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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. This
will be a simple unifiedfield 3body problem.
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, 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 1,070 for solo gravity and 796 for charge,
which sums to 274.
The same applies to the Moon, where I have shown solo gravity is
2.668 while charge is 1.051, leaving us the current number 1.62.
In the same way, for the Earth 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 as it approaches the Earth/Moon, 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 from the Moon 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 part of the unified
field equations: eq.2
Gravity from Earth to Moon 9.7895/60.27 Earth radii=
.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}.
That is the total unified field acceleration upon the Moon. So
we compare that number to the current number of the Moon, which
is .002725. That is said to balance the orbital speed of the
Moon, creating the known orbit. But that number is also achieved
by faulty equations, as
I show here. Due to problems with the equation v=2πr/t,
that number also requires a correction, the right number being
.002208. Which means that if we include all my unified field
corrections so far, my error is .000013 or .059%. You will say
that doesn't solve the field down to zero, but it would if I
included perturbations from Jupiter and the other Jovians. The
Earth/Moon/Sun problem is not isolated in real life, so it is not
really a 3body problem. To solve it down to zero error, we
would have to include all solar system bodies and the galactic
core. Which I am not going to do here.
Please notice that I have
solved this problem with five equations, composed of fractions
and sums. Then remind yourself of the math string current
mathematicians are throwing at this same problem. Even
superstring theory is attempting to solve this one, by creating 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
indiscriminately 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
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