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Trouble with Tides
by
Miles Mathis
Abstract:
I will analyze Newton's Proposition LXVI from The
Principia,
which is the foundation of modern tidal theory. I will show that
it is false. I will then show that its extension by Maclaurin is
also false. I will show that current equations fail to predict
the known eccentricity of the Moon, being off by a factor of ten.
I will then show the simple math proving that the eccentricity of
the Moon is caused by the charge field and the Solar Wind, not by
gravity.
Modern tidal theory,
like many other things, comes from Newton. Newton was only a
beginning, and it is admitted that he made some mistakes, but all
the major additions like those of Bernoulli and Laplace and
Maclaurin take Newton's basic gravitational theory as given. We
can see this in recent modern books like one from 2001 by David
Cartwright (of Cambridge and NASA), where the exposition of
“correct” tidal theory begins with Newton's Proposition 66,
from The Principia.
It is this proposition that I will analyze in this
paper.
Basically, this proposition shows a circular orbit
thrown into ellipse by a third body. Later tidal theorists (like
Maclaurin) then borrowed this proposition to show that the water
around the Earth could be taken as a third body, and that it
would therefore be thrown into ellipse, creating the tidal bulges
we have been talking about in other papers. I have already shown
that this solution has been falsified by lots of conspicuous
modern data (see the negative tide on the front of the Moon,
below). Here I will show the solution is illogical and false,
even before any data is presented. I will also show that Newton's
proposition was false to begin with, destroying the edifice at
the foundation.
In
Proposition 66, Newton gives us two smaller bodies orbiting one
larger body. The larger “central” body is T, the nearer
orbiter is P, and the distant orbiter is S (see illustration
under title). David Cartwright and modern theorists try to get
you thinking that S stands for the Sun, but if we look at
Newton's initial assignments, we find that is not so. S is
orbiting T, so T cannot be the Earth and S the Sun. The Sun does
not orbit the Earth, and it was not thought to do so in Newton's
time.
The first thing we find if we study Newton's own
assignments is that he does not give us any orbital velocities
for S and P. He clearly intends that his theorem will be proven
for any and all velocities, so that they are not important.
However, I will now show a simple falsification of his
proposition, using a set of velocities for S and P. If I can show
one falsification, the proposition, as stated, must be false.
Newton, in his illustration (above), draws S and P
initially orbiting T in circles. His claim is that S, the outer
moon, will necessarily throw P into ellipse. The case that
falsifies that proposition is the case that S and P have the same
time of one orbit. In other words, S is traveling much faster
than P, so that the two remain in the same position relative to
one another. The easiest way to see this falsification is to put
P and S in the same line to start with. Nothing in Newton's
setup disallows that. Well, if that is the case, then S and P
will remain in a line always, and this will only have the long
term effect of increasing the radius of P's orbit. P will be
thrown into a bigger circle, not an ellipse.
I will be
told that Newton's math and his proposition also tell us that T
will be thrown into a barycenter motion by the attractions of S
and P. This must cause an ellipse. No, it causes the appearance
of an ellipse only if we measure from T, and if T assumes it is
static. But if we measure the orbits from S, P, or any other
place in the field other than T, then P remains in a circular
orbit. No ellipse is created, and Newton's proposition is false.
I will then be told that the barycenter causes an ellipse
after the fact, since the barycenter creates a wobble. But the
barycenter does not create a wobble relative to the two orbiters,
if the two
orbiters were in round orbits to start with, and if
the inner orbiter is not thrown into ellipse. This is because the
two orbiters, if they are stable relative to one another, only
tend to pull the central body toward them. If they are stable,
they pull the central body toward them an equal amount at all
times, which means the central body is always the same distance
away from them. So the central body can
wobble without throwing the orbiters into ellipse.
This
also works if S and P are not in a line. They only have to have
the same orbital period. This is because P will always have the
same force vector from S, and this means that the orbit will be
changed the same amount all the way round. If you change a circle
the same all the way around, you get a bigger circle, not an
ellipse. To create an ellipse, you have to vary the change on the
circle. You can do a lot of math to prove this to yourself, but
it should be obvious at a glance. The only reason no one saw this
with Newton is that he couches everything in stilted and
convoluted language, and lots of dense geometry.
