Stellar Aberration from Earth and from a Satellite

Caesar Viazminsky; Piere Vizminiska

doi:doi:10.11648/j.ajaa.20210903.11

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Stellar Aberration from Earth and from a Satellite

Caesar Viazminsky, Piere Vizminiska

Published in American Journal of Astronomy and Astrophysics (Volume 9, Issue 3)

Received: 4 June 2021 Accepted: 28 June 2021 Published: 9 July 2021

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Abstract

In his endeavor to find a concrete evidence in favor of the Copernican picture of the solar system, the English astronomer James Bradley made a series of astronomical observations during the period (1725-1728) aiming to detect a stellar parallax. His findings, which manifested indeed an annual apparent cyclic motion of a star, were however at conflict with what is expected in a parallax. To his surprise, the result of every measurement obtained corresponded to what he expected to get in a measurement done three months earlier. Bradley realized that he was witnessing a new physical effect, and he presented an explanation that conceived light as a corpuscular stream travelling at finite velocity. Despite that Bradley’s explanation of the stellar aberration effect was inadequate, the equation which he derived to quantify the aberration angle, predicted a better estimation of light velocity, and the aberration phenomenon itself was a concrete support of heliocentrism. Stellar aberration as well as some other optical experiments, whose explanations posed challenges to the existing physical theories in the late nineteenth century paved the way for the emergence of the special theory of relativity. In the current work we employ the theory of universal space and time to show that a given direction in a frame of reference is tilted when observed in a moving frame by an angle that depends on the direction itself and the velocity of the moving frame. The latter fact is utilized to explain stellar aberration, determine the deviation of a star’s vision direction from its true one, and deduce its apparent position at any instant as a function of its latitude and time. The novel concept of aberration correction vector is employed to derive the apparent elliptic path of an observed celestial object at any time. The concept of graded inertial frames is introduced and utilized to deal with aberration when observed from a satellite in a similar way to its treatment when observed from Earth. The transformation matrix between a geocentric frame and a satellite’s non-rotating frame is derived and used to transform temporary Earthly vision directions to the satellite’s frame. Furthermore, the transformed vectors are adopted as transient fixed directions relative to which the vision directions of a star from the satellite are specified throughout one revolution. Satellites connective matrices are constructed to make geometric information regarding the celestial sphere in one frame immediately usable by observers on Earth and in all other satellites.

Published in	American Journal of Astronomy and Astrophysics (Volume 9, Issue 3)
DOI	10.11648/j.ajaa.20210903.11
Page(s)	22-31
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2021. Published by Science Publishing Group

Keywords

Stellar Aberration, Aberration in a Satellite, Graded Inertial Frames, Stars’ Apparent Elliptic Trajectories, Aberration Correction Vector, Satellites Connective Matrices

References

[1]	Kovalevsky, Jean and Seidelmann, P. Kenneth (2004), Fundamentals of Astrometry. Cambridge: Cambridge University Press. ISBN 0-521-64216-7.
[2]	Bradley, James (1729). "An account of a new discovered motion of the fixed stars". Philosophical Transactions of the Royal Society. 35: 637–661. doi: 10.1098/rstl.1727.0064.
[3]	Berry, Arthur (1961). A Short History of Astronomy, Dover.
[4]	French A. P. (1968) Special relativity. Butler & Tanner Ltd, Frome and London, Ch. 2&3.
[5]	Russo D. (2007) "Stellar aberration: the contradiction between Einstein and Bradley", Apeiron, 14, no 2.
[6]	Brown, Kevin (2020), Reflection of Relativity, 2.5, Stellar Aberration, Publisher: Lulu.com.
[7]	Stokes G. G. (1845) On the aberration of light, Philosophical Magazine 27, p. 9-15; (1848) On the constitution of luminiferous ether, Philosophical magazine 32, p 343-349.
[8]	Whittaker, Edmund Taylor (1910), A History of the theories of aether and electricity (1. ed.), Dublin: Longman, Green and Co., archived from the original on 2016-02-15.
[9]	Schaffner, Kenneth F. (1972), Nineteenth-century aether theories, Oxford: Pergamon Press, pp. 99–117 und 255–273, ISBN 0-08-015674-6.
[10]	Viazminsky C. P. and Vizminiska P. K. (2014) On Universal Space and Time. Applied Mathematics, 5, 2530-2546. http://dx.doi.org/10.4236/am.2014.516243.
[11]	Viazminsky C. P. and Vizminiska P. K. (2014) On Universal Mechanics and Superluminal Velocities. Applied Mathematics, 5, 2728-2738. http://dx.doi.org/10.4236/am.2014.517260.
[12]	Viazminsky C. P. and Vizminiska P. K. (2019) Universal Space and Time, Proper Velocity and Undoing Space Contraction. General Sciences Journal, https://www.gsjournal.net/Science-Journals/Research%20Papers-Relativity%20Theory/Download/7907.
[13]	Viazminsky C. P. and Vizminiska P. K., Rays’ Change of Directions between Inertial Frames and Stellar Aberration. Applied Mathematics, 2015, 6, 1553-1562 Published Online August 2015 in SciRes. http://www.scirp.org/journal/am.
[14]	Rindler W. (1977) Essential Relativity. Springer-Verlag, New York.
[15]	Viazminsky C. P. (2008). The Scaling Theory V: Aberration, https://www.gsjournal.net/Science-Journals/Research%20Papers-Mechanics%20/%20Electrodynamics/Download/1953.
[16]	Newcomb, Simon (1960), A Compendium of Spherical Astronomy, Macmillan.
[17]	Earth Fact Sheet, the NSSDCA –NASA https://nssdc.gsfc.nasa.gov/planetary/factsheet/earthfact.html.
[18]	Airy, G. B. (1871). "On the Supposed Alteration in the Amount of Astronomical Aberration of Light, Produced by the Passage of the Light through a Considerable Thickness of Refracting Medium". Proceedings of the Royal Society of London. 20 (130–138): 35–39.
[19]	Pauli, W. 1958. Theory of relativity, Dover Publications.

