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EXPLAINING the ELLIPSE
by
Miles Mathis
First
posted October 9, 2005
The
Problem
All
experiments and observations have confirmed that Kepler's
equations are correct and that the shape of the orbit is indeed
an ellipse, as he told us. Most physicists have been content to
leave it at that. If you are an engineer and you have equations
and a diagram, you have all you really need. If you are a physics
teacher and you have equations and a diagram, you are well
prepared: you can answer almost any question that is likely to
come up. But in my paper on Celestial
Mechanics, I showed that the accelerations and velocities in
the elliptical orbit were impossible to explain with the
gravitational field. That is to say, we have the correct
equations, the correct shape, but the wrong mechanics. We have
left the equations and the diagram with no foundation for almost
four centuries! The proposed and accepted kinematics and
dynamics, studied closely, cannot support the motions in the
field. Since physics is supposed to be a mechanical explanation
of natural phenomena, we have a very real problem here. We have
titled this part of physics "celestial mechanics", but
we have left out the mechanics almost entirely. This should be a
concern to all real scientists, and not just theorists or
philosophers, either. If your field does not explain your
equations or your diagrams, you are not lacking in metaphysics,
you are lacking in physics. What we currently have is a set of
equations hanging from sky hooks.
A
set of freefloating equations is not physics, it is heuristics.
All
orbits, whether elliptical or circular, are assumed by historical
and current theory to be composed of only two motions, a
centripetal acceleration caused by gravity, and a velocity due to
the orbiter’s “innate motion.” This term
“innate motion” was most famously used by Newton, and
it has never been updated. It is still considered to be the
velocity that the orbiter carried into the orbit from prior
forces or interactions. It may also be a motion caused by the
formation of a nebula or solar disc, but it cannot be caused by
the gravitational field of the current orbit. Why? Because there
is no mechanism to impart tangential velocity by a gravitational
field. Both Newton and Einstein agreed on this. Einstein’s
tensor calculus shows unambiguously that there is no force at a
perpendicular to the field, and Einstein stated it in plain
words. How could there be? The force field is generated from the
center of the field, and there is no possible way to generate a
perpendicular force from the center of a spherical or elliptical
gravitational field.
The
orbital velocity of an orbiter at any point in the orbit is the
vector addition of the two independent motions; that is to say,
the centripetal acceleration at that point in the field and the
perpendicular velocity, which is a constant. If you study the
diagram below, you will find that this can be shown quite simply.
The orbiter must retain its innate motion throughout the orbit,
no matter the shape of the orbit. If it did not, then its innate
motion would dissipate. If it dissipated, the orbit would not be
stable. Therefore, the orbiter always retains its innate motion
over each and every differential. If we take the two most
important differentials, those at perihelion and aphelion, and
compare them, we find something astonishing. The tangential
velocities due to innate motion are equal, meaning that the
velocity tangent to the ellipse is the same in both places. But
the accelerations are vastly different, due to the gravitational
field. And
yet the ellipse shows the same curvature at both places. The
ellipse is a symmetrical shape, just like the circle.
This is physically impossible. Using the given motions,
the ellipse is impossible to explain. The logical creation of an
ellipse requires forces from both foci, but one of our foci is
empty. It is a ghost. Every explanation I have seen of the
elliptical orbit, including—perhaps most famously—Feynman’s
explanation, uses the visualization of string and thumbtacks (see
diagram above, below title). But this visualization requires two
foci. It cannot work with an ellipse and only one focus.
I
know that many will cringe that I have claimed in my illustration
that v_{1}
= v_{2}.
Don't I know that the orbital velocity varies in an elliptical
orbit? Yes I do. Once more, my velocities are not orbital
velocities, they are tangential velocities. I refer the readers
who do not comprehend my point to my paper
on circular motion. In a nutshell, the orbital velocity
describes an arc or curved line. It is the vector addition of the
tangential velocity and the centripetal acceleration, over the
same interval. Newton first created this analysis, and I do not
disagree with it. Unfortunately, contemporary physics has
forgotten his distinction. It usually conflates orbital velocity
and tangential velocity. But the tangential velocity does not
curve. It is a straightline vector with its tail at the tangent.
It does not curve even at the limit. It only gets very small at
the limit. By going to the limit or to Newton's ultimate interval
we do not curve the tangential velocity, we straighten out the
arc. That is to say, we straighten out the orbital velocity so
that we can apply a vector addition to it, putting it in the same
equation as the straight tangential velocity.
Am I saying
that celestial bodies cannot be in elliptical orbits? No. I am
saying that these elliptical orbits cannot be explained with the
theory we currently have. What we currently have is a very
complex set of equations for determining the orbits we actually
see. This is called heuristics. The theory underlying this math,
which is called the theory of the gravitational field, cannot
explain the most basic math it contains. From the time of Newton
and Kepler, the foundational theory of ellipses has existed with
a ghost in it. That is to say, a huge theoretical hole. It is
time to fill that hole.