Newton's
geometry fails because it contains the unstated assumption that S
never moves. If S never moves, then Newton's theorem does
work: P is thrown into ellipse. But Newton states that S is in
orbit around T, and you cannot maintain an orbit with zero
velocity. Therefore, proposition 66 is false.
We can see
how confused Newton is by looking at cors. 3, 4, and 5. In these,
it is clear he thinks that the ellipse is pointy in the
quadratures, rather than at conjunction and opposition. In other
words, he in not telling us the ellipse is pointing at S, but the
reverse. In his corollaries, the bulges are not pointing at the
perturber S, the bulges are to the sides. Since his main
proposition is false, and his first corollaries are false, we
must assume all his corollaries are false.
Newton starts
corollary 5 by telling us P is closest to T at conjunction and
opposition. He then switches, telling us that IF P were in
ellipse to begin with (had an initial eccentricity), then “it
may sometimes come to pass” that P would be farther from T at
the syzygies. I take this to mean that an initial ellipse will be
made more elliptical, and that the ellipse will travel.
Newton
could have made it easier to understand by drawing an ellipse at
some point. But instead he just draws the same circle over and
over. He publishes the same stinking diagram six times in this
section, and never once draws the ellipse to show us where it is.
Newton then uses the next several corollaries to push the
ellipse from the quadratures to the syzygies. He creates several
variations or “errors” to make the apsides travel. In the
first variation (cor. 6), he lets the force from S vary. This
creates a motion of the apsides forward and backward, but “more
forwards than backwards.” But, again, he fails utterly to prove
this “more forwards than backwards.” He says it is because KL
is greater than LM (see diagram), but that is an accident of his
diagram. By varying the distance of S, we can make LM equal to or
greater than KL. So it is clear Newton is just pushing his
numbers here. It is less clear why
he is doing it. He wouldn't have needed to push his apsides to
the syzygies if he had just found his ellipse pointing at S to
start with, as they now do. Modern physicists no longer use this
push of Newton, and it is probably because they know it is a push
(supposing they can make any sense of this text at all).
But
that begs this very big question: if Newton's initial proposition
is false and all his corollaries are false, up to corollary 18,
why have we built 300 years of tidal theory upon corollary 18?
Corollary 18 is where Newton applies proposition 66 to tides.
Corollary 18 is one of the shortest corollaries in this section,
being less than 15 lines long, but it supports all of modern
tidal theory. In it, Newton proposes that we replace the orbiter
P by a fluid annulus or ring. “And the several parts of this
annulus, performing their motions by the same laws as the body P,
will draw nearer to the body T, and move swifter in the
conjunction and opposition of themselves and the body S, than in
the quadratures.”
That “swifter in conjunction”
means that once again Newton has his ellipse pointing the wrong
way. The apsides are in the quadratures, which is opposite the
modern drawings. More than that, in this corollary 18, Newton
never stabilizes his apsides in the syzygies. Yes, he proposes
that the apsides move, but they do not move to the syzygies and
stop there, as modern theory would have it. No, “the axis will
oscillate each revolution.”
Terrible problems there,
but we aren't finished. The tides cannot “perform their motions
by the same laws as the body P,” because the body P is an
orbiter and the tides are not. Apsides are qualities of an orbit,
and the tide cannot be assigned apsides. The reason for that is
the particles in Newton's fluid ring “move swifter in
conjunction;” but the tide cannot move swifter in conjunction.
The tide need have no orbital motion, at conjunction or anywhere
else, since motion at conjunction is defined as tangential motion
uncaused by the field, and the tidal motion, whatever it is, in
not motion of that sort.
To say it another way: in
earlier parts of The Principia,
Newton defines orbital motion as a compound of “innate motion”
and centripetal motion caused by gravity. The innate motion is
tangential motion that the orbiter carried into the orbit. It is
uncaused by the field. But the tides do not and cannot have this
motion. Since they are not in orbit, and since they have no
innate tangential motion, they cannot “perform their motions by
the same laws as the body P.”