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APA Style

Caesar Viazminsky, Piere Vizminiska. (2021). Stellar Aberration from Earth and from a Satellite. American Journal of Astronomy and Astrophysics, 9(3), 22-31. https://doi.org/10.11648/j.ajaa.20210903.11

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ACS Style

Caesar Viazminsky; Piere Vizminiska. Stellar Aberration from Earth and from a Satellite. Am. J. Astron. Astrophys. 2021, 9(3), 22-31. doi: 10.11648/j.ajaa.20210903.11

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AMA Style

Caesar Viazminsky, Piere Vizminiska. Stellar Aberration from Earth and from a Satellite. Am J Astron Astrophys. 2021;9(3):22-31. doi: 10.11648/j.ajaa.20210903.11

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@article{10.11648/j.ajaa.20210903.11,
  author = {Caesar Viazminsky and Piere Vizminiska},
  title = {Stellar Aberration from Earth and from a Satellite},
  journal = {American Journal of Astronomy and Astrophysics},
  volume = {9},
  number = {3},
  pages = {22-31},
  doi = {10.11648/j.ajaa.20210903.11},
  url = {https://doi.org/10.11648/j.ajaa.20210903.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20210903.11},
  abstract = {In his endeavor to find a concrete evidence in favor of the Copernican picture of the solar system, the English astronomer James Bradley made a series of astronomical observations during the period (1725-1728) aiming to detect a stellar parallax. His findings, which manifested indeed an annual apparent cyclic motion of a star, were however at conflict with what is expected in a parallax. To his surprise, the result of every measurement obtained corresponded to what he expected to get in a measurement done three months earlier. Bradley realized that he was witnessing a new physical effect, and he presented an explanation that conceived light as a corpuscular stream travelling at finite velocity. Despite that Bradley’s explanation of the stellar aberration effect was inadequate, the equation which he derived to quantify the aberration angle, predicted a better estimation of light velocity, and the aberration phenomenon itself was a concrete support of heliocentrism. Stellar aberration as well as some other optical experiments, whose explanations posed challenges to the existing physical theories in the late nineteenth century paved the way for the emergence of the special theory of relativity. In the current work we employ the theory of universal space and time to show that a given direction in a frame of reference is tilted when observed in a moving frame by an angle that depends on the direction itself and the velocity of the moving frame. The latter fact is utilized to explain stellar aberration, determine the deviation of a star’s vision direction from its true one, and deduce its apparent position at any instant as a function of its latitude and time. The novel concept of aberration correction vector is employed to derive the apparent elliptic path of an observed celestial object at any time. The concept of graded inertial frames is introduced and utilized to deal with aberration when observed from a satellite in a similar way to its treatment when observed from Earth. The transformation matrix between a geocentric frame and a satellite’s non-rotating frame is derived and used to transform temporary Earthly vision directions to the satellite’s frame. Furthermore, the transformed vectors are adopted as transient fixed directions relative to which the vision directions of a star from the satellite are specified throughout one revolution. Satellites connective matrices are constructed to make geometric information regarding the celestial sphere in one frame immediately usable by observers on Earth and in all other satellites.},
 year = {2021}
}

