510
R. Plamondon
neglected, the Hubble constant H 0 can be linked to σ Sun and the secular increase of
the astronomical unit V AU to σ Earth , which leads to accurate numerical predictions:
H 0 = 74.42(.02)(km/s)/Mpc and V AU ∼ = 7.8cm - yr −1 . Moreover, investigating the
expected impacts of the erfc potential on the fly-bys anomalies and the residual
Pioneers’ delay lead to corrections for the osculating asymptotic velocity of a flyby at the perigee of the order of 10 mm/s and an inward radial acceleration of
8.34 × 10 −10 m/s 2 affecting the Pioneer spacecrafts.
To the best of our knowledge, the Bayesian paradigm proposed in this paper has
never been investigated. Bayesian approaches have extensively been used to explore
complex problems from a probabilistic point of view in numerous fields of science
[17, 18], including quantum physics [19], astronomy [20], artificial intelligence
[21], and neuroscience [22], to name a few examples. The present model adds up to
this exhaustive list.
Acknowledgements This work has been partly supported over the years by RGPIN-2015-06409
discovery grants from NSERC Canada to Réjean Plamondon, as well as by the Department of
Electrical Engineering, Polytechnique Montréal. The author thanks Claudéric Ouellet-Plamondon
and André Laveau for their kind help with computer simulations and Richard Gagnon for his
constructive comments.
References
1. M. Mitchelle, Complexity: A Guided Tour (Oxford University Press, Oxford, 2009), 349p
2. I. Licata, A. Sakaji (eds.), Physics of Emergence and Organization (World Scientific, Singapore, 2008)
3. W.J. Adams, The Life and Times of the Central Limit Theorem, vol 35, 2nd edn. (American
Mathematical Society, London Mathematical Society, History of Mathematics, Providence,
2009), 195p
4. C. Barcelo, S. Liberati, M. Visser, Analogue gravity. Living Rev. Relativ. 14(3), 1–15 (2011)
http://www.livingreviews.org/lrr-2011-3
5. V. Faraoni, Cosmology in Scalar-Tensor Gravity (Fundamental Theories of Physics) (Springer
Sciences and Business Media, Dordrecht, 2004)
6. T.P. Sotiriou, V. Faraoni, f(R) theories of gravity. Rev. Mod. Phys. 82, 451 (2010)
7. S. Capoziello, V. Faraoni, Beyond Einstein Gravity, a Survey of Gravitational Theories for
Cosmology and Astrophysics (Springer, Dorrdrecht, 2010)
8. A. De Felice, S. Tsujikawa, Living Rev. Relativ. 13, 3 (2010). https://doi.org/10.12942/lrr2010-3
9. T. Clifton, P.G. Ferreira, A. Padilla, C. Skordis, Modified gravity and cosmology. Phys. Rep.
513, 1–189 (2012)
10. R. Plamondon, General relativity: An erfc metric. Results Phys. 9, 456–462 (2018)
11. R. Plamondon, Solar system anomalies: revisiting Hubble’s law. Phys. Essays 30(4), 403–411
(2017)
12. J.A. Wheeler, K.W. Ford, Geons, black holes, and quantum foam: a life in physics (W. W.
Norton & Company, New York, 2000)
13. W.J. Lindeberg, Eine neue Herleitung des Exponential-gesetze in der Wahscheinlichkeitsrechnung. Math Zeit 15, 211 (1922)
14. A. Einstein, Die Grundlage der Allegemeinen Relativitatstheorie. Ann. Phys. 49, 769 (1916)
R. Plamondon
neglected, the Hubble constant H 0 can be linked to σ Sun and the secular increase of
the astronomical unit V AU to σ Earth , which leads to accurate numerical predictions:
H 0 = 74.42(.02)(km/s)/Mpc and V AU ∼ = 7.8cm - yr −1 . Moreover, investigating the
expected impacts of the erfc potential on the fly-bys anomalies and the residual
Pioneers’ delay lead to corrections for the osculating asymptotic velocity of a flyby at the perigee of the order of 10 mm/s and an inward radial acceleration of
8.34 × 10 −10 m/s 2 affecting the Pioneer spacecrafts.
To the best of our knowledge, the Bayesian paradigm proposed in this paper has
never been investigated. Bayesian approaches have extensively been used to explore
complex problems from a probabilistic point of view in numerous fields of science
[17, 18], including quantum physics [19], astronomy [20], artificial intelligence
[21], and neuroscience [22], to name a few examples. The present model adds up to
this exhaustive list.
Acknowledgements This work has been partly supported over the years by RGPIN-2015-06409
discovery grants from NSERC Canada to Réjean Plamondon, as well as by the Department of
Electrical Engineering, Polytechnique Montréal. The author thanks Claudéric Ouellet-Plamondon
and André Laveau for their kind help with computer simulations and Richard Gagnon for his
constructive comments.
References
1. M. Mitchelle, Complexity: A Guided Tour (Oxford University Press, Oxford, 2009), 349p
2. I. Licata, A. Sakaji (eds.), Physics of Emergence and Organization (World Scientific, Singapore, 2008)
3. W.J. Adams, The Life and Times of the Central Limit Theorem, vol 35, 2nd edn. (American
Mathematical Society, London Mathematical Society, History of Mathematics, Providence,
2009), 195p
4. C. Barcelo, S. Liberati, M. Visser, Analogue gravity. Living Rev. Relativ. 14(3), 1–15 (2011)
http://www.livingreviews.org/lrr-2011-3
5. V. Faraoni, Cosmology in Scalar-Tensor Gravity (Fundamental Theories of Physics) (Springer
Sciences and Business Media, Dordrecht, 2004)
6. T.P. Sotiriou, V. Faraoni, f(R) theories of gravity. Rev. Mod. Phys. 82, 451 (2010)
7. S. Capoziello, V. Faraoni, Beyond Einstein Gravity, a Survey of Gravitational Theories for
Cosmology and Astrophysics (Springer, Dorrdrecht, 2010)
8. A. De Felice, S. Tsujikawa, Living Rev. Relativ. 13, 3 (2010). https://doi.org/10.12942/lrr2010-3
9. T. Clifton, P.G. Ferreira, A. Padilla, C. Skordis, Modified gravity and cosmology. Phys. Rep.
513, 1–189 (2012)
10. R. Plamondon, General relativity: