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THE CHARGE
FIELD causes LAGRANGE
POINTS
by
Miles Mathis
Abstract:
In this paper I will continue to extend my unified field, and
more specifically my charge field, to explain other current
anomalies. As I have done in the past, I will solve both
anomalies that are admitted to exist and anomalies that are not
admitted to exist. Here I will show that the current Lagrange
points are misplaced in the field, due to mathematical errors by
Lagrange. I will rerun the 3body problem with my simple unified
field equations, showing not only the new points of balance for
the Moon, for a point, and for a satellite like SOHO; but also
the precise places where the current math and theory fail. I will
also pull apart the Lagrangian, showing that although it is
claimed to represent action, or a sum of potential and kinetic
energy, it is actually trying to represent my unified field, with
gravity and charge. In other words, I will show that the
equations of celestial mechanics continue to fail not because of
chaos, but because of simple and longstanding errors. Lagrange
failed to identify the charge field in the equations of Newton
and in the data, and he failed to see how the field varies as it
moves in and out from the Sun. Without that knowledge, he could
not get his operators to work. He could only push them, and we
continue to push them to this day.
We are taught that Kepler showed all
orbits are ellipses, and that even the round ones are very
slightly elliptical or eccentric. But I
have shown in great detail that current orbits, either
circular or elliptical, are not supported by the historical
fields, neither those of Newton nor of Einstein (nor, as you will
soon see, of Lagrange). Although physicists can write tortuous
equations for orbits, they cannot explain their causes. Lagrange,
along with Euler and Laplace, recognized this early on. Since I
have already written a long paper about
Laplace and his equations, we will look at Lagrange's here.
Lagrange discovered that in real life, Newton's fields and
physical explanations don't work. If we have just three bodies,
Newton's equations show a necessary instability. Since we know
that threebody problems have a real solution and a high degree
of stability (think the Moon), Lagrange needed to find a way to
write new equations, which he did. However, he never fleshed out
Newton's physical field, to show how the mechanics caused the
math. We have had a hole in celestial mechanics ever since,
though it doesn't seem to bother many people.
Rather than
sum forces in the
threebody problem, Lagrange summed kinetic and potential
energies, creating a thing called action. Action is the "least
motion" in these two fields. Yes, by looking at both
potential energy and kinetic energy, Lagrange was able to extend
Newton's one field into two. He created a sort of unified field,
with two parts. But since potential and kinetic energy both seem
to come from the same underlying field of gravity, it was thought
he had only performed some sort of mathematical trick, creating
two degrees of freedom where there was only one before. In a way,
that is precisely what he did. He waved his wand and created a
field out of thin air, without any mechanical or physical
assignment. He and everyone since has either run past the
problem, or they have assumed that his potential and kinetic
energies are both explained by Newton's gravity field.
I
will show that they aren't. What Lagrange actually did is intuit
the solution, then write math to fit it (as we all do
occasionally). He saw what the answer must be, then found a dual
field that would allow for or cause the degree of correctibility
that he saw must exist in the orbit. This is why his equations
have been so successful, and why physicists have not wanted to
analyze them too closely for bugs. Don't look a gift horse in the
mouth, you know, especially after he has won the Kentucky Derby.
Murray GellMann, one of the fathers of quantum
chromodynamics, put it this way when explaining how QCD worked as
a math:
In order to obtain such
relations that we conjecture to be true, we use the method of
abstraction from a Lagrangian fieldtheory model. In other words,
we construct a mathematical theory of the strongly interacting
particles, which may or may not have anything to do with reality,
find suitable algebraic relations that hold in the model,
postulate their validity, and then throw away the model.
This
is very interesting, because it means that the top physicists
have always understood that the Lagrangian math is a method of
abstraction that may or may not have anything to do with reality.
Whenever anyone says "may or may not", you may read
"may not." Whenever anyone says that, you may assume
they don't really care one way or the other. Lagrange, GellMann,
and all the rest have made it very clear that they do not care
whether any of their maths match reality. All they want is a
number at the end that matches data: they could care less about
physics. Modern physicists preen themselves on this attitude, but
any sensible person must find it strange to see physicists
bragging that they do not care about physics. This is what
GellMann is telling you here, in very clear sentences, and he is
like all his modern precursors, all the way back to Lagrange.
They are looking for "suitable algebraic relations"
only. But even in this, they fail. The most suitable algebraic
relations are relations that match reality, so you cannot sniff
at reality. Physicists now pretend they don't care about reality,
but that is only because they haven't been able to shake its
hand. It is like the monk claiming he doesn't like girls anyway.
Unfortunately, the equations of Lagrange (and those of
Laplace) did contain some remaining glitches, which led to
perturbation theory, chaos theory and so on. But I won't go there
in this paper. An even bigger glitch is that he never bothered to
define or explain the physical genesis of this second degree of
freedom or his second field. But failing to assign your fields
like this is not a metaphysical error. It is a physical error.
AND it is a mathematical error. Rather than admit that, all
assumed that this field assignment was not important, since
Lagrange assured everyone it was just potential energy. Since
everyone had equations for potential energy already, they assumed
this was the familiar old potential energy of Newton, just a
byproduct or restatement of gravity. Since they had familiar
equations for potential, they forgot to ask questions about it.
