Noninertial Freely Falling Frames Affected by Gravitational Tidal Forces

Steven D. Deines

doi:doi:10.11648/j.ijamtp.20170301.11

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Noninertial Freely Falling Frames Affected by Gravitational Tidal Forces

Steven D. Deines

Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 3, Issue 1)

Received: 8 August 2016 Accepted: 23 September 2016 Published: 9 November 2016

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Abstract

It is a major misconception that freely falling reference frames are inertial in a gravitational field. This is one outcome when employing Einstein’s principle of equivalence between a dynamical acceleration and a homogeneous gravity, which does not exist technically in nature, because gravity is radial from all mass centers, even at nearly infinite distances between masses. Even though floating objects within a space station orbiting Earth appear to move with constant inertial velocities, tidal forces exist to accelerate all such objects. The four oceanic tides of Earth prove that the Moon and Sun are the two external gravitational bodies pulling on Earth, even if an earthbound observer cannot physically feel the tidal forces. Theoretical experiments demonstrate how to observe tidal effects internally to determine the external gravitational forces. Tidal forces make dumbbell-shaped artificial satellites rotate around a heavenly body once per orbit. A liquid in free fall like mercury becomes prolate in shape and aligns with the external gravitational force if the liquid’s surface tension can be minimized. Today’s technology is very precise and can detect most subtle forces, so that local experiments can distinguish between a reference frame in free fall versus a truly inertial frame placed far away from gravitational bodies. Tidal forces always exist in any neighborhood of a test mass due to the radial gravitational force from any external mass, so the mathematical limit of a shrinking local reference frame always contains tidal forces within its domain. Thus, Einstein’s equivalence principle is an approximation and is technically applicable for only point masses.

Published in	International Journal of Applied Mathematics and Theoretical Physics (Volume 3, Issue 1)
DOI	10.11648/j.ijamtp.20170301.11
Page(s)	1-6
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), 2024. Published by Science Publishing Group

Keywords

Freely Falling Frames, Relativity, Equivalence Principle, Local Frames

References

[1]	Einstein, A., “How I Constructed the Theory of Relativity”, translated by Masahiro Morikawa from the text recorded in Japanese by Jun Ishiwara, Association of Asia Pacific Physical Societies (AAPPS) Bulletin, Vol. 15, No. 2, pp. 17-19, April 2005. Einstein recalled events of 1907 in a talk in Japan on 14 December 1922.
[2]	Einstein, A., "Relativitätsprinzip und die aus demselben gezogenen Folgerungen (On the Relativity Principle and the Conclusions Drawn from It)", Jahrbuch der Radioaktivität (Yearbook of Radioactivity), (1908) 4: pp. 411–462.
[3]	Serway, R. A. and Jewett Jr., J. W., Physics for Scientists and Engineers, Cengage Learning, 9th ed. (2014).
[4]	Weinberg, S., Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity, John Wiley & Sons, New York (1972).
[5]	Seidelmann, P. K., [Ed.] Explanatory Supplement to the Astronomical Almanac, U.S. Naval Observatory, University Science Books (1992).
[6]	Britting, K. R., Inertial Navigation Systems Analysis, Wiley & Sons (1971).
[7]	Ohanian, H. C. and Ruffini, R., Gravitation and Spacetime, 2nd ed., Norton and Co., New York (1994).
[8]	Olah, S., “Solar and Lunar Tides”, General Physics Journal (2009).
[9]	Kaplan, M. H., Modern Spacecraft Dynamics and Control, John Wiley & Sons, New York (1976).
[10]	Marion, J. B., Classical Dynamics of Particles and Systems, 2nd ed., Academic Press, New York (1970).
[11]	Einstein, A., “The effect of gravity on light”, (1911), translated and reprinted in The Principle of Relativity, by Davis, F. A., Dover Publications (1928).

