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ABSOLUTE STATES OF MOTION. PART II
INTRODUCTION Readers are referred to Absolute States of Motion, Part 1 of the theory for the assumptions and explanation of the difference between a lab in absolute "at rest" state and a lab in uniform rectilinear motion (abbreviated URM), in term of space-density distribution in the labs. The assumptions are as follows.
D.N. Giao
This article contains part 2 of the theory, which explains the difference between a lab in absolute "at rest" state and a lab in uniform gyratory motion (abrreviated UGM), in term of space-density distribution in the labs.
RESULTS
Fig 1 shows uniform space density in the equatorial XY plane of a lab in absolute "at rest" state, and the characteristic flatness of this plane.

Let the lab in the state of UGM around ZZ’ axis, relative to some outside observer. By assumption 2, UGM state entails a special mode of space-density distribution in XY plane (Fig 2).

To the UGM observer (who is in UGM with the lab), XY plane might be flat, but the correct interpretation is that the plane is conical. This conicalness brings on two geometrical abnormalities in the UGM lab, from the official observer’s viewpoint.
1. Fan shape of the UGM equatorial plane
This fan-shapedness is manifested by a shift in direction of radial lines in the plane (Fig 3).

Continuous shift in direction is illustrated by Fig 4.

2. Split in the UGM hemisphere
Fig 5 shows the split in upper hemisphere and lower hemisphere along ZZ’ axis.

This vertical split is manifested by the existence of an axial force in either hemisphere, which resists every movement directed across ZZ’ axis (Fig 6); the faster the movement, the harsher the resistance. The axial force appears to originate at the center of the lab; the farther from the origin, the weaker the force.

Shift in direction: first evidence
A lab situated at North Pole is in slow UGM with the North Pole. A pendulum hung at the ceiling and oscillating in the equatorial plane of such a lab, from the official observer’s viewpoint, would not follow one permanent direction (Fig 7a), it would continually shift direction (Fig 7b). Such a shift has been demonstrated by the famous Foucault’s experiment, the shift progressing against the direction the lab (and the Earth) rotates. The faster the UGM rate of the lab, the faster the progress of the shift. (Fig 7 is just illustration.)

Shift in direction: second evidence
In the said experiment, if we’d replace an oscillating pendulum with a light ray reflected back and forth between consecutive points on the periphery of the equatorial plane of the UGM lab, from the official observer’s viewpoint, we’d get the same result: the reflected light ray would shift direction continually in the same way as the oscillating pendulum would (Fig 7b). This effect has not yet been verified.
Shift in direction: third evidence
Let there be, on the periphery of the equatorial plane of a lab, sources of light which emit light rays radially toward the observer who is located at the center of the plane. If the plane is absolutely at rest, the observer of course sees all the light rays (Fig 8a). Now set the whole lab (including its equatorial plane and the periphery of this plane) in UGM. Does the UGM observer see the light rays? Well, he might. But, from the official observer’s viewpoint, the correct interpretation is that, in a UGM plane, no light rays emitted radially from the periphery would ever strike on the center (Fig 8b). This "blackout" effect has not yet been verified.

Shift in direction: fourth evidence
A lab situated at the equator is in slow counterclockwise UGM with the Earth. In such a lab, from the official observer’s viewpoint, a spinning top never stands exactly upright, it always inclines a little to the West direction) (Fig 9). This effect, if verified, would be one more indication that the lab (and the Earth) is currently in UGM.

Shift in direction: fifth evidence
Suppose a tiny mass A is in uniform curvilinear motion around a huge mass B due to the gravitational force of mass B, in plane P. If mass B (and plane P) is absolutely at rest, mass A traces a full circle of 360O in one cycle from points 1 to 3, or 180O from points 1 to 2 plus 180O from points 2 to 3 (Fig 10a). Mass A always orbits along a closed path (Fig 11a). What happens if mass B (and plane P) is in UGM, counterclockwise for example, to the UGM observer located at the same position as mass B, from the official observer’s viewpoint? There are 2 cases:
(1) Mass A revolves in same direction as plane P gyrates.
In its first cycle, mass A would cover less than 180O from points 1 to 2 and less than 180O from points 2 to 3, or less than one full circle from points 1 to 3 (Fig 10b). Then, in its second cycle, mass A covers less than 180O from points 3 to 4 and less than 180O from points 4 to 5, or less than one full circle from points 3 to 5 (Fig 10c). Every cycle, mass A always moves a shorter-than-normal distance.