But this wasn't what Lagrange was up to. What I will show
you is that when Lagrange's unified field is working, it is
working because it parallels my unified field, where
charge is the second field. And when Lagrange's unified field
isn't working, it is because it isn't
paralleling my unified field. In other words, his sum was an
approach to the correct field math, but it wasn't quite the
correct field math. The actual field math, which I have finally
provided, is so good at explaining the motions we don't even need
chaos theory or perturbation theory anymore. Once you replace his
kinetic energy with charge, and fix
Relativity, there is no remaining error.
[For a full
analysis of the Lagrangian, you may go to my paper "Unlocking
the Lagrangian."]
Yes, it is the kinetic
energy of Lagrange's equations that was unassignable. In his
equations, it is the potential that is standing for the gravity
field, and kinetic energy is physically unassigned. Some will be
shocked by that, and others won't understand what I mean. So I
will explain it in full detail. Since the time of Newton,
gravitational potential and gravity had been two expressions of
the same field, one simply the reverse of the other. When I say
that they were the same field, I mean that they had the same
mechancial cause. Newton's gravity field was a mass field, and
the mass caused both the gravity and the potential. But Newton
wrote the equations as complements of one another, and for him
they always resolved. That is why he called it potential.
Gravitational potential energy was just energy that would
be expressed kinetically if you allowed an object to move in the
field, by the field. So kinetic energy and potential energy
weren't really two separate things. One was gravity being
expressed by motion, and the other was gravity about
to be expressed by motion.
To give an analogy, say you
are about to take a walk. You can say, "I am about to take a
walk." That is potential. It is in the future. Then you take
the walk, and while walking you say, "I am walking."
That is kinetic and present. But you only took one walk. Only one
parcel of energy was expended and only one distance was covered.
So you cannot sum potential and kinetic energy in a gravitational
field. You cannot sum those two sentences above. You cannot sum
the future with the present, and claim you have two different
things. This is how Lagrange cheated.
Let me restate
that, for good measure. In the Lagrangian, the potential and
kinetic energy don't resolve. If they did, the Lagrangian would
always be zero. For Newton, any sum of potential and kinetic
energy would have equalled zero, by definition, since the one
field creates them both and since one is the physical inverse of
the other. But Lagrange discovered, to his eternal credit,
that the two don't resolve, in fact. A celestial body has kinetic
energy that can't be explained by the gravity equations or the
potential. In other words, there is more to the field than just
mass and distance. Once we have exhausted the potential, we still
have kinetic energy left over. Given the definitions of Newton,
that can't be. What this should have told Lagrange is that there
is another mechanism at work in the field, to give us that
residual kinetic energy. Something else is driving celestial
bodies besides gravity. The very fact that the Lagrangian is not
zero is proof of a second field of some sort. But Lagrange never
bothered to notice that, or if he did, it was ignored. He buried
the field mechanics under a successful math, and no one has taken
the time to dig the physics out of the math since then.
What
this all means is that Lagrange had a hidden unified field, just
like Newton. Newton's unified field was
hidden in G, and Lagrange's unified field is hidden in the
Lagrangian. It is hidden in the fact that the Lagrangian is not
zero. There is a residual force not accounted for in the field
mechanics. The math is hiding a large part of the field.
As
I said, his equations often work, and they work because they
create a field out of thin air. They magically double a single
field, by taking a thing and its shadow as two different things.
But as it happens, there was a real
field there, invisible to Lagrange and everyone else, and his
equations expressed it fairly well. The charge field was there.
Not only was it there, but it was already inside Newton's gravity
equations, and no one knew that either. The second field was
there, it was hidden inside the constant G, and what is more, it
was aligned opposite to solo gravity, as a vector. In other
words, it was a differential, not a sum. The Lagrangian is not
really a sum, it is a differential, since potential energy and
kinetic energy are arrayed opposite to one another as vectors.
You subtract. Well, you do the same thing with charge and solo
gravity, so the Lagrangian is pretty good math in that regard.
Lagrange understood that he needed a differential in order to
create the correctibility. You have to have two fields working in
opposition in order to create that degree of float that we see in
real orbits.
However, I have shown that Lagrange made
many big errors. I have already written a paper on
the Virial, showing that the biggest standing error in the
Virial and the Lagrangian is an extra 2 in the field equations.
According to the math of Lagrange, you can fall to the center of
a gravity field and still have half your potential left. The
reason he has that huge error in his math is that he borrowed
Newton's math without analyzing it, and Newton's math already
contained that huge error. It was already embedded in the
equation a=v^{2}/r,
and Lagrange didn't spot it. According to Newton's own variable
assignments and math, it should have been a=v^{2}/2r.
Newton made a basic
calculus error. Langrange hid Newton's error and physicists
since Lagrange have hid his errors.
You can see that
without even reading my paper on that orbital equation, since the
Lagrangian has always had that unexplainable 2 in it. If you
don't like my explanation of why it is there, you tell me why it
is there. It conflicts loudly with Newton, but no one deigns to
notice that.
Lagrange also performed some shocking cheats
with the calculus, as I have shown in
previous papers. He did a switcheroo in front of everyone's
eyes, like a man with three shells and quick hands, and nobody
has spotted the switch in all these years. But you will have to
read that paper to see the trick.
Anyway, anytime you
have fundamental equations with extra twos in them, you are going
to get chaos. You are going to get physicists trying to push the
equations and pinch them and jerryrig them to match data, which
is what we have seen. We have seen centuries of embarrassing
pushes and fudges, and the entire field of Chaos theory is based
on this fudge. Same for most of perturbation theory, and other
large areas of current physics. If we removed all the subfields
of physics that were created to push faulty equations like this
into line, we would have to remove at least 75% of the field as a
whole.
