From the Chalkboard

This is topic # 04,  "On the Aberration of Gravitation"

{Posted May 2003}

Let us briefly review the concept of the Aberration of Light.  Let a distant light source have a given fixed position in the celestial sky as would be noted by an observer in the same frame of reference as that of the source.  The true position of this light source in space would be revealed to the fixed observer by the direction of propagation of the photons of light.  The true position would be apparent to any observer who happens to be in the frame of reference of the source.  To a hypothetical observer only, the undisturbed velocity of propagation of these photons would be exactly c according to the Galilean Transformation of velocities c'=c+v, since the relative velocity v of the source and the observer is zero.

Now let the observer move.  Assume the motion of the observer is now in a direction perpendicular to the direction of propagation of the photons emitted from the fixed source with velocity c relative to the source only.  Equivalently, the velocity vector v points in a  direction perpendicular to the line joining the observer and the source.  As a consequence of this motions, an aberration of the source's position would be noted by the moving observer and would have an angular deviation of exactly

from the normal to the plane of the ground.  Note: Although the ground is not moving, the moving observer here notes an apparent aberrational effect relative to the ground.

As an analogy to this problem, let it rain photons. We may assume we now have a rain shower where the raindrops are photons pouring straight down upon us from the source directly above.  The drops hit the ground perpendicularly with velocity c relative to the plane of the ground and with angle of zero degrees relative to the normal of the plane of the ground.  Now we decide to run with velocity v relative to the ground.  As moving observers, we now note that the photons fall with a slanted angle relative to the ground surface and at a new angle deviating from the normal to the ground surface as is depicted in our animated image.

Now let us assume that these raindrops are gravitons falling upon us at high noon directly from the sun.  We may safely assign a velocity for these gravitons as being exactly equal to that of the velocity of light c.  As we have seen and have mathematically verified {see book}, using Keplar's orbital equations of motion, the precise results obtained by Relativity for the planet Mercury and also for the PSR13+16 neutron-pulsar star Perihelion rotation effects are gotten by applying pure classical approaches of the Extinction Shift Principle alone. Assigning a value to the velocity v of orbit of the Earth about the sun of approximately 30 Km/sec, one would obtain an aberrational effect of exactly

for our rainfall of gravitons which is precisely the magnitude of the effect gotten for light photonsNote again: The observer here does not have to run. The ground of the Earth serves as our moving laboratory.  We are all moving observers.

We note that the solar disc has a radius of R0= 6.96E8 meters. Since the distance from the Earth to the sun is d=1.496E11 meters, this radius would correspond to an angle of

a radius of nearly 0.27 degrees and a solar width of nearly 0.5 degrees.  This radius is roughly 50 times that of the expected amplitude of the aberration of gravitation.  This means that any aberrational effect of gravitation would lie well within the solar disc itself.  Thus, classically predicted by this emission theory, the effect of gravitational attraction would appear to come from a point lying well within the solar disc of radius 960 arcsec, as view from Earth, but off-set by only 20.5 arcsec from the center of the solar disc.

Thus, the Earth is being pulled towards a point that is off-set from the center of the solar disk by at least 20.5 arcsec as is predicted using simple tools of this emission theory.

Important Note:  The off-set point as seen from Earth is also orbiting about the center-of-mass of the sun while the Earth orbits about the very same center of the solar mass.  Assuming a circular orbit, any aberrational effect of gravitation would remain relatively constant. The solar off-set point, however, becomes a virtual body and remains relatively stationary (fixed in space) as seen from the Earth.}  Recall that the sun also orbits about a center-of-mass of the Earth-Sun system and sees also an aberrational effect of the Earth's gravitational field.  The relative constancy {steady-state} of this aberrational effect requires nothing other than that of the normal Laws of Conservation of Energy and of Momentum; a Principle of Classical Mechanics.  Therefore, there is no requirement to assume a spiraling down effect of orbital motion due to an aberrational effect on gravitation.

This therefore verifies the validity of the Galilean transformation of velocities in Euclidean Space Geometry, applying these to the Principal Axioms of the Extinction Shift Principle to gravitation alone.

Thus, an instantaneous effect or an action at a distance would not be required or necessary for an explanation of a "spiraling down effect" on gravitation.