Also, if the tidal bulges
were created by an ellipse in this way, then that would mean that
the bulges were the apsides of the ellipse. Since the Moon
travels within 30^{o}
of the equator, the tide should travel mainly equatorially, and
mainly east to west, with a maximum speed of travel between the
two bulges and a minimum speed under the bulges. Is that what we
find? Not even close. Even if we give the tide some time lag, it
doesn't work at all like that. If it did, we would see the
largest tides near the equator. In fact, we don't. The waters of
the Earth aren't even trying to orbit the Earth equatorially. If
anything, they are moving east to west, because they can't keep
up with the rotation of the Earth. That is not an orbit, that is
a resistance to an orbit, as we would expect.
Despite all
that, Newton tries (cor. 19) to force a comparison to Earthly
tides by proposing that his annulus of orbiting water is now
matched in speed by the rotation on its axis of T. Note well that
Newton simply proposes that the period of rotation of T is the
same as the period of rotation of the water. T does not cause
the rotation of the water, it simply spins underneath it, the two
periods of rotation matching by fiat. Is that really how we think
the oceans work? Are the oceans independent of the spin of the
Earth, the rotation of the Earth and the rotation of the water
just happening to match? We could ask the same question about my
couch. Is my couch orbiting the Earth, with a tangential velocity
of its own? Or is my couch moving due to direct contact with the
Earth? I had always assumed that my couch was just along for the
ride, but maybe Newton and modern physicists really believe it is
selfpropelled.
Honestly, I have to laugh sometimes. When
reading Newton I have to look twice at the cover, to be sure I am
not reading Swift by mistake. Passages like this one have the
flavor of the Laputians' floating island, except that Swift's
expositions are clearer.
By the way, Newton does get
around to switching his bodies, so that by cor. 14, T and P are
orbiting S. But if that is the case, we have to ask why Newton
didn't just let T and P orbit S to start with. Why do all the
math for one threebody problem, then switch the bodies at the
last minute? It looks like a shell game to me, and we had better
check his proposal. He simply states that all the math will be
the same as before, but is that true? It could hardly be true,
since in the first case we had two moons orbiting one body, and
in the second case we have a planet and a moon circling the Sun.
As just one example of how they are not equivalent, let us ask if
we can propose any velocities for T and P that will keep S and P
in a line. No, if we are given that P is still orbiting T, there
is no velocity for T that can change the nature of that orbit
relative to S. We cannot maintain constant relationships, and
therefore cannot maintain circles.
Modern physicists will
say, “Yes, you have shown some problems, but we don't care
about that. We only care that once Newton makes the switch,
defining S as the Sun, the Moon must be thrown into ellipse. If
the Moon is thrown into ellipse, then the tides must be, too. You
have admitted that the Moon must be thrown into ellipse, haven't
you?”
Yes, I have, but the problems remain. To start
with, physicists now use Newton's math in this section to show
why the Moon's apsides travel. The Moon's ellipse does not always
point at the Sun. It travels. If that is so, then the apsides of
the tide should travel in the same way, by the same general math.
Thing is, modern physicists want the apsides of the Moon to
travel, since they do, but they don't
want the apsides of the tide to travel, since there is no
indication that they do. They always draw the tidal apsides
pointing at the Moon, and they do that because if the apsides
travel, there is no way to get them to meet up with the Solar
bulges at the right times. Remember that the spring tide is
explained as a conjunction or opposition of the Sun's and Moon's
tidal apsides. But if the lunar apsides travel, they can be
anywhere. A conjunction of Sun and Moon can explain spring tides
only if the tidal apsides follow the position of the Moon. But
neither Newton nor Maclaurin or anyone else has shown that they
must. In fact, the math shows the opposite. If lunar apsides
travel, then tidal apsides should, too. You cannot have it both
ways.
Another problem is that by the current equations,
the eccentricity of the Moon's orbit should be easy to estimate.