Notice that in the Virial, which leads to the
Lagrangian, the potential energy is twice the kinetic energy. The
problem with that is this implies Lagrange's invisible second
field is the same size as his visible field. Lagrange has written
an equation in which the charge field is the same size as the
gravity field. I have shown that isn't physically true. Or, it is
true only for objects of a certain size. It is true for objects
that are around 1 to 10 meters in diameter. This is why the
Lagrangian works well at the human scale. But for smaller and
larger objects, the Lagrangian is false. Lagrange has correctly
found the two degrees of freedom in the field, but he has not
combined them correctly, because he didn't know the mechanics of
the two fields. To know how they combine physically, you have to
know what is causing the motions in each field, and Lagrange
didn't know that. Nobody has known that until now. So the
Lagrangian was a step in the right direction, since it gave us a
dual field, with one field in vector opposition to the other. But
the Lagrangian is still incomplete, since it doesn't combine the
two vectors in the right way. As we know, the charge field
diminishes as a fraction of the whole as we go larger, and
increases as a fraction of the whole as we go smaller. The
Lagrangian doesn't include that fact in the math. In other words,
radius matters, and the Lagrangian fails to incorporate that
variable in the right way. There is a third degree of freedom in
the math caused by the freedom between the two fields. There is a
size variation in the way the fields stack, and that is a third
degree of freedom in the math.
One way that Lagrange's orbital
equations are semisuccessful is in their prediction of Lagrange
points. Jupiter's Trojans are cited as proof of this success, and
that is in indeed what is happening with the Trojans. They are
inhabiting areas where the field more or less balances. However,
this has nothing to do with kinetic and potential energy, it has
to do with gravity and charge. Neither kinetic energy nor
potential energy can hold real objects at a distance, and the
only way that the Trojans can be kept from moving closer to
Jupiter is with some real force of exclusion.
Some will
say, "What do you mean, kinetic energy cannot keep things at
bay? That is precisely what does keep things at bay!" No,
Lagrange must mean gravitational kinetic energy, and
gravitational kinetic energy does not keep anything at bay.
Gravitational kinetic energy has no exclusionary power, by
definition. Gravitational kinetic energy is the energy a body has
due to the field, and that energy is always toward
the central object. So the vector is wrong. There is no possible
gravitational kinetic energy that could be keeping the Trojans
from moving closer to Jupiter. Gravitational kinetic energy is
always toward an object, not away from it.
We can say the
same for potential energy. Potential energy has no exclusionary
power. I hope that is obvious.
The Trojans must be
excluded for some other reason. Some other field must be
balancing the gravitational field here. Which means that the
Trojans are just one more proof of my unified field, and of
charge. The Trojans are held at bay by the charge field of
Jupiter.
We can see this most clearly if we go to
Lagrange point 1, instead of 4 and 5. It is known that Lagrange's
points 1 and 2 don't really exist where they are supposed to. We
have tried to take satellites to the Earth's point 1, with no
success. I mean, the satellites are there, but there is only a
reduced instability, not a stability. Not only is there no
stability there, there is no stability around the point. The most
stable orbit in the area is the halo orbit near point 1, where
the Solar and Heliospheric Observatory (SOHO) exists. But even
halo orbits aren't stable, and they require stationkeeping or
governors. The same is true of Lissajous orbits, which means that
Lagrange's equations are only generally correct. He sends us to
the right general area, but not to the right point, and not with
the right governors. We haven't really solved the field equations
yet, because we don't understand the make up of the fields. The
engineers know this, but they are kept quiet by the theorists.
The engineers push the equations to make them work, and then they
are told to stay mum about it. I will recalculate point 1 below
with my unified field, showing the errors in the current math. It
turns out that Lagrange's equations don't even send us to the
current Lagrange points without a lot of very unsightly
tinkering.
First, let's compare the Earth's points 1 and
2 to the motion of the Moon. It seems to me that a single Moon
would try to hit those points, since it would be a great energy
saver if it did. Action is supposed to be "least motion",
which would imply an energy saving like this, but according to
the current math the Moon ignores the points, orbiting well
inside them. That is the first sign something is wrong with the
equations.
Next, let us look at the eccentricity of the
Moon. According to current equations, the Moon should have an
eccentricity of infinity. It
should crash into the Sun. They don't admit that, of course,
and if you show the imbalance in the equations, they point to the
sum, which resolves. But the problem is not the sum, it is the
individual differentials. At New Moon the Moon is seriously out
of balance, for instance, and although it corrects that, there is
no physical explanation of how
it corrects that. In other words, the current equations are
garbage. They are pushed. They resolve only as a sum. As a theory
or a mechanics, they miss by infinity.
We find the Moon
has an eccentricity of .055, and, again, current equations can
show that only with a major push. As we will see below with the
Lagrange point math, physicists switch to noninertial math and
bring in centrifugal forces and Coriolis forces and so on. This
despite the fact that gravity is inertial. Gravity practically
means inertial, and yet they have the gaul to hide in
noninertial math. Even worse, they claim to do noninertial
math, but then propose Coriolis forces and centripetal forces
inside this math. The problem there? Forces are inertial, by
definition. Going to noninertial math and then proposing new
forces is absurd. It is somewhat like an ichthyologist doing all
his research on dry land, and then writing equations for bouyancy
with solid state equations, instead of liquids.
