DOCSLIB.ORG

Absolute Velocity and Total Stellar Aberration

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Absolute Velocity and Total Stellar Aberration 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( − ) .
Load more

Recommended publications
  • Galileo and the Telescope
    Galileo and the Telescope A Discussion of Galileo Galilei and the Beginning of Modern Observational Astronomy ___________________________ Billy Teets, Ph.D. Acting Director and Outreach Astronomer, Vanderbilt University Dyer Observatory Tuesday, October 20, 2020 Image Credit: Giuseppe Bertini General Outline • Telescopes/Galileo’s Telescopes • Observations of the Moon • Observations of Jupiter • Observations of Other Planets • The Milky Way • Sunspots Brief History of the Telescope – Hans Lippershey • Dutch Spectacle Maker • Invention credited to Hans Lippershey (c. 1608 - refracting telescope) • Late 1608 – Dutch gov’t: “ a device by means of which all things at a very great distance can be seen as if they were nearby” • Is said he observed two children playing with lenses • Patent not awarded Image Source: Wikipedia Galileo and the Telescope • Created his own – 3x magnification. • Similar to what was peddled in Europe. • Learned magnification depended on the ratio of lens focal lengths. • Had to learn to grind his own lenses. Image Source: Britannica.com Image Source: Wikipedia Refracting Telescopes Bend Light Refracting Telescopes Chromatic Aberration Chromatic aberration limits ability to distinguish details Dealing with Chromatic Aberration - Stop Down Aperture Galileo used cardboard rings to limit aperture – Results were dimmer views but less chromatic aberration Galileo and the Telescope • Created his own (3x, 8-9x, 20x, etc.) • Noted by many for its military advantages August 1609 Galileo and the Telescope • First observed the
    [Show full text]
  • Autobiography of Sir George Biddell Airy by George Biddell Airy 1
    Autobiography of Sir George Biddell Airy by George Biddell Airy 1 CHAPTER I. CHAPTER II. CHAPTER III. CHAPTER IV. CHAPTER V. CHAPTER VI. CHAPTER VII. CHAPTER VIII. CHAPTER IX. CHAPTER X. CHAPTER I. CHAPTER II. CHAPTER III. CHAPTER IV. CHAPTER V. CHAPTER VI. CHAPTER VII. CHAPTER VIII. CHAPTER IX. CHAPTER X. Autobiography of Sir George Biddell Airy by George Biddell Airy The Project Gutenberg EBook of Autobiography of Sir George Biddell Airy by George Biddell Airy This eBook is for the use of anyone anywhere at no cost and with almost no restrictions whatsoever. You may copy it, give it away or re-use it under the terms of the Project Gutenberg Autobiography of Sir George Biddell Airy by George Biddell Airy 2 License included with this eBook or online at www.gutenberg.net Title: Autobiography of Sir George Biddell Airy Author: George Biddell Airy Release Date: January 9, 2004 [EBook #10655] Language: English Character set encoding: ISO-8859-1 *** START OF THIS PROJECT GUTENBERG EBOOK SIR GEORGE AIRY *** Produced by Joseph Myers and PG Distributed Proofreaders AUTOBIOGRAPHY OF SIR GEORGE BIDDELL AIRY, K.C.B., M.A., LL.D., D.C.L., F.R.S., F.R.A.S., HONORARY FELLOW OF TRINITY COLLEGE, CAMBRIDGE, ASTRONOMER ROYAL FROM 1836 TO 1881. EDITED BY WILFRID AIRY, B.A., M.Inst.C.E. 1896 PREFACE. The life of Airy was essentially that of a hard-working, business man, and differed from that of other hard-working people only in the quality and variety of his work. It was not an exciting life, but it was full of interest, and his work brought him into close relations with many scientific men, and with many men high in the State.