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APA Style

Steven D. Deines. (2016). Noninertial Freely Falling Frames Affected by Gravitational Tidal Forces. International Journal of Applied Mathematics and Theoretical Physics, 3(1), 1-6. https://doi.org/10.11648/j.ijamtp.20170301.11

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ACS Style

Steven D. Deines. Noninertial Freely Falling Frames Affected by Gravitational Tidal Forces. Int. J. Appl. Math. Theor. Phys. 2016, 3(1), 1-6. doi: 10.11648/j.ijamtp.20170301.11

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AMA Style

Steven D. Deines. Noninertial Freely Falling Frames Affected by Gravitational Tidal Forces. Int J Appl Math Theor Phys. 2016;3(1):1-6. doi: 10.11648/j.ijamtp.20170301.11

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@article{10.11648/j.ijamtp.20170301.11,
  author = {Steven D. Deines},
  title = {Noninertial Freely Falling Frames Affected by Gravitational Tidal Forces},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {3},
  number = {1},
  pages = {1-6},
  doi = {10.11648/j.ijamtp.20170301.11},
  url = {https://doi.org/10.11648/j.ijamtp.20170301.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20170301.11},
  abstract = {It is a major misconception that freely falling reference frames are inertial in a gravitational field. This is one outcome when employing Einstein’s principle of equivalence between a dynamical acceleration and a homogeneous gravity, which does not exist technically in nature, because gravity is radial from all mass centers, even at nearly infinite distances between masses. Even though floating objects within a space station orbiting Earth appear to move with constant inertial velocities, tidal forces exist to accelerate all such objects. The four oceanic tides of Earth prove that the Moon and Sun are the two external gravitational bodies pulling on Earth, even if an earthbound observer cannot physically feel the tidal forces. Theoretical experiments demonstrate how to observe tidal effects internally to determine the external gravitational forces. Tidal forces make dumbbell-shaped artificial satellites rotate around a heavenly body once per orbit. A liquid in free fall like mercury becomes prolate in shape and aligns with the external gravitational force if the liquid’s surface tension can be minimized. Today’s technology is very precise and can detect most subtle forces, so that local experiments can distinguish between a reference frame in free fall versus a truly inertial frame placed far away from gravitational bodies. Tidal forces always exist in any neighborhood of a test mass due to the radial gravitational force from any external mass, so the mathematical limit of a shrinking local reference frame always contains tidal forces within its domain. Thus, Einstein’s equivalence principle is an approximation and is technically applicable for only point masses.},
 year = {2016}
}

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TY  - JOUR
T1  - Noninertial Freely Falling Frames Affected by Gravitational Tidal Forces
AU  - Steven D. Deines
Y1  - 2016/11/09
PY  - 2016
N1  - https://doi.org/10.11648/j.ijamtp.20170301.11
DO  - 10.11648/j.ijamtp.20170301.11
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 1
EP  - 6
PB  - Science Publishing Group
SN  - 2575-5927
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AB  - It is a major misconception that freely falling reference frames are inertial in a gravitational field. This is one outcome when employing Einstein’s principle of equivalence between a dynamical acceleration and a homogeneous gravity, which does not exist technically in nature, because gravity is radial from all mass centers, even at nearly infinite distances between masses. Even though floating objects within a space station orbiting Earth appear to move with constant inertial velocities, tidal forces exist to accelerate all such objects. The four oceanic tides of Earth prove that the Moon and Sun are the two external gravitational bodies pulling on Earth, even if an earthbound observer cannot physically feel the tidal forces. Theoretical experiments demonstrate how to observe tidal effects internally to determine the external gravitational forces. Tidal forces make dumbbell-shaped artificial satellites rotate around a heavenly body once per orbit. A liquid in free fall like mercury becomes prolate in shape and aligns with the external gravitational force if the liquid’s surface tension can be minimized. Today’s technology is very precise and can detect most subtle forces, so that local experiments can distinguish between a reference frame in free fall versus a truly inertial frame placed far away from gravitational bodies. Tidal forces always exist in any neighborhood of a test mass due to the radial gravitational force from any external mass, so the mathematical limit of a shrinking local reference frame always contains tidal forces within its domain. Thus, Einstein’s equivalence principle is an approximation and is technically applicable for only point masses.
VL  - 3
IS  - 1
ER  -

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Author Information

Steven D. Deines

Donatech Corporation Inc., Fairfield, Iowa, USA

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Plain Text BibTeX RIS

APA Style

Steven D. Deines. (2016). Noninertial Freely Falling Frames Affected by Gravitational Tidal Forces. International Journal of Applied Mathematics and Theoretical Physics, 3(1), 1-6. https://doi.org/10.11648/j.ijamtp.20170301.11