Most
won't understand what I mean by that either, so I will elaborate.
Historically, noninertial has just meant any situation that
includes accelerations, so gravity seems noninertial. That is
what people are taught, so that is all they know. But gravity
isn't noninertial, since gravity doesn't avoid inertia. It only
avoids the easy solutions, and it only avoids them because
mathematicians have preferred to muck up the math. Gravity is
inertial for two reasons: 1) it is a field of forces,
specifically centripetal forces, and forces are inertial. You
can't have gravity without inertia and you can't have inertia
without gravity, so gravity is inertial. You will understand what
I mean if you consider that in the end, Einstein considered his
field equations to be noninertial. But by that he didn't mean
that they included accelerations; no, he meant they bypassed
accelerations. In curving his field with new math, Einstein got
rid of centripetal accelerations. It was the curves that caused
the motions, not the force. So what noninertial really means in
General Relativity is no forces. It means curves rather than
forces. 2) Gravity is inertial because the line of influence
between two bodies is a line, not a curve. Even AFTER Einstein
made his field noninertial in both ways, the line of influence
was still a straight line. That is the one line that
nonEuclidean math doesn't make into a curve. Since gravity works
along that straight line of influence, gravity is inertial for
Newton, and it is inertial for Einstein. Both of those guys, and
everyone else since, has tried to deflect you from seeing that,
but it has always been true and still is. Gravity is inertial
because it concerns forces; and gravity is inertial because it
can be solved along straight lines. You have been taken into
curves and other noninertial math because the old guys couldn't
solve this one in a straightforward manner, so they decided to
hide in big equations. Why couldn't they solve it? They didn't
have that second field. Even after Lagrange gave them a second
field (kind of) with the Lagrangian, they forgot to assign it to
something real. If they had recognized that the second field was
not potential, they might have been able to unify long ago.
Instead, they have had this "successful" math sitting
around for centuries, and never thought to look for the E/M field
inside it. It never occurred to them that charge, electricity and
magnetism had already been included in the Lagrangian from the
beginning.
But if we go back to the eccentricity of the
Moon with all this in mind, we can solve it. I
have shown that we require the Solar Wind, which is an E/M
effect, to calculate it. If we know how the field really works,
we can solve such problems without any difficult math at all. All
we need is fractions. Yes, the Solar Wind at the distance of the
Earth/Moon is strong enough to positively affect the Moon's
orbit. Not only is charge an effect of the unified field, but
secondary effects of charge also have to be factored in, like the
Solar Wind.
Another oddity of current math concerns the
spreading of Lagrange points. We are told that ellipses cause
Lagrange points to spread out or blur, but that is just
rationalizing. It is especially sad regarding points 1, 2, and 3,
which are in a line. How can an ellipse spread that math? It
isn't that the Earth's eccentricity spreads or hides point 1, for
instance, it is that the satellites are in the wrong place. They
are thousands of kilometers away from the true points of balance,
and so they require halo orbits and governors to overcome the
forces they still feel. I will prove that below.
I will
now recalculate Lagrange point 1 for the Earth. I have done
similar math in my papers on
weight and on the
magnetosphere, showing where the two fields balance.
According to current math, Lagrange point 1 is about 1.5 million
km from the Earth. To find that, at Wiki we are currently told
this
L_{1}
is about 1.5 million kilometers from the Earth. Gravity from the
Sun is 2% (118μµm/s^{2})
more than from the Earth (5.9μm/s^{2}),
while the reduction of required centripetal force is half of this
(59μm/s^{2}).
The sum of both effects is balanced by the gravity of the Earth,
which is here also 177μm/s^{2}.
See, no Lagrangian there. Notice how
that looks a lot like tidal math. "The reduction of the
required centripetal force" means they are calculating a
centrifugal force, caused by the angular momentum, and it is half
the main force. Funny that they include that here but not in the
tidal equations for the Earth. As I showed in my first
paper on tides, they "forget" that the Earth is
orbiting the Sun, so that they can force the number 46% to
appear. Or, if they include it, they then use the same equation
on the tide from the Moon, which would imply that the Earth is
also orbiting the Moon. If you correct their fudge there, the
number is 67%, which doesn't match data.
But here, they
include it when they have no mechanical justification for it. The
centrifugal effect or the "reduction of centripetal force"
(which is supposed to be the same thing, I assume) might possibly
enter the tidal math in a logical way—supposing the Earth were
on a string tied to the Sun—because the centripetal and
centrifugal forces oppose in a way that would pull on a real
object, stretching it radially. But the centrifugal force can't
be used here as they are using it, since it doesn't just "reduce"
the centripetal force. They both have to act on the body, which
will stretch it. Notice that is not what is happening here. They
aren't applying both the force and the reaction to the force to
the real object in the field, they are just subtracting out the
reaction before any forces are applied! That is a cheat of
magnificent proportion. Newton is turning over in his grave. The
centrifugal force isn't an automatic "reduction" of the
centripetal force, it is a reaction to it. This is because the
centrifugal force can cause stretching, but it can't cause motion
in the field. It is force felt internally by the object, and so
it can't cause motion.
The same force can't cause two
field effects. The centrifugal force can't cause a tide and also
cause a field vector. It is either expended internally or
externally. The centrifugal force is the body's own reaction to
the orbit, and so it is not part of the field equations.