Current
theory attempts to plaster up that hole by summing the closed
circuit, whether it is circular or elliptical, showing that
everything resolves. But this proves nothing, since they cannot
help but resolve. We are talking about a closed circuit, by
definition. It would be very surprising if the sums did not
resolve. What I am talking about here is differentials. Just like
in orbital theory, the differentials betray huge holes in the
theory. These differentials can be summed, to show a circuit, but
the variance they contain cannot be explained by the
gravitational field or the innate motion.
To
make the ellipse work, you have to vary not only the orbital
velocity, but also the tangential velocity. To
get the correct shape and curvature to the orbit, you have to
vary the object's innate motion.
But the object's innate motion cannot vary. The object is not
selfpropelled. It cannot cause forces upon itself, for the
convenience of theorists or diagrams. Celestial bodies have one
innate motion, and only one, and it cannot vary.
[This
section added May 2008] Some have still not understood my point
here, so I am adding another diagram.
In
this diagram you can see that the vectors given by Newton and
Kepler demand more curvature at perihelion than aphelion. When
the orbiter is nearer the sun, its orbital path must show more
curvature. The vector v
is a constant, by definition or axiom, so the variance in a
must determine the curvature of the path at any point. I have
also diagrammed the orbital velocities, v_{o},
to show how they are found by adding the other two vectors. As
you can see, the orbital
velocity at perihelion is indeed greater than at aphelion, as
shown by the length of that vector. But the tangential or
perpendicular velocities at all points on the orbital path must
be the same. Therefore, we must find the curvatures as I have
drawn them here. Now, perhaps, you can more clearly see that
these two "ends" of the ellipse cannot be made to meet
up. You cannot have greater curvature at perihelion and lesser
curvature at aphelion and draw any shape that will meet up. This
is my central thesis in this paper. I am not claiming that
Kepler's or Newton's math is wrong. I am not claiming that
planets do not draw ellipses. Empirically we know that both the
equations and the orbital shapes are correct. The problem is with
the underlying mechanics. The gravitational field, as it is
currently defined, cannot support the shape or the equations.
Since the shape and the equations are known to be correct from
experiment, we must create a unified field that explains them. I
do that in the next section and in my
Unified Field paper.
The
Solution
Fortunately,
the solution is just as simple as the problem. It has been
overlooked for centuries, but that does not mean it must be
esoteric. It only means that the problem was hidden for a long
time. Newton hid the problem so cunningly that no one has
detected it since his time.
The solution
is that the orbital field is a twoforce field. It is not just
determined by gravity. Therefore any orbiter must be exhibiting
at least three basic motions. The two above, and one other. This
other is a motion due to the combined E/M fields of the orbiter
and the object orbited. In this case, the Sun and the Earth. The
force created by the E/M fields is a repulsive force, like that
between two protons. It is therefore a negative vector compared
to the gravitational field, which is an attractive field. And so
the total field described by gravity and E/M is a differential of
the two. In the end, you subtract the E/M acceleration from the
acceleration due to gravity.
This explains
the ellipse because the E/M repulsive force increases as the
objects get nearer. As the gravitational acceleration gets
bigger, so does the repulsive acceleration due to E/M.
We have a
balancing of forces. This not only explains the varying shape of
the orbit, from circle to ellipse to parabola, it explains the
correctability of the orbit. It explains why we don’t often
find orbiters crashing into primaries. It explains how we had a
ghost in the other focus of the ellipse: the ghost was inhabited
by the E/M field.
This also explains the cause of the
ellipse. It has never been understood why some orbits were
elliptical and some were nearly circular. Various explanations
have been offered, from initial spin, to various perturbations,
to an initial angle at intersection to the field. My theory would
explain the ellipse in the orbit of captured orbiters by simply
showing that the orbiter intersected the field too far from its
center. The captured orbiter does not have to intersect the field
at just the right distance. It can be captured over a large range
of distances, since if it is captured too far away, it will just
be thrown into ellipse.
This makes my
analysis the opposite of the current analysis. I showed in my
Celestial Mechanics paper that current analysis explains the
circular orbit as the orbiter intersecting the field at a
distance where the two motions balance. By this theory, the
ellipse would have to be caused by an initial intersecting radius
that was smaller than this balancing radius. I have a
diagram in that paper that proves this. If the orbiter is
captured at aphelion, for instance, it would begin to get closer
to the Sun due to the shape of the ellipse. This could only be
explained by showing that the centripetal acceleration
overpowered the tangential velocity.