    [Show full text]
  • History of the Speed of Light ( C )
    History of the Speed of Light ( c ) Jennifer Deaton and Tina Patrick Fall 1996 Revised by David Askey Summer RET 2002 Introduction The speed of light is a very important fundamental constant known with great precision today due to the contribution of many scientists. Up until the late 1600's, light was thought to propagate instantaneously through the ether, which was the hypothetical massless medium distributed throughout the universe. Galileo was one of the first to question the infinite velocity of light, and his efforts began what was to become a long list of many more experiments, each improving the Is the Speed of Light Infinite? • Galileo’s Simplicio, states the Aristotelian (and Descartes) – “Everyday experience shows that the propagation of light is instantaneous; for when we see a piece of artillery fired at great distance, the flash reaches our eyes without lapse of time; but the sound reaches the ear only after a noticeable interval.” • Galileo in Two New Sciences, published in Leyden in 1638, proposed that the question might be settled in true scientific fashion by an experiment over a number of miles using lanterns, telescopes, and shutters. 1667 Lantern Experiment • The Accademia del Cimento of Florence took Galileo’s suggestion and made the first attempt to actually measure the velocity of light. – Two people, A and B, with covered lanterns went to the tops of hills about 1 mile apart. – First A uncovers his lantern. As soon as B sees A's light, he uncovers his own lantern. – Measure the time from when A uncovers his lantern until A sees B's light, then divide this time by twice the distance between the hill tops.
    [Show full text]
  • Positional Astronomy Coordinate Systems
    Positional Astronomy Observational Astronomy 2019 Part 2 Prof. S.C. Trager Coordinate systems We need to know where the astronomical objects we want to study are located in order to study them! We need a system (well, many systems!) to describe the positions of astronomical objects. The Celestial Sphere First we need the concept of the celestial sphere. It would be nice if we knew the distance to every object we’re interested in — but we don’t. And it’s actually unnecessary in order to observe them! The Celestial Sphere Instead, we assume that all astronomical sources are infinitely far away and live on the surface of a sphere at infinite distance. This is the celestial sphere. If we define a coordinate system on this sphere, we know where to point! Furthermore, stars (and galaxies) move with respect to each other. The motion normal to the line of sight — i.e., on the celestial sphere — is called proper motion (which we’ll return to shortly) Astronomical coordinate systems A bit of terminology: great circle: a circle on the surface of a sphere intercepting a plane that intersects the origin of the sphere i.e., any circle on the surface of a sphere that divides that sphere into two equal hemispheres Horizon coordinates A natural coordinate system for an Earth- bound observer is the “horizon” or “Alt-Az” coordinate system The great circle of the horizon projected on the celestial sphere is the equator of this system. Horizon coordinates Altitude (or elevation) is the angle from the horizon up to our object — the zenith, the point directly above the observer, is at +90º Horizon coordinates We need another coordinate: define a great circle perpendicular to the equator (horizon) passing through the zenith and, for convenience, due north This line of constant longitude is called a meridian Horizon coordinates The azimuth is the angle measured along the horizon from north towards east to the great circle that intercepts our object (star) and the zenith.