To
make this even clearer, notice this contradiction: if the
centrifugal force were a field
response (instead of a response internal to the object) to the
centripetal force, and if we could thereby add or subtract it
from the centripetal force in the field equations, then we would
create an infinite feedback mechanism. Say the centripetal force
is x, and the centrifugal force is x/2, which we add, achieving
3x/2. Does the body now feel 3x/2? And if so, why doesn't the
centrifugal force increase to respond to half of that?
In
a Newtonian orbit, the body orbits because it is feeling a
centripetal force. It is not orbiting because it is feeling a
centripetal force plus or minus a centrifugal force. For Newton,
the centrifugal force was included in tidal equations, but it
would not have been included in these Lagrange point equations,
for strictly logical and definitional reasons. I find it
extremely sad that I have to be here telling anyone this.
Not
only is including the centrifugal force illogical as a piece of
Newtonian mechanics, but we know from data that celestial bodies
don't feel centrifugal forces. We have mountains of evidence that
they don't, straight from the Moon. I have been screaming about
this evidence for years. Rather than argue about whether the
Earth shows centrifugal forces in its tides, we can go to the
Moon, where we don't have to look for fleeting evidence in
liquids. We can look for evidence in the crust. Since the Moon is
in tidal lock, the forces don't travel. Therefore they should
stack, year after year after millions of years, making the
evidence obvious. If we had centrifugal forces, we would see
their effects on the Moon. We would see a big tide at the front
and back, and we would see shearing sideways, one direction
forward and one direction back. What do we have? The most glaring
negative data imaginable. No tide in the back, and a negative
tide in the front. And no shearing. We also have negative data
that is very easy to read from the moons of Jupiter and Saturn,
including the very small moons inside the Roche limit. But I have
covered those extensively in another
paper.
So the current math is a complete
misunderstanding and misrepresentation of the field. Let's return
to the Lagrange point math. I don't even understand where the
numbers at Wiki come from. The number 177μm/s^{2}
above comes from this equation
a_{E}
= GM_{E}/R^{2}
But where does the number 118 come from? The gravity from
the Sun at that point must be
a_{S}
= GM_{S}/(1AU –
1.5 million km)^{2}
= 6082μm/s^{2}
The Sun's gravity is not 2% more than the Earth's, it is
3400% more. Even with some jerryrigged centrifugal force, or
reduction in centripetal force, we can't get those two numbers to
balance.
Wikipedia is normally bursting with university
people to correct things like this and/or defend them, but even
on the discussion page I found nothing. No one else found those
two sentences strange, although they aren't even readable. Beyond
the numbers, the sentences make no sense. Why are the Wiki police
letting that stand? Do they really believe math or the English
language is represented there? To find out, I went to a
university site.* This site linked to the "full math".
The full math started out like this:
The
procedure for finding the Lagrange points is fairly
straightforward: We seek solutions to the equations of motion
which maintain a constant separation between the three bodies. If
M_{1} and M_{2}
are the two masses, and r_{1}
and r_{2} are
their respective positions, then the total force on a third mass
m at position r will be
F = GM_{1}m(r
 r_{1})/(r –
r_{1})^{3}
 GM_{2}m(r 
r_{2})/(r –
r_{2})^{3}
The catch is that r_{1}
and r_{2} are
functions of time, since M_{1}
and M_{2} are
orbiting each other.
This is used as
an excuse to bring in not only a centrifugal force, but also a
Coriolis force! Notice that we are being misdirected here just as
at Wiki, although the misdirection here is done with more
finesse. That equation is a straight expansion of the math I just
did, but it has been mucked up to make it seem more complicated
than it is. Why the cubes? Why the point coodinates and vectors
instead of just distances? Also, when we look at the Lagrange
points 1, 2, and 3, r_{1}
and r_{2} are not
functions of time, or, if they are, it doesn't matter to the
math. We don't have to "adopt a corotating frame of
reference in which the two large masses hold fixed positions."
This is because M_{1}
and M_{2} are not
"orbiting eachother." M_{2}
is orbiting M_{1},
and M_{1} can
remain fixed. All this math is just deflection, to get the reader
confused. If the reader is confused enough by the math, he won't
notice that it doesn't make any sense.
The only way that
r_{2} is a
function of time is if we have to include the eccentricity of M_{2}.
But we can estimate a solution without that, since the Earth's
eccentricity is low. And if we estimate a number, it is nothing
like the number from this full solution, with Coriolis effects
and so on. As you just saw, the answer is hundreds of thousands
of kilometers different!
The author says, "The only
drawback of using a noninertial frame of reference is that we
have to append various pseudoforces to the equations of motion."
So he admits that the Coriolis force and the centrifugal force
are pseudoforces! And clearly it is not really a drawback to
have to muck up the math like this, since that was the whole
point. The math is being mucked up on purpose, to hide the fact
that it is all completely unsupported. It is a hash. It is a
fancier hash than the hash at Wiki, but it is still hash.
Yes,
these samples of "full math" are always just
misdirection. They are not posted to provide you with the full
math. They are provided to prevent you from seeing the mechanics.
They are provided to finesse some answer they desire from pages
full of nonsense, making sure that no one can possibly follow the
nonsense.