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TY  - JOUR
T1  - Stellar Aberration from Earth and from a Satellite
AU  - Caesar Viazminsky
AU  - Piere Vizminiska
Y1  - 2021/07/09
PY  - 2021
N1  - https://doi.org/10.11648/j.ajaa.20210903.11
DO  - 10.11648/j.ajaa.20210903.11
T2  - American Journal of Astronomy and Astrophysics
JF  - American Journal of Astronomy and Astrophysics
JO  - American Journal of Astronomy and Astrophysics
SP  - 22
EP  - 31
PB  - Science Publishing Group
SN  - 2376-4686
UR  - https://doi.org/10.11648/j.ajaa.20210903.11
AB  - In his endeavor to find a concrete evidence in favor of the Copernican picture of the solar system, the English astronomer James Bradley made a series of astronomical observations during the period (1725-1728) aiming to detect a stellar parallax. His findings, which manifested indeed an annual apparent cyclic motion of a star, were however at conflict with what is expected in a parallax. To his surprise, the result of every measurement obtained corresponded to what he expected to get in a measurement done three months earlier. Bradley realized that he was witnessing a new physical effect, and he presented an explanation that conceived light as a corpuscular stream travelling at finite velocity. Despite that Bradley’s explanation of the stellar aberration effect was inadequate, the equation which he derived to quantify the aberration angle, predicted a better estimation of light velocity, and the aberration phenomenon itself was a concrete support of heliocentrism. Stellar aberration as well as some other optical experiments, whose explanations posed challenges to the existing physical theories in the late nineteenth century paved the way for the emergence of the special theory of relativity. In the current work we employ the theory of universal space and time to show that a given direction in a frame of reference is tilted when observed in a moving frame by an angle that depends on the direction itself and the velocity of the moving frame. The latter fact is utilized to explain stellar aberration, determine the deviation of a star’s vision direction from its true one, and deduce its apparent position at any instant as a function of its latitude and time. The novel concept of aberration correction vector is employed to derive the apparent elliptic path of an observed celestial object at any time. The concept of graded inertial frames is introduced and utilized to deal with aberration when observed from a satellite in a similar way to its treatment when observed from Earth. The transformation matrix between a geocentric frame and a satellite’s non-rotating frame is derived and used to transform temporary Earthly vision directions to the satellite’s frame. Furthermore, the transformed vectors are adopted as transient fixed directions relative to which the vision directions of a star from the satellite are specified throughout one revolution. Satellites connective matrices are constructed to make geometric information regarding the celestial sphere in one frame immediately usable by observers on Earth and in all other satellites.
VL  - 9
IS  - 3
ER  -

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Author Information

Caesar Viazminsky

Department of Physics, University of Aleppo, Aleppo, Syria
Piere Vizminiska

Department of Accounting, Faculty of Business, Eastern Michigan University, Ypsilanti, MI, USA

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Caesar Viazminsky, Piere Vizminiska. (2021). Stellar Aberration from Earth and from a Satellite. American Journal of Astronomy and Astrophysics, 9(3), 22-31. https://doi.org/10.11648/j.ajaa.20210903.11

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ACS Style

Caesar Viazminsky; Piere Vizminiska. Stellar Aberration from Earth and from a Satellite. Am. J. Astron. Astrophys. 2021, 9(3), 22-31. doi: 10.11648/j.ajaa.20210903.11

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AMA Style

Caesar Viazminsky, Piere Vizminiska. Stellar Aberration from Earth and from a Satellite. Am J Astron Astrophys. 2021;9(3):22-31. doi: 10.11648/j.ajaa.20210903.11