So what? The orbit of mass A appears to spiral and spiral inward, contracting gradually (Fig 11b). How fastly it contracts depends on how fastly mass B (and plane P) gyrates.
This strange effect is not due to any actual change whether in the velocity of mass A or in the value of mass B, and definitely not due to mass B "frame dragging" mass A.

Our Solar System is currently in very slow UGM with the Sun, all the planets orbiting in the same direction as the Sun rotates. To the Sun UGM observer, it might be no problem with the system; but from the official observer’s viewpoint, the orbits of all the planets are contracting little by little! This phenomenon has not been verified.
This "contracted orbit" effect should also show up in the case of a satellite orbiting the Earth over the equator in the same direction as the Earth rotates, from the official observer’s viewpoint. This phenomenon has not been verified, either.
(2) Mass A revolves clockwise against the direction plane P gyrates.
From the official observer’s viewpoint, mass A would cover more than 180O from points 1 to 2 and more than 180O from points 2 to 3, or more than one full circle in one cycle from points 1 to 3 (Fig 12). Every cycle, mass A always moves a longer-than-normal distance.

So what? The orbit of mass A appears to spiral and spiral outward, expanding graduallly (Fig 13). How fastly it expands depends on how fastly mass B (and plane P) gyrates. This strange effect is not due to any actual change whether in the velocity of mass A or in the value of mass B.

Shift of direction: sixth evidence
The appearance of "folding arms" or "unfolding arms" in a spiral galaxy is usually attributed to the fast gyratory motion of the whole galaxy. The problem is, the arms seem to not gyrate at all.
The "open orbit" effect explained above would show up in the case of a spiral galaxy as well, if the galaxy were a system consisted of stars in uniform curvilinear motion around some central source of gravitational force (which, for convenience, is hereby called "nucleus").
Therefore, the arms do not revolve: they are the paths in which stars revolve. And stars revolve at an unchanged velocity in any one specific arm.
What remains to be confirmed is the existence and the nature of the nucleus.

Shift of direction: seventh evidence Let there be a source of light at the center of the equatorial plane of a lab, which emits light rays in all directions toward the periphery of the plane. If the plane is absolutely at rest, the periphery of course receives light from every directions, all points on it are lighted equally (Fig 15a). Now set the whole lab (including its equatorial plane and the periphery of this plane) in UGM. Does the same thing happen, to the UGM observer? Well, it might. But, the correct interpretation is that, the periphery would not receive light from all directions, only "privileged" points on it would be lighted (Figs 15b-c). The faster the UGM rate of the plane, the sparser the lighted points on its periphery. (Figs 15b-c are illustration only.)

And these "privileged" points are not fixed on the periphery of the UGM plane. The lighted-point pattern depends on the angle which the official observer views the periphery. For example, with seven "privileged" points, the official observer may see such patterns as in Figs 16a-c.

This strange effect has not yet been verified.
Existence of axial force – first evidence
Consider a vortex on the sea, which is water in UGM, and an airplane which is flying over the vortex. To the UGM at the center of the vortex, from the official observer’s viewpoint, there would be an axial force which seemingly steers the airplane out of its normal course into the vortex (Fig 17). This force has not yet been verified.

Existence of axial force – second evidence
Axial force should also exist and exert the same effect to airplanes flying over Antartica, which is in UGM with the Earth (Fig 18). The force, if verified, would be one more indication that Earth is currently in UGM.

DISCUSSION
SOLAR SYSTEM
The Solar System even though in UGM does not lose any of its stability; only the planets which, unfortunately, happen to revolve in the same direction as the System gyrates, move shorter distances, so their orbits contract gradually, from the official observer’s viewpoint. The rate of the contraction is very low, according to a very slow gyratory motion of the System.
In this scenario:
SPIRAL GALAXY
A spiral galaxy, as discussed above, is similar to the Solar System: both are in UGM and both are consisted of masses being held by a central source of gravitational force. No additional "dark matter" is required. What is required here is a sufficiently big source of gravitational force at sufficiently high rate of UGM, located in the center of the galaxy, which has not yet been verified.
27-Dec-04