As for the Coriolis force, it is also a ghost
here. Physically, there is no Coriolis force. It is not even a
pseudoforce, it is only a curve caused by position. It is a
simple outcome of preEinstein relativity and has absolutely
nothing to do with the inertial or noninertial field. That is
why it only pops up in the socalled "nonenertial"
math. That is to say, it is not dynamic or kinematic. It is
fabulously easy to pick a frame of reference in which it doesn't
play a part, so the choice by physicists to include it in any
math should be a big red flag. Currently, it is only included as
an excuse to fudge the math. I haven't seen any example where it
wasn't used that way, and it is used that way here. I haven't
written a paper on the Coriolis effect yet [ I
have now ], but I do hit the fundamental problem with some
degree of rigor in my first paper on General
Relativity (the merrygoround is an example of the Coriolis
effect). I should probably give it paper all to itelf, and show
the various ways it is misused. Just as a teaser, it is falsely
used as the solution to the wind and water currents problem,
north and south of the equator. These aren't caused by the
Coriolis effect, they are caused by. . . yes, the charge field.
To see how far the current equations have been pushed, we
just complete the math I started, or solve for zero using the
first equation from the university pdf, as I have copied it
above. We find that at 2.586 x 10^{5}
km, the Earth's acceleration upon point 1 matches that of the
Sun. That is a long way from the current Lagrange point.
Hmm.
Let's write that out in the long way and study it. 258,600 km.
That's in the same ballpark as the orbit of the Moon. Maybe the
Moon really IS hitting the Lagrange points, or trying to. The
Moon is inclined five degrees to the ecliptic, so it doesn't hit
the right plane every month, but it isn't far away. And since the
nodes travel, it will hit them occasionally. We know that from
eclipses. At Solar eclipse, the Moon is nearest Lagrange point 1,
one way or another, since it is right between Earth and Sun. So
let's do the math using my unified field equations, instead of
Newton's equations or Lagrange's. And let's do them following
this idea: perhaps the Lagrange point is varying in practice
because it depends on the charge of the object in question. If we
solve for a mathematical point, for instance, that point will
have no charge. In which case we will do a straight balance of
solo gravity from Sun and Earth. But if we solve for a satellite
like SOHO, we must remember that its charge, though small, is not
zero. It cannot act like a point, therefore it will not go to the
actual Lagrange point. It may go near it, but it will act a bit
differently than a point. And if we take a large body like the
Moon, with a large charge of its own, it will go to a Lagrange
point many thousands of kilometers away from the Lagrange point
proper. In other words, the Lagrange point or balancing point of
1) a point, 2) of SOHO, and 3) of the Moon may be very different.
Again, the math will be simple, because there are no
centrifugal forces in my math. The centrifugal force was proposed
as the equalandopposite reaction to the centripetal force, but
my math, like Einstein's, contains no centripetal force. There is
no string between here and the Sun, not even an abstract string
or a mathematical string. Einstein's equations have no
centrifugal force because he has no centripetal force. You cannot
have a reaction to nothing. My equations do not contain a
centrifugal force because I have shown that neither the object
nor the field contains one. Both logic and all data tell us that.
A centrifugal force is a reaction of the body, not the field, so
it is not included in field equations, ever. And it is not
included in celestial field equations because the field is not
created by a string between objects, or any other pull.
We
will calculate for the Moon first. Since 384,400 km is about
60.27 Earth radii, we can see if the unified field balances
there. But we have to put a real body there, not a point. We
can't calculate charge for a point.
Let me explain the
math before I do it. I will calculate the important accelerations
due to the three bodies and the two fields. Once I have separated
gravity and charge in the unified field, gravity is only a
function of radius. It is no longer a function of the inverse
square. Unified, the two fields still follow the inverse square
(roughly), but once separated, they don't. I will also use my new
numbers for solo gravity, calculated by subtracting the charge
field from the old gravity number. For instance, the current
surface gravity of the Sun is said to be 274m/s^{2},
but I have shown
that we really have 1070 for solo gravity and 796 for charge,
which sums to 274. The same applies to the Moon, so my number for
the Moon, 2.668, is also not the current one. It is g/3.67
because solo gravity follows radius only. I use 9.7895 for g
because that is the current number 9.78 + the number I have found
for the Earth's charge .009545. I always use equatorial numbers,
because charge is heaviest at the equator. Besides that, we need
one more correction to the field. In my long unified
field paper, I developed equations for a twobody problem.
But here we have a threebody problem. This changes the charge
math, since the charge of the two smaller bodies is in the
greater field of the largest body. As I showed in my papers on
axial tilt and Bode's law, this directionalizes the main charge
field. In other words, charge emitted toward the Sun acts
differently than charge emitted away from it. Charge out drops by
1/r^{4}, while
charge in increases by the distance. I showed that this is due to
the field lines, whereby charge density increases as you go in
and decreases as you go out. The field itself is already denser
as you go in, as charge is channeled into the center, and this
greatly affects all the charge math. Threebody problems are
therefore completely different mathematically than twobody
problems, since you have an ambient charge field already existing
before any emission by the bodies. Of course without this
knowledge, previous math could not hope to match the motions
without huge amounts of pushing. I will use the same math I used
in my paper's on Bode's
law and axial
tilt, since that math is the simplest and most transparent as
a matter of mechanics and vectors.
We start with charge.
I have shown that charge is a function of both mass and density.
Since we seek a charge density to work with, and since mass and
charge are equivalent in the field equations, we seek a mass
density. So to calculate relative charge (charge of one body
relative to another), you multiply mass times density. This means
that the Sun has 85,063 times as much charge as the Earth.