The Sun has a force on the Moon 2.2 times that of the Earth on
the Moon. At closest approach, the Sun would have an even greater
relative force on the Moon. Unless the Moon moved close to the
Earth at this time, it would escape. This means that by the
current equations, the Moon's eccentricity would be infinity. The
Moon would move in a beeline toward the Sun.
Is that what
we find? Of course not. The Moon's orbit has an eccentricity of
.055, but the current equations predict infinity. Off by a factor
of infinity. The current math doesn't
work.
I think many mainstream
scientists recognize that gravity theory has many problems. But
since they see no clear answers, their only hope is that string
theory or brane theory may eventually come to the rescue. Until
then, they are not prepared to look hard at Newton or Laplace or
Einstein or any of the other big names. What we have doesn't
work, but it is all we have. Therefore we must defend it, they
think. Honorable, in a certain sense, but foolhardy nonetheless.
If the various standard models weren't sold and defended with
such certainty and gusto, more scientists would be prepared to
offer corrections. As it is, only outsiders like me are “allowed”
to spend any time studying alternatives. Peer pressure prevents
academics from doing basic science. Only a handful of top
theorists are allowed to speculate, and they have proved that
they are not able to solve this one. After a century of work,
they have only muddied up the water even more with all their new
maths and their fancy lingo. Rather than correcting Newton or
Laplace or Einstein, they have only whitewashed the old theories
with ever more coats of obscuring equations. But as we have seen
here, Newton was already dense and opaque enough. We did not
require more density, complexity, and opacity, we required a
cleanup. Now, 300 years later, we require a much larger
cleanup.
Gravity by itself cannot explain tides, it
cannot explain perturbations,
it cannot explain resonances, and it cannot explain the size of
ellipses (the actual eccentricities we see). To really begin to
explain all these things, we have to have two fields, gravity and
E/M. We have to have a unified field, and we have to have a
unified field where E/M is large enough at the macrolevel to
enter the equations. In my other papers, I have begun to show how
to do that.
I have shown that ellipses aren't caused by
gravity at all. Ellipses are an E/M phenomenon, caused by charge
field interaction. I will now show the cause of the Moon's
eccentricity very quickly and directly. That number .055 is the
same as 1/18, so all I have to do is show why the Sun's field is
1/18th that of the Earth. I have previously done
the math showing that the Solar Wind supplies a force 2/5th
that of the Moon's force on the Earth. That was my explanation of
the spring and neap variations. So we just need to find the Solar
Wind force as a fraction of the Earth's force on the Moon. Let's
do the math in reverse, to see what number we would need to find.
Obviously, we need to find that the Earth's force on the Moon is
7 times the Moon's force on the Earth. Because 2/5 x 1/7 ≈
1/18. Fortunately, I have already shown that math elsewhere. In
my long unified field
theory paper, I said it this way:
So,
if the Moon’s (radius x density) is 1/6 that of the Earth, then
if the Moon’s number is 1, the Earth’s number is 6. And the
total number for the combined field would be 7. But we want to
give the entire effect to the Moon, keeping the Earth as a fixed
point. So we multiply .151 x 7 to get 1.057m/s^{2}.
That is how fields work. And that
is where the number 7 comes from. The Earth's charge effect on
the Moon is 7 times the Moon's charge effect on the Earth.
Therefore, the Solar Wind's effect on the Moon is 1/18 that of
the Earth's charge effect on the Moon. And that gives us the
Moon's eccentricity of .055. The Moon's ellipse is caused by
charge, not by gravity. Newton's first postulate was wrong. He
began by assuming that bodies influenced each other by gravity.
But, in this case, they don't. Ellipses aren't caused by gravity.
Neither are perturbations or axial tilts or resonances. This is
not to say that I have ditched gravity. I haven't. I keep it in
my unified field equations, and it is just as strong as it ever
was. In fact, it is stronger, because I
have shown its presence in quantum interactions, increasing
its power there by a factor of 10^{22}.
But in this problem, as in all others, we have to monitor both
gravity and the charge field. It turns out that ellipses are
caused by the charge field.
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