Copy | Download

@article{10.11648/j.ajaa.20210903.11,
  author = {Caesar Viazminsky and Piere Vizminiska},
  title = {Stellar Aberration from Earth and from a Satellite},
  journal = {American Journal of Astronomy and Astrophysics},
  volume = {9},
  number = {3},
  pages = {22-31},
  doi = {10.11648/j.ajaa.20210903.11},
  url = {https://doi.org/10.11648/j.ajaa.20210903.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajaa.20210903.11},
  abstract = {In his endeavor to find a concrete evidence in favor of the Copernican picture of the solar system, the English astronomer James Bradley made a series of astronomical observations during the period (1725-1728) aiming to detect a stellar parallax. His findings, which manifested indeed an annual apparent cyclic motion of a star, were however at conflict with what is expected in a parallax. To his surprise, the result of every measurement obtained corresponded to what he expected to get in a measurement done three months earlier. Bradley realized that he was witnessing a new physical effect, and he presented an explanation that conceived light as a corpuscular stream travelling at finite velocity. Despite that Bradley’s explanation of the stellar aberration effect was inadequate, the equation which he derived to quantify the aberration angle, predicted a better estimation of light velocity, and the aberration phenomenon itself was a concrete support of heliocentrism. Stellar aberration as well as some other optical experiments, whose explanations posed challenges to the existing physical theories in the late nineteenth century paved the way for the emergence of the special theory of relativity. In the current work we employ the theory of universal space and time to show that a given direction in a frame of reference is tilted when observed in a moving frame by an angle that depends on the direction itself and the velocity of the moving frame. The latter fact is utilized to explain stellar aberration, determine the deviation of a star’s vision direction from its true one, and deduce its apparent position at any instant as a function of its latitude and time. The novel concept of aberration correction vector is employed to derive the apparent elliptic path of an observed celestial object at any time. The concept of graded inertial frames is introduced and utilized to deal with aberration when observed from a satellite in a similar way to its treatment when observed from Earth. The transformation matrix between a geocentric frame and a satellite’s non-rotating frame is derived and used to transform temporary Earthly vision directions to the satellite’s frame. Furthermore, the transformed vectors are adopted as transient fixed directions relative to which the vision directions of a star from the satellite are specified throughout one revolution. Satellites connective matrices are constructed to make geometric information regarding the celestial sphere in one frame immediately usable by observers on Earth and in all other satellites.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Stellar Aberration from Earth and from a Satellite
AU  - Caesar Viazminsky
AU  - Piere Vizminiska
Y1  - 2021/07/09
PY  - 2021
N1  - https://doi.org/10.11648/j.ajaa.20210903.11
DO  - 10.11648/j.ajaa.20210903.11
T2  - American Journal of Astronomy and Astrophysics
JF  - American Journal of Astronomy and Astrophysics
JO  - American Journal of Astronomy and Astrophysics
SP  - 22
EP  - 31
PB  - Science Publishing Group
SN  - 2376-4686
UR  - https://doi.org/10.11648/j.ajaa.20210903.11
AB  - In his endeavor to find a concrete evidence in favor of the Copernican picture of the solar system, the English astronomer James Bradley made a series of astronomical observations during the period (1725-1728) aiming to detect a stellar parallax. His findings, which manifested indeed an annual apparent cyclic motion of a star, were however at conflict with what is expected in a parallax. To his surprise, the result of every measurement obtained corresponded to what he expected to get in a measurement done three months earlier. Bradley realized that he was witnessing a new physical effect, and he presented an explanation that conceived light as a corpuscular stream travelling at finite velocity. Despite that Bradley’s explanation of the stellar aberration effect was inadequate, the equation which he derived to quantify the aberration angle, predicted a better estimation of light velocity, and the aberration phenomenon itself was a concrete support of heliocentrism. Stellar aberration as well as some other optical experiments, whose explanations posed challenges to the existing physical theories in the late nineteenth century paved the way for the emergence of the special theory of relativity. In the current work we employ the theory of universal space and time to show that a given direction in a frame of reference is tilted when observed in a moving frame by an angle that depends on the direction itself and the velocity of the moving frame. The latter fact is utilized to explain stellar aberration, determine the deviation of a star’s vision direction from its true one, and deduce its apparent position at any instant as a function of its latitude and time. The novel concept of aberration correction vector is employed to derive the apparent elliptic path of an observed celestial object at any time. The concept of graded inertial frames is introduced and utilized to deal with aberration when observed from a satellite in a similar way to its treatment when observed from Earth. The transformation matrix between a geocentric frame and a satellite’s non-rotating frame is derived and used to transform temporary Earthly vision directions to the satellite’s frame. Furthermore, the transformed vectors are adopted as transient fixed directions relative to which the vision directions of a star from the satellite are specified throughout one revolution. Satellites connective matrices are constructed to make geometric information regarding the celestial sphere in one frame immediately usable by observers on Earth and in all other satellites.
VL  - 9
IS  - 3
ER  -

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