Therefore, if we give the Earth a charge of 1, the Sun has a
charge of 85,063. Since the Sun's charge is moving out from
center, we take the fourth root. ^{4}√85,063
= 17.078 But since the charge field of the Earth is actually
.009545m/s^{2},
not 1 [see here
for short proof], the actual charge field of the Sun is
17.078(.009545) = .16301m/s^{2} Since
the Earth is 1/388 times as far away as the Sun, the Earth's
relative charge at the Moon is only .000025. To find the
total charge field at the Moon, we add eq.1
.16301 + .000025 = .163035m/s^{2}
Now we do the gravity. eq.2
Gravity from Earth to Moon 9.7895/60.27 = .162427 eq.3
Gravity from Moon to Earth 2.668/60.27 = .044267 eq.4
Gravity from Sun to Moon 1070/23,395 = .045736 eq.5
Gravity from Moon to Sun 2.668/23,395 =
.000114
We add eqs.4 and 5, then subtract 3 from that,
then subtract that from 2, to get .16084. Then we subtract that
from eq.1, giving us .002195m/s^{2}.
Since that is very close to my corrected number for the offset of
the tangential velocity
of the Moon (calculated in
another paper) of .002208m/s^{2}**,
I think I may claim to have solved the problem.
Please
notice that I have solved this problem with five equations,
composed of fractions and sums. Then remind yourself of the math
string theory is throwing at this same problem. Yes, superstring
theory is attempting to create a unified field. We are told that
supercomputers are needed just to store the postulates and
operations, and we are expected to be impressed by that. But the
ones who used to trumpet elegance were correct. The right answer
is always much simpler than we imagine. It is just difficult
these days to imagine a simple answer. The waters have been so
muddied by so many unclean swimmers thrashing about and by so
many years of pollution being dumped indiscrimately into the
river, a lonely bather cannot imagine looking down and seeing the
bottom, even when his feet are firmly planted on it.
The
only remaining disclarity in my math is the subtracting of the
last numbers, instead of adding. It has seemed to some of my
readers that the charge force of the Sun must be out, and the
gravity of the Earth on the Moon, also out. I have shown that
charge is a bombardment of charge photons, therefore the Sun must
push the Moon out. And the Earth also pulls the Moon out.
Therefore, shouldn't we add them? No, although I see the
fuzziness there. I admit that it is sometimes beastly difficult
to keep track of these field vectors. If it were easy, this
problem wouldn't have sat unsolved for centuries. Again, the
answer is that both the Moon and Earth are in the the greater
field of the Sun. Therefore, as vectors, we can't just measure
the Moon relative to the Earth. We have to measure both the Moon
and Earth relative to the Sun. In other words, if we wanted to
take the gravity vector of the Earth on the Moon as pointing out,
we would have to take the Earth as a fixed point. But the Earth
is not the fixed point in this field, the Sun is. Remember, the
Earth also has an acceleration vector pointing at the Sun,
although we have been able to ignore it in this math.
You
will say, "But you just showed that the Earth's gravity is
stronger than the Sun's in these equations. If the Sun's field is
weaker at the Moon, then shouldn't the Earth define the gravity
field there?" No. I only showed that the Earth's apparent
force at the distance of the Moon is greater than the Sun's, but
of course I did not show that the Earth's field is greater than
the Sun's overall. That would be impossible, wouldn't it? The
Sun's gravity field is the baseline field, and it therefore sets
the direction of all the vectors. It doesn't matter that the
Earth's "pull" is greater at a certain place in the
field. What matters for the vectors is the baseline field, and
the Sun's field is obviously the baseline field. Since the Sun's
gravity is in vector opposition to the Earth's gravity in this
position, it has the effect of flipping the vector. So, yes, it
almost looks like the gravity of the Earth is pushing the Moon
nearer the Sun. It isn't, but it does kind of look like that in
the math, at a glance. [This is also why we add the charges in
the first part.]
So I have found that the Moon is
at its own Lagrange point 1, given its velocity. I have shown
that all the accelerations and vectors balance, at a single
position, without any difficult math. No Lagrangians, no Coriolis
forces, no centrifugal forces, no pseudoforces or pseudomath.
No curves. Just fractions. This has never been done before. The
current and historical math only solves by integrating or
summing, or by isolating forces. For example, we are currently
taught that the orbital velocity of the Moon balances the
centripetal force from the Earth. The centripetal force of the
Earth at that distance is .002725, and that balances the Moon's
velocity. Unfortunately, that leaves the Sun out of it. I suppose
we are expected to believe that the Sun's force is the same all
around the Earth, and sums to zero or something, but that isn't
borne out by a close examination of either Newton's field or
Lagrange's.
Another thing to notice is that we only have
to slow the Moon down a bit to make it hit a more tightly defined
Lagrange point. Historically, the Lagrange point hasn't been
stationary in the field, of course, since if the Earth is moving,
the point has to move with it. We would drop the Moon's velocity
from 31km/s to just under 30km/s, to make it stop orbiting. If we
could slow it instantaneously right at that position, we might
make it hover in eclipse, permanently. Of course there are other
instabilities in a real problem, including the Solar Wind and
charge from Venus and Jupiter, to name the largest, but we won't
concern ourselves with that here.