But my orbit
is the balancing of three motions, not two. Therefore, the
circular orbit would be caused by an intersecting radius where
the gravitational and E/M fields balanced. So that to create the
ellipse, you would go farther away, not closer. Remember that the
E/M field drops off faster than the gravity field. Gravity
decreases as 1/R^{2}. E/M decreases as 1/R^{4}.
If you go farther out, gravity overpowers E/M and the orbiter
immediately begins to move closer to the Sun.
To show this,
I will gloss the capture for an elliptical orbit: 1) the orbiter
intersects the field too far away for a circular orbit—meaning
that it is beyond the balancing of the three independent motions,
but travelling slow enough that the acceleration due to gravity
captures it; 2) since the centripetal acceleration initially
overpowers the E/M field and the tangential velocity, the orbiter
begins to circle closer to the center; 3) but as it does so, the
E/M field increases, keeping the orbiter from crashing; 4) the
orbiter reaches a minimum orbital distance where the E/M field
and the gravitational field [almost] balance; 5) since the
orbiter in question is a very large body and the E/M field is
made up of very small bodies, the momentum of the orbiter will
actually have taken it a small distance inside the
balancing radius; 6) the object being slightly below its radius
where the two forces balance, the E/M field force is, for a short
time, greater than the gravitational force; 7) this creates a
very small slingshot effect; 8) due to this effect, the orbiter’s
momentum carries it outside the balancing radius; 9) if the
initial intersection angle was not too steep—so that we
didn’t get too far under the balancing radius—then we
are back to 1). Otherwise we create a parabola instead of an
ellipse, and the object escapes a semistable orbit.
The
only step that needs further comment, I think, is step 5. Another
way to state step 5 is that the E/M field is a physical object
that is much more fluid than the planet that intersects it. The
planet is a solid object whose own E/M field is quite rigid. But
the central E/M field contains more space and less structure, so
that its effect on a solid object will be delayed in this
instance.
A useful
visualization is to compare the planet intersecting the E/M field
to a heavy wooden ball being thrown into deep water. Because the
ball is wood, we know that the water will float it—that is,
repel it. But if you give the ball enough initial velocity, it
will dive into the water to a certain depth before the water
begins to reject it. A planet is like a very heavy wooden
ball, and the E/M field is like a very weak water. The
planet therefore dives to a great depth before the E/M field
overcomes the initial momentum. The planet may be “under
water” for months. But at last the E/M field floats it.
The buoyancy
of the wooden ball determines it force of rejection by the water,
and the E/M field of the planet determines its force of rejection
by the central field. Its E/M field is determined by its mass and
its density.
The
visualization is analogous in another way. When the water finally
rejects the wooden ball, the ball pops out of the water, often to
a measurable height. You have probably experienced this at the
swimming pool. If you hold a plastic, airfilled ball under water
and then let it go, it will explode out of the water and jump a
foot or more into the air. The E/M field of the Sun ultimately
rejects the planet in the same way. This is the slingshot effect.
Current
theory makes use of this same slingshot effect, but it does not
explain the foundational mechanics of it. Current theory tries to
build the same unbalanced field as I have, so that the orbiter
goes into a sort of gravitational “well.” But this
unbalance cannot be created with a single field. Any close
analysis explodes the whole theory. Current theory has the right
effects and the right ideas, it just has the wrong forces. The
gravitational field by itself cannot create the forces required
to display the effects and curvatures and differentials that are
required. To create unbalanced forces and slingshot effects and
correctable orbits, you have to have two major intersecting
fields. The innate motion is not a field. It is just a simple
velocity. In this way it is a constant. It cannot create all the
effects that current theory wants to give to the orbit.
Implications
The greatest
implication of all this is that Newton’s fundamental
gravitational equation must be reconsidered. The force in the
equation F = GMm/r^{2}
can no longer be considered the expression of a single field.
The equation still works, but F must now be understood as the
differential between the gravitational field and the E/M field.
It is a compound field. All the accelerations we measure are the
result of both fields working simultaneously to yield a total
force and a total acceleration. This total acceleration is a
vector addition of the two constituent accelerations.
A
smaller implication is that comets might now be shown to burn not
simply from solar radiation, but from the E/M field. That is, the
tails of the comet would be produced mainly by electrical
considerations. The comet is on electrical fire. This may seem at
first to be splitting hairs, but it is not. Solar radiation is
not thought to be radiation from an E/M field. It is thought to
be ions created as byproducts of nuclear fusion. But E/M fields
are created independently of nuclear fusion. The Sun would have a
powerful E/M field even if it were not a giant nuclear reactor.
Therefore, it may be the E/M field that is the main cause for the
spectacular effects of comets.
You may
now see the simple unified field equations for the threebody
problem (Sun, Earth, Moon) in my newest paper on Lagrange
Points. Using the charge field, I am able to show that the
Moon is in fact hitting these points of field balance. This
proves my assertions in this paper.
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