The Complete Nature of Stellar Aberration
Copyright © 2010 Joseph A. Rybczyk
Abstract Presented is a detailed explanation of the complete nature of stellar aberration that goes beyond the basic principles associated with the effect in direct relation to Earth’s orbital motion. The intent is to make the entire process clear in order to understand its full implications with regard to the principles of astronomy, cosmology, and physics as applied to constant relative motion and acceleration. Only then can the effect be properly integrated into the principles of relativistic physics.
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The Complete Nature of Stellar Aberration
Copyright © 2010 Joseph A. Rybczyk
1. Introduction Stellar aberration1 is a process whereby the velocity of the Earth in its orbit around the Sun causes a small displacement of where the stars and other celestial objects in space are seen in the Earth frame. The problem with stellar aberration is that it appears to violate the principle of relative motion2 because it appears to be absent in a reciprocal manner in relation to the transverse motion of the stars and other celestial objects observed from Earth. This behavior will be explored in detail in this present work and shown not to be in violation of the principle of relative motion at all when the behavior is properly understood.
2. The Standard Theory of Stellar Aberration According to the standard theory of stellar aberration, the observed location of celestial objects is affected by the objects’ directional relationship to the Earth’s orbital plane and the speed of the Earth along its orbital path. Though very small, the affect is consistent and is supposedly greatest for objects located perpendicular to the Earth’s orbital plane as illustrated in Figure 1.
Starlight from a perpendicular direction to the Earth’s orbital plane
Telescope tilted toward reader Telescope tilted away from reader
Sun Telescope
Earth FIGURE 1 Starlight Perpendicular to Earth’s Orbital Plane
As shown in Figure 1, when viewing the same star located in a direction perpendicular to the Earth’s orbital plane, the telescope always leans slightly in the direction of the Earth’s orbital motion as the Earth travels around the Sun. This, of course, means that the direction of the telescope at any point in the orbit will be exactly opposite to what it was ½ an orbit previously. And that, along with the fact that the angle of tilt is always in the direction of the Earth’s orbital motion, was the behavior that made discovery of the effect possible. By associating the speed of light with the Earth’s orbital speed a precise relationship to the angle of tilt is found as will be shown next. Referring to Figure 2-A, a telescope in the Northern Hemisphere of Earth is shown tilted in the direction of the Earth’s orbit around the Sun as starlight enters in a perpendicular direction to Earth’s orbital plane. Since the telescope is moving along with the Earth in the direction 2 shown, the light that enters the telescope travels the dotted line path through the telescope and exits in a straight line path as illustrated in Figure 2-B. Although the angle of tilt shown is greatly exaggerated for illustrative purposes, such angle is significant enough to be measured and is found to be in agreement with the triangular relationships defined in Figure 2-C. Using a revised version of those relationships as will be discussed next in relation to Figure 3, we can derive a formula for finding the angle of stellar aberration.
Direction of light Direction of light Apparent direction to source
c Light path through θ Telescope telescope L L θ (Tilt angle)
Direction of Earth Direction of Earth v Direction of light
A B C FIGURE 2 Stellar Aberration – Standard Theory
For clarity purposes, the angle of tilt, θ, has been exaggerated even more in Figure 3 than it was in Figure 2. But an even more important change to the relationships originally shown in Figure 2-C has been incorporated as will be discussed next.
Apparent direction to source θ c L c
θ Light path through L is direction of light telescope in Sun Frame v FIGURE 3 Stellar Aberration - Revised
Contrary to what was shown in Figure 2-C, side c of the triangle has been changed to the hypotenuse of the triangle shown in Figure 3 and side L is now the perpendicular side. This switch in designators between the two sides of the triangle brings the relationships into agreement with the principles of relativity with virtually no effect in regard to the evidence supported principles of stellar aberration. More specifically, the angle at which the light passes through the center of the telescope, represented by the hypotenuse of the right triangle, has been designated as side c to bring the principle of stellar aberration into agreement with the relativistic
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principle that light travels at speed c relative to the reference frame in which it is observed. If the light is traveling in a perpendicular direction to the Earth’s orbital plane, then according to the principles of relativity, it is traveling in that direction relative to the stationary frame of the Sun, and not the moving frame of the Earth. Thus it will have a speed c in that direction relative to the stationary frame of the Sun and not the moving frame of the Earth. Since speed c in the frame of the Sun is different from speed c in the frame of the Earth, and it is the Earth’s frame in which we are interested, the switching of speeds L and c in Figure 3 is necessary. In the moving fame of the Earth, the light travels at speed c along the vectored path defined by the L designated Sun frame light speed, Earth’s orbital speed v, and the angle of observation θ. This means the correct formula for determining the angle θ associated with stellar aberration is