What I want to do now
is see if that Lagrange point is at the distance we found above,
using Newton's simple equations. Remember that we found the
number 258,600 for the Lagrange point, using Newton's math
instead of Lagrange's. What if we put the Moon at that point with
an Earthshadowing velocity of 29.75km/s? Would it stay there,
without orbiting the Earth (ignoring other instabilities)? No, if
we run the numbers again, we find a repulsion of .101m/s^{2},
so we have gone way too close. What we find is that the correct
distance for balance, with no orbit, is around 380,500km. We only
have to move the Moon 3,500 km from its average orbital distance
to achieve a nonorbiting balance at Lagrange point 1. Since that
is already in the current range of the Moon, you can see that the
forces that cause the Moon to orbit aren't very different from a
nonorbiting balance. In other words, it wouldn't take much of a
blow at eclipse to make the Moon hover in eclipse (or it wouldn't
if the Moon were orbiting retrograde). We just slow it from about
31km/s to about 29.5km/s, relative to the Sun.
And so,
the Moon's Lagrange point 1 is at about 380,500km. The Moon is
where it is because it is staying near its Lagrange point, which
completely contradicts current math and theory. However, it
confirms logic. As I said, we should have expected
the Moon to hit its Lagrange point at Solar eclipse, since we
know the Moon is in balance. If the Moon weren't in balance, it
would fly off into space. In fact, some of the old guys like
Euler and Lagrange did
expect it. Some of them were surprised that the Moon didn't hit
this balancing point at eclipse.
Now let us calculate the
Lagrange point for a point. To do this is completely theoretical,
since points don't exist, either in fields, in math, or in
Nature. But if we want to understand how the current equations
fail, we can correct them while staying as close to their
postulates as is physically possible. A point will feel no
charge, since charge is a collision. You can't collide with a
point. Our point also can't have its own gravity, since a point
can't have mass. And so our math is just that much simpler. We
only need equations 2 and 4. We find the Lagrange point at 1.3565
million km.
eq.2 Gravity from Earth to point
9.7895/212.68 = .04603 eq.4 Gravity from Sun to point
1070/23,243 = .04603
This is closer to the current
number, 1.5 million km, but that number is almost 10% off. Even
when they try to match their math to real orbits, they still fail
by 10%! You will say, "How can they be 10% wrong, when the
satellites are there? Are you saying the satellites aren't
there?" No, of course not. I am saying that the satellites
are neither points nor bodies with much charge, so they won't go
to either the Lagrange point for a point or the Lagrange point
for a Moon. To understand why they are near 1.5 million km with
some degree of stability, you have to study the actual Halo orbit
or Lissajous orbit that they are in. Both the Lissajous and Halo
orbits act to make the orbiter seem bigger than it is in the
field. So, in effect, what they have done is stretch out the
radius of the "point", while keeping its mass and
charge near zero. The less motion they gave to the satellite, and
the smaller the satellite, the closer they could take it to the
Lagrange point at 1.3565. But tiny satellites aren't useful, and
tiny governors aren't either. It is much easier to let a
satellite move, and govern its motion. That is why they use these
pattern orbits.
Lissajous
"orbit"
Anyway, if we start
at my Lagrange point 1, and we expand the point by giving it both
radius and mass, it will have charge also, and we will have to go
closer to the Earth to keep the balance. The Sun will respond to
the increasing charge, and will push it away. That is why the
Moon is inside the Lagrange point proper. But if we increase the
radius and don't
increase the mass, we will have to go away from the Earth to keep
the balance. The larger radius makes the Earth seem to push it
away, as in the equations above. But the Sun does not respond in
kind, because the charge hasn't increased. This is what is
happening with our satellites that are supposed to be at Lagrange
point 1. They are mimicking a larger object with a fast halo
orbit or something, and the field takes them to be an object with
the radius of the halo. But since the halo is empty, with no
charge, the Sun does not respond in kind. The Lagrange point has
seemed to move away from the Earth.
Now, I have just
claimed to have solved another 300 year old problem, but skeptics
will say, "This is just a general solution to the 3body
problem, and we have had those since Newton. At the end of your
math, you still miss by a fraction, so how can you claim to have
bypassed chaos theory and perturbation theory? You would need to
solve to fifty decimal places to do that, and you haven't even
solved to six!" This critique completely misses the
significance of what I have just done. I have shown you that the
field equations were fundamentally in error, which means they
weren't right at any decimal point. The equations added by
Lagrange weren't a correction, extension, clarification, or even
a finetune, they were only a complex mathematical push. To be
specific, the current field equations are wrong because they
can't insert the
field numbers I just inserted. For instance, they can't use the
number 1,070 for the Sun because they have no way of calculating
it, straight from first postulates. And they can't represent the
degree of freedom in the charge field, because they don't
understand there IS a charge field, much less that it changes in
a different way out than in. They haven't got the right
exponents; they don't have the plus and minus signs in the right
place; they don't have the right two fields. And so their math is
wrong. It is that simple. I can make my numbers out better by
using better numbers in; they can't. My error is just a matter of
measurement, and of inserting more data. Their error is caused by
faulty equations. There is a big difference. For this reason, I
don't need to solve to fifty decimal points. Using my new
equations, any monkey can extend them into nbody problems or
into real engineering problems. I did not approach this problem
or write this paper intending to solve down to the atom, I
intended to show and fix the unified field under the old
equations, and I have done that.
*http://www.physics.montana.edu/faculty/cornish/lagrange.pdf **I
found that number instead of the current number .002725, by using
4 instead of π.
If this paper was useful to you in
any way, please consider donating a dollar (or more) to the SAVE
THE ARTISTS FOUNDATION. This will allow me to continue writing
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paying Melisa Smiththat is just one of my many noms de
plume. If you are a Paypal user, there is no fee; so it might
be worth your while to become one. Otherwise they will rob us 33
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