Journal of Applied Mathematics and Physics, 2018, 6, 1034-1054 http://www.scirp.org/journal/jamp ISSN Online: 2327-4379 ISSN Print: 2327-4352 Absolute Velocity and Total Stellar Aberration Miloš Čojanović Independent Researcher, Montreal, Canada How to cite this paper: Čojanović, M. Abstract (2018) Absolute Velocity and Total Stellar Aberration. Journal of Applied Mathemat- It is generally accepted that stellar annual or secular aberration is attributed to ics and Physics, 6, 1034-1054. the changes in velocity of the detector. We can say it in a slightly different https://doi.org/10.4236/jamp.2018.65090 way. By means of the all known experiments, stellar aberration is directly or Received: April 2, 2018 indirectly detectable and measurable, only if a detector changes its velocity. Accepted: May 27, 2018 Our presumption is that stellar aberration is not caused by the changes in the Published: May30, 2018 velocity of the detector. It exists due to the movement of the detector regard- ing to an absolute inertial frame. Therefore it is just the question of how to Copyright © 2018 by author and Scientific Research Publishing Inc. choose such a frame. In this paper it is proposed a method to detect and This work is licensed under the Creative measure instantaneous stellar aberration due to absolute velocity. We can call Commons Attribution International it an “absolute” stellar aberration. Combining an “annual” and an “absolute” License (CC BY 4.0). we can define a “total” stellar aberration. http://creativecommons.org/licenses/by/4.0/ Open Access Keywords Annual Stellar Aberration, “Absolute” Stellar Aberration, “Total” Stellar Aberration, Absolute Velocity, One-Way Velocity of Light 1. Introduction It is commonly assumed that due to the aberration the observed position of a star is displaced of about 150” toward the direction of the instantaneous velocity of the observer with respect to an inertial reference frame at rest. But, for an ob- server located at the barycenter of the solar system, the instantaneous effect of the relativistic aberration due to the galactic motion of the solar system (220 km/s) is not directly observable because the velocity-induced aberration pattern is constant [1] [2] [3]. Our hypothesis is in contradiction to the relativistic view on stellar aberration, because according to this theory an absolute frame does not exist nor a mea- surement of the absolute aberration is possible. We will start a discussion by the classical explanation of the annual stellar ab- DOI: 10.4236/jamp.2018.65090 May 30, 2018 1034 Journal of Applied Mathematics and Physics M. Čojanović erration. A star (Z) is stationary, and the light travels from the star at velocity c con- stant speed of light in the stationary frame. A telescope is in motion at velocity v regarding to the heliocentric-ecliptic coordinate system. Suppose that AB represents a median line of the telescope at the instant t0 and A'B' represents a median line of the telescope at the instant t1 . In the ref- erence frame of the telescope AB is identical to A'B'. But in the sun’s reference frame median lines AB and A'B' are represented by two different positions. In referring to Figure 1, the following definitions apply Δt—a time required for light to traverse the length of the telescope θ—an angle between the earth velocity about the sun and light ray from the star Δθ—an angle at which a telescope should be tilted in the direction of motion in order for the photons move along the median line of the telescope. Actually this angle is obtained by the two measurements at six months intervals. ∆=tt10 − t (1.1) ∆=∠θ ( ABA′) =∠( B ′′ A B) (1.2) θ = ∠(SA′ B) (1.3) θθ−∆ =∠( ABB′′) (1.4) BB′ =∆∗ t v (1.5) BA′ =∆∗ t c (1.6) vt∗∆ ct ∗∆ = (1.7) sin(∆θ) sin ( θθ −∆ ) cv∗∆=∗∗sin( θ) sin( θ) cos( ∆−∗ θ) v cos( θθ) ∗∆ sin ( ) (1.8) v ∗sin (θ ) tan (∆=θ ) c (1.9) v 1+∗ cos(θ ) c for θ = Π 2 , Equation (1.9) is being reduced to the equation Figure 1. Stellar aberration according to Bradley. DOI: 10.4236/jamp.2018.65090 1035 Journal of Applied Mathematics and Physics M. Čojanović v tan (∆=θ ) (1.10) c assuming that ∆θ 1 and after neglecting terms higher than the second or- der with the respect to ∆θ we have that xx352 tan ( xx) =++ + (1.11) 3 15 v ∆θθ352 ∗∆ =∆+θ + + (1.12) c 3 15 we can say that an approximate value for the stellar aberration ∆θ is equal to v ∆≈θ (1.13) c Its maximal value is approximately the same for all stars. The accepted value is 20.49552 arc seconds. The problems related to the stellar aberration that are being treated in this paper, had been already defined and mentioned in the numerous works for ex- ample [4]. 