    [Show full text]
  • The Luminiferous Ether Consequences of the Ether
    Experimental basis for The luminiferous ether special relativity • Mechanical waves, water, sound, strings, etc. require a medium • Experiments related to the ether • The speed of propagation of mechanical hypothesis waves depends on the motion of the • Experiments on the speed of light from medium moving sources • It was logical to accept that there must be a • Experiments on time-dilation effects medium for the propagation of light, so that • Experiments to measure the kinetic energy em waves are oscillations in the ether of relativistic electrons • Newton, Huygens, Maxwell, Rayleigh all believed that the ether existed 1 2 The aberration of starlight Consequences of the ether (James Bradley 1727) • If there was a medium for light wave • Change in the apparent position of a star due to changes in the velocity of propagation, then the speed of light must be the earth in its orbit measured relative to that medium • Fresnel attempted to explain this • Thus the ether could provide an absolute from a theory of the velocity of light reference frame for all measurements in a moving medium • According to Fresnel, the ether was • The ether must have some strange properties dragged along with the earth and this – it must be solid-like to support high-frequency gave rise to the aberration effect transverse waves • However, Einstein gave the correct – yet it had to be of very low density so that it did not explanation in terms of relativistic velocity addition. A light ray will have disturb the motion of planets and other astronomical a different
    [Show full text]
  • EXPLORING SPECIAL RELATIVITY (Revised 24/9/06)
    EXPLORING SPECIAL RELATIVITY (revised 24/9/06) Objectives The aim of this experiment is to observe how things would appear if you could travel at speeds near that of light, c = 3×108 m/s. From your observations you can deduce, or verify, aspects of relativistic physics. Both qualitative and quantitative understanding is sought. Important Information The “Real Time Relativity” (RTR) simulator you will use in this lab was created at ANU by Lachlan McCalman, Antony Searle, and Craig Savage. It is under development and has many limitations. In particular you may not be able to make precise measurements. When you are asked for a quantitative result just do the best you can: 10% accuracy is fine. If you have trouble using RTR, ask a demonstrator for help. Take a note of things that make it difficult to use, and include them on the post-lab evaluation. Thanks for your patience! Evaluation This is a new lab, and we are evaluating its effectiveness. To help us, please answer the questions on the evaluation handouts: complete one before the lab, and one after the lab. This will help us to assess the effectiveness of the lab, and to improve it. To receive a bonus mark, hand them in by 5pm on the Friday of the week of your lab. Skills In this experiment you will practice: making observations, critical evaluation, designing experiments. Basic Principles Computer simulations are used in science to conduct investigations that might otherwise be difficult or impossible. The objects in the simulation are big, because the speed of light is fast.
    [Show full text]
  • Effect of the Gravitational Aberration on the Earth Gravity Field
    ARTIFICIAL SATELLITES, Vol. 56, No 1 – 2021 DOI: 10.2478/arsa-2021-0001 EFFECT OF THE GRAVITATIONAL ABERRATION ON THE EARTH GRAVITY FIELD Janusz B. ZIELIŃSKI1, Vladimir V. PASHKEVICH2 1 Space Research Centre, Polish Academy of Sciences, Warsaw, Poland 2 Central Astronomical Observatory at Pulkovo, Russian Academy of Sciences, St. Petersburg, Russia e-mails: [email protected], [email protected] ABSTRACT. Discussing the problem of the external gravitational potential of the rotating Earth, we have to consider the fundamental postulate of the finite speed of the propagation of gravitation. This can be done using the expressions for the gravitational aberration compared to the Liénard–Wiechert solution of the retarded potentials. The term gravitational counter- aberration or co-aberration is introduced to describe the pattern of the propagation of the gravitational signal emitted by the rotating Earth. It is proved that in the first approximation, the classic theory of the aberration of light can be applied to calculate this effect. Some effects of the gravitational aberration on the external gravity field of the rotating Earth may influence the orbit determination of the Earth artificial satellites. Keywords: propagation of gravitation, speed of gravity, aberration of gravity, retarded potential, Earth gravitational potential 1. INTRODUCTION In the excellent book Relativistic Celestial Mechanics of the Solar System (Kopeikin et al., 2011), we find the notion aberration of gravity, understood as the effect of the Liénard– Wiechert retarded potential of the moving mass on the propagation of gravity. It is a very interesting concept, which could be discussed more closely in the context of the classic definitions of the aberration of light and the relativistic gravitational potential.