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ACS Style

Steven D. Deines. Noninertial Freely Falling Frames Affected by Gravitational Tidal Forces. Int. J. Appl. Math. Theor. Phys. 2016, 3(1), 1-6. doi: 10.11648/j.ijamtp.20170301.11

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AMA Style

Steven D. Deines. Noninertial Freely Falling Frames Affected by Gravitational Tidal Forces. Int J Appl Math Theor Phys. 2016;3(1):1-6. doi: 10.11648/j.ijamtp.20170301.11

Copy | Download

@article{10.11648/j.ijamtp.20170301.11,
  author = {Steven D. Deines},
  title = {Noninertial Freely Falling Frames Affected by Gravitational Tidal Forces},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {3},
  number = {1},
  pages = {1-6},
  doi = {10.11648/j.ijamtp.20170301.11},
  url = {https://doi.org/10.11648/j.ijamtp.20170301.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20170301.11},
  abstract = {It is a major misconception that freely falling reference frames are inertial in a gravitational field. This is one outcome when employing Einstein’s principle of equivalence between a dynamical acceleration and a homogeneous gravity, which does not exist technically in nature, because gravity is radial from all mass centers, even at nearly infinite distances between masses. Even though floating objects within a space station orbiting Earth appear to move with constant inertial velocities, tidal forces exist to accelerate all such objects. The four oceanic tides of Earth prove that the Moon and Sun are the two external gravitational bodies pulling on Earth, even if an earthbound observer cannot physically feel the tidal forces. Theoretical experiments demonstrate how to observe tidal effects internally to determine the external gravitational forces. Tidal forces make dumbbell-shaped artificial satellites rotate around a heavenly body once per orbit. A liquid in free fall like mercury becomes prolate in shape and aligns with the external gravitational force if the liquid’s surface tension can be minimized. Today’s technology is very precise and can detect most subtle forces, so that local experiments can distinguish between a reference frame in free fall versus a truly inertial frame placed far away from gravitational bodies. Tidal forces always exist in any neighborhood of a test mass due to the radial gravitational force from any external mass, so the mathematical limit of a shrinking local reference frame always contains tidal forces within its domain. Thus, Einstein’s equivalence principle is an approximation and is technically applicable for only point masses.},
 year = {2016}
}

Copy | Download

TY  - JOUR
T1  - Noninertial Freely Falling Frames Affected by Gravitational Tidal Forces
AU  - Steven D. Deines
Y1  - 2016/11/09
PY  - 2016
N1  - https://doi.org/10.11648/j.ijamtp.20170301.11
DO  - 10.11648/j.ijamtp.20170301.11
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 1
EP  - 6
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20170301.11
AB  - It is a major misconception that freely falling reference frames are inertial in a gravitational field. This is one outcome when employing Einstein’s principle of equivalence between a dynamical acceleration and a homogeneous gravity, which does not exist technically in nature, because gravity is radial from all mass centers, even at nearly infinite distances between masses. Even though floating objects within a space station orbiting Earth appear to move with constant inertial velocities, tidal forces exist to accelerate all such objects. The four oceanic tides of Earth prove that the Moon and Sun are the two external gravitational bodies pulling on Earth, even if an earthbound observer cannot physically feel the tidal forces. Theoretical experiments demonstrate how to observe tidal effects internally to determine the external gravitational forces. Tidal forces make dumbbell-shaped artificial satellites rotate around a heavenly body once per orbit. A liquid in free fall like mercury becomes prolate in shape and aligns with the external gravitational force if the liquid’s surface tension can be minimized. Today’s technology is very precise and can detect most subtle forces, so that local experiments can distinguish between a reference frame in free fall versus a truly inertial frame placed far away from gravitational bodies. Tidal forces always exist in any neighborhood of a test mass due to the radial gravitational force from any external mass, so the mathematical limit of a shrinking local reference frame always contains tidal forces within its domain. Thus, Einstein’s equivalence principle is an approximation and is technically applicable for only point masses.
VL  - 3
IS  - 1
ER  -

Copy | Download