if it be
more rare, it will approach to the centre. Therefore it can never
continually go round in the same orbit, unless it be of the same
density with the fluid. But we have shewn in that case that it
would revolve according to the same law with those parts of the
fluid that are at the same or equal distances from the centre of
the vortex.

COR. 1. Therefore a solid revolving in a vortex, and continually
going round in the same orbit, is relatively quiescent in the fluid
that carries it.

COR. 2. And if the vortex be of an uniform density, the same body
may revolve at any distance from the centre of the vortex.

SCHOLIUM.

Hence it is manifest that the planets are not carried round in
corporeal vortices; for, according to the Copernican hypothesis,
the planets going round the sun revolve in ellipses, having the sun
in their common focus; and by radii drawn to the sun describe areas
proportional to the times. But now the parts of a vortex can never
revolve with such a motion.

Let AD, BE, CF, represent three orbits described about the sun
S, of which let the utmost circle CF be concentric to the Sun ; and
let the aphelia of the two innermost be A, B ; and their perihelia
D, E. Therefore a body revolving in the orb CF, describing, by a
radius drawn to the sun, areas proportional to the times, will move
with an uniform motion. And, according to the laws of astronomy,
the body revolving in the orb BE will move slower in its aphelion
B, and swifter in its perihelion E; whereas, according to the laws
of mechanics, the matter of the vortex ought to move more swiftly
in the narrow space between A and C than in the wide space between
D and P; that is, more swiftly in the aphelion than in the
perihelion. Now these two conclusions contradict each other. So at
the beginning of the sign of Virgo, where the aphelion of Mars is
at present, the distance between the orbits of Mars and Venus is to
the distance between the same orbits, at the beginning of the sign
of Pisces, as about 3 to 2; and therefore the matter of the vortex
between those orbits ought to be swifter at the beginning of Pisces
than at the beginning of Virgo in the ratio of 3 to 2 ; for the
narrower the space is through which the same quantity of matter
passes in the same time of one revolution, the greater will be the
velocity with which it passes through it. Therefore if the earth
being relatively at rest in this celestial matter should be carried
round by it, and revolve together with it about the sun, the
velocity of the earth at the beginning of Pisces would be to its
velocity at the beginning of Virgo in a sesquialteral ratio.
Therefore the sun's apparent diurnal motion at the beginning of
Virgo ought to be above 70 minutes, and at the beginning of Pisces
less than 48 minutes; whereas, on the contrary, that apparent
motion of the sun is really greater at the beginning of Pisces than
at the beginning of Virgo, as experience testifies; and therefore
the earth is swifter at the beginning of Virgo than at the
beginning of Pisces; so that the hypothesis of vortices is utterly
irreconcileable with astronomical phenomena, and rather serves to
perplex than explain the heavenly motions.

How these motions are performed in free spaces without vortices,
may be understood by the first Book; and I shall now more fully
treat of it in the following Book."

PS. It should be noted that also the mathematics of the motion of a spinning
solid disc (in line perhaps with the ideas of Aristotle or early Kepler), do
not match the mathematics of the actual motion of the planets around the sun.
So neither the mathematics of the motion of a spinning solid disc nor of the
motion of a spinning fluid, match the mathematics of the actual motion of
the planets around the sun. Only the mathematics of Gilbert-Newton attraction
physics match the mathematics of the actual motion of the planets around the sun.
Newton showed that no simple-push physics can explain planet motion, though possibly
several different forms of pushings in combination might. Of course some later thinkers like Einstein did try to develop a more suited
mathematics using different theories, but even where their mathematics looks good
their theories maybe remain doubtful.

Though never publishing it, Newton seems to have considered that he had also
disproved Descartes' theory of terrestrial gravity as he conjectured in his
unpublished notes 'Certain Philosophical Questions'. For terrestrial gravity to
be due to some matter pushing bodies towards the Earth, as per Descartes, must
require perfect penetration which contradicts pushing - and matter causing
gravity by pushing must also push itself and that cause further contradictory
effects.

See http://www.newtonproject.sussex.ac.uk/view/texts/normalized/THEM00092 at 97r

(Note that reception plus re-emission could appear to be penetration, but
gravitational attraction by pushing has further problems)

At 113r-v there Newton also conjectured that collision motion must be due to a force like gravity,
and said that a thing that penetrates all matter he terms a 'spirit' - though William Gilbert
earlier had preferred the term 'non-corporeal body'.

[Try colliding two magnets North-to-North in a tube at different velocities, and observe their collision and rebound ?]
[In similar manner to Newton's disproof of Cartesian planet orbit vortex theory, it should be possible to disprove the general Cartesian small-particle-push theory of matter-penetrating magnetism and gravity. The experiments could involve a series of metal meshes of differing hole size allowing 1%, 50%, 99% air penetration and measuring the actual push forces produced for each to give a penetration/push-force equation to find if the Cartesian theory is or is not practicable physics ?]

As well as disproving several aspects of Descartes mechanical
theory like his planet motion vortex theory, Newton also disproved Galileo's
mechanical theory of Earth tides in general favour of the
earlier Gilbertian theory that tides were caused
chiefly by the attraction of the Moon. Newton often avoided ascribing poorer Descartes theories to Descartes when disproving them, as a
kindness towards Descartes that was not returned by his opponents who could only create lies about Newton 'having a bad personality'.
Newton was maybe also showing some kindness towards Descartes and others in not naming those he considered science giants on whose shoulders he stood ?
He certainly seems to have considered that most if not all of his physics peers of that time were very second rate scientists, though refraining from saying so.
But Newton's not naming those he considered science giants was no doubt also part of his determined efforts to avoid himself being associated with the then demonised William Gilbert whose physics he privately favoured.

That gravitational force is produced by objects only proportional
to their inertia or mass, seems proven by Galileo's on-Earth
experiments, by Newton's proof that in-space planet motions seem
consistent with that and more recently also by near-Earth space
measurements of variations in Earth's gravity by NASA's orbiting
GRACE project. (Newton did demonstrate that gravitational
attraction could maintain solar system orbits for a very long time,
though he did not examine all possible solar system gravity issues
- for more on this see our Solar
System Problems.)

And that gravity decreases with distance from a producing object
was demonstrated by numbers of physicists including Cavendish in
1798 (see Vision Learning) and was also recently confirmed
for short distances by a University of Washington project as in Physical Review Focus at
http://focus.aps.org/story/v7/st8

Galileo showing that all objects tend to fall to the surface of the
earth with the same acceleration, is evidence that response to
gravity seems proportional to inertia or mass.

Of course Einstein later claimed that Newtonian gravitation does
not always hold accurately, with some claimed evidence of
that.

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