    [Show full text]
  • 1 Fresnel's (Dragging) Coefficient As a Challenge to 19Th Century Optics
    1 Fresnel’s (Dragging) Coefficient as a Challenge to 19th Century Optics of Moving Bodies John Stachel Center for Einstein Studies, Boston University, Boston, MA 02215, U.S.A., [email protected] 1.1 Introduction It has been suggested that, during the latter half of the 19th century up to about 1890, the optics of moving bodies was considered to be a more-or-less unproblematic branch of physics. In view of the continuing success of Fresnel’s formula for the dragging coefficient (hereafter called Fresnel’s coefficient) in explaining all new experimental optical data to order v/c, “There were simply no major problems to solve here, or so it was generally thought” (Buchwald 1988, 57). These words are the summation of the following quotation: “In 1851 Armand Fizeau was able to measure the Fresnel “drag” coefficient, and in 1873 Wilhelm Velt- mann demonstrated that no optical experiment with a terrestrial source of light can, to first order, detect motion through the ether if the drag coefficient obtains. Conse- quently, to this degree of accuracy, Fresnel’s original theory which requires a very slight transport of the ether by transparent bodies was quite satisfactory (ibid.)” (Schaffner 1972) includes a similar comment: “...Fresnel was able to formulate a simple and elegant explanation of Arago’s results on the basis of the wave theory of light; an explanation which not only accounted for aberration effects then known but which was subsequently confirmed in a number of ways throughout the nineteenth century (ibid., 24).” As we shall see, both Buchwald and Schaffner conflate the continued empirical success of Fresnel’s formula with the ultimately unsuccessful attempts by Fresnel and others to find a satisfactory theoretical explanation of the formula.
    [Show full text]
  • Rethinking the Foundations of the Theory of Special Relativity: Stellar Aberration and the Fizeau Experiment
    Rethinking the Foundations of the Theory of Special Relativity: Stellar Aberration and the Fizeau Experiment 1 2 A.F. Maers and R. Wayne 1Department of Biological Statistics and Computational Biology, Cornell University, Ithaca, NY 14853 USA 2Department of Plant Biology, Cornell University, Ithaca, NY14853 USA In a previous paper published in this journal, we described a new relativistic wave equation that accounts for the propagation of light from a source to an observer in two different inertial frames. This equation, which is based on the primacy of the Doppler effect, can account for the relativity of simultaneity and the observation that charged particles cannot exceed the speed of light. In contrast to the Special Theory of Relativity, it does so without the necessity of introducing the relativity of space and time. Here we show that the new relativistic wave equation based on the primacy of the Doppler effect is quantitatively more accurate than the standard theory based on the Fresnel drag coefficient or the relativity of space and time in accounting for the results of Fizeau’s experiment on the optics of moving media—the very experiment that Einstein considered to be “a crucial test in favour of the theory of relativity.” The new relativistic wave equation quantitatively describes other observations involving the optics of moving bodies, including stellar aberration and the null results of the Michelson- Morley experiment. In this paper, we propose an experiment to test the influence of the refractive index on the interference fringe shift generated by moving media. The Special Theory of Relativity, which is based on the relativity of space and time, and the new relativistic wave equation, which is based on the primacy of the Doppler effect, make different predictions concerning the influence of the refractive index on the optics of moving media.
    [Show full text]
  • Experimental Evidence of the Ether-Dragging Hypothesis in GPS Data
    Experimental evidence of the ether-dragging hypothesis in GPS data Masanori Sato Honda Electronics Co., Ltd., 20 Oyamazuka, Oiwa-cho, Toyohashi, Aichi 441-3193, Japan Abstract In global positioning system (GPS) satellites, the earth-centered locally inertial (ECI) coordinate system is used for calculations. We cannot use other reference frames, for example one based on the solar system, in the calculation of GPS satellites, because if the relative velocities in the solar system are used, large periodic orbital deviations of reference time are calculated. Therefore, the ECI coordinate system is a stationary gravitational frame. This fact provides experimental evidence for the ether-dragging hypothesis in which the ether is assumed to be the permittivity of free space, ε0, and the permeability of free space, µ0. This is interpreted using the analogy of an acoustic wave that is traveling in the atmosphere which is dragged by the gravity of the earth. PACS number: 03.30.+p Key words: GPS, ECI coordinate system, Lorentz transformation, ether-dragging hypothesis 1. Introduction The global positioning system (GPS) is used in car navigation systems. The use of special relativity in GPS has been summarized by Ashby [1]. The GPS satellites orbit in a region of low gravity (20,000 km from ground level) at vG(t)= 3.874 km/s. Therefore, the difference in gravitational potential between the ground and the location of the GPS satellites and the transverse Doppler shift effect of special relativity on the motion of the GPS satellites are considered. The transverse Doppler shift, or second-order Doppler shift, can be calculated by the Lorentz transformation of reference time.