2. Description and Role of the “Telescope” In this paper we will use a term “telescope”, although a standard telescope is not suitable for this experiment. In other to perform this experiment instead of using a such telescope one have to design and build a new apparatus. Because of that it will be given its description, but just in few words. Point S represents a center of the top “plane” while S' represents a center of the bottom “plane” of the telescope. Photons enter the telescope at the point S and their direction is perpendicular to the top plane. This means that there is a some part of the telescope who has a role to point the “telescope” in such direc- tion that median line SS′ becomes parallel to the starlight. At the bottom plane of the telescope it should be installed a camera in order to take an image of the star (Z) at the point A. It will be assumed that a star (Z) is extremely far away, so that a parallax may be ignored. For now we can assume that extra-galactic stars are being observed only. Starlight moves in straight line and will remain in the same direction re- garding to the ecliptic plane. Photons enter in a perpendicular direction to the top plane of the telescope. The starlight represents an inertial frame of reference marked by (L) and the telescope represents a moving frame of reference that is marked by (T). We will assume that P1 —speed of light c is constant and equal in all inertial frames (L) P2 —there is a one common time for the all frames (L) and the moving frame (T) P3 —frame (T) is moving uniformly in a straight line regarding the frame (L) Now we will discuss the three cases that are depicted on the Figure 2. DOI: 10.4236/jamp.2018.65090 1036 Journal of Applied Mathematics and Physics M. Čojanović (a) (b) (c) Figure 2. (a) A frame of the telescope is stationary regarding to the starlight; (b) A frame of the telescope is moving perpendicular regarding to the starlight; (c) A frame of the telescope is moving by some arbitrary velocity regarding to the starlight. The effect of the velocity v on the position of the telescope is not depicted on the last two figures. -In the first case Figure 2(a), the relative velocity of the telescope v regarding to the frame of the starlight is equal to the 0. At some instant t0 photon hits the top “plane” at the point S and at some instant t1 hits the bottom “plane” at the point S'. -In the second case Figure 2(b), under the same circumstances except that v ≠ 0 contrary to our expectations photon does not hit the bottom plane at the point S' but rather at a some point A. Referring to the Figure 2(b) it follows d= SS′ (2.1) d ∆=tt − t = (2.2) 10c d SA′ = −∆t ∗ v = ∗ v (2.3) c SA 22 c= = vc + speed of light in the frame (T) (2.4) (T ) ∆t SA′ d∗ v v tan (∆=θ ) =−=− (2.5) d cd∗ c v ∆θ ≈− (vc ) (2.6) c -In the third case Figure 2(c), velocity at which a telescope moves relative to the starlight is decomposed to the two components. The first component noted by v is perpendicular to the starlight and the second one noted by u is parallel to starlight. Referring to the Figure 2(c), it follows d= SS′ (2.7) dx+ x d xx u =⇒ =−⇒=∗xd (2.8) c u c u c cu− DOI: 10.4236/jamp.2018.65090 1037 Journal of Applied Mathematics and Physics M. Čojanović uc xd+=+∗ dd =∗ d (2.9) cu−− cu d ∆=tt − t = (2.10) 10cu− d SA′ = −∆t ∗ v = − ∗ v (2.11) cu− 2 ∗ −+2 2 22 d 2d( cu) v SA= S′ A += d ∗v += d (2.12) cu−−cu SA 2 2 c==( cu −+) v speed of light in the frame (T) (2.13) (T ) ∆t SA′ d∗ v v tan (∆=θ ) = = (2.14) d d∗−( cu) cu − v ∆≈θ (u cv, c) (2.15) cu− An additional explanation will be given for the third case. -From the point view of a spectator at the frame (L) a photon hits top plane at the point S (this point is identical to the fixed point SL at the frame (L)). The telescope is moving parallel with the starlight by velocity u, therefore a distance between the point SL and the bottom plane changes. A total distance that photon travels from the instant t0 to the instant t1 is equal to (dc∗−) ( cu) . Time that it takes for the photon to travel from the top to the bottom plane of the telescope is equal to dcu( − ) .