    [Show full text]
  • 2.5 Aberration of Starlight and Stellar Parallax
    2.5 Aberration of Starlight and Stellar Parallax PRE-LECTURE READING 2.5 • Astronomy Today, 8th Edition (Chaisson & McMillan) • Astronomy Today, 7th Edition (Chaisson & McMillan) • Astronomy Today, 6th Edition (Chaisson & McMillan) VIDEO LECTURE • Aberration of Starlight and Stellar Parallax1 (12:35) SUPPLEMENTARY NOTES Tests of the Geocentric and Heliocentric Models • Venusian Phases (see Galilean Revolution) • Aberration of Starlight • Stellar Parallax Venusian Phases • Geocentric model predicts phase of Venus to change from new (when it is closest and largest) to crescent to new (when it is farthest and smallest) to crescent and back to new • Heliocentric model predicts phase of Venus to change from new (when it is closest and largest) to quarter to full (when it is farthest and smallest) to quarter and back to new (like the moon) • In 1609, Galileo confirmed the heliocentric prediction. Aberration of Starlight • See Aberration of Starlight2. • Heliocentric model predicts stars to appear to be shifted toward Earth's direction of motion, some by as much as 20 arcseconds. As Earth's direction of motion changes as it orbits the sun, so do the apparent positions of the stars, accordingly. • Geocentric model predicts no aberration of starlight because in the geocentric model, Earth is stationary. • By the mid-1700's, telescopes improved to the point that astronomers could, and did, con- firm the heliocentric prediction. 1http://youtu.be/kqvBVC8hkTs 2http://en.wikipedia.org/wiki/Aberration of light c 2011-2014 Advanced Instructional Systems, Inc. and Daniel Reichart 1 Stellar Parallax • See Stellar Parallax3. • Heliocentric model predicts stars to appear to be shifted opposite Earth's direction of mo- tion.
    [Show full text]
  • Proving Heliocentrism and Measuring the Astronomical Unit in A
    Draft version September 5, 2018 Typeset using LATEX RNAAS style in AASTeX62 Proving Heliocentrism and Measuring the Astronomical Unit in a Laboratory Astronomy Class via the Aberration of Starlight 1 Jason T. Wright 1Department of Astronomy & Astrophysics and Center for Exoplanets and Habitable Worlds 525 Davey Laboratory The Pennsylvania State University University Park, PA, 16802, USA Keywords: history and philosophy of astronomy — methods: observational — celestial mechanics The objective reality of the Earth’s motion about the Sun was finally proven observationally by Bradley (1727) when he correctly explained the ∼ 20′′ annual, elliptical motions of stars as being due to aberration of starlight caused by the motion of the Earth. The effect is so large that at first blush it seems that it should be quite easily measured with modern equipment of the sort used in astronomy laboratory courses, but since the effect is an absolute displacement of all stars, it is not detectable with the usual methods of differential astrometry. One must instead measure stellar positions with respect to some absolute reference direction. Happily, there is an absolute reference readily available to many telescopes: the true Celestial Poles, which are, by definition, directions parallel to the Earth’s rotation axis. To use this reference, one could point an imaging telescope at the Celestial Pole and turn off tracking, taking exposures throughout the night. Then, a stack of all of these images should reveal star trails centered on the true Celestial Pole, allowing one to measure its position with respect to the apparent positions of the stars. Since the stars (unlike the poles) are subject to aberration, they will appear to move throughout the year with respect to the Celestial Pole by ∼ 20′′.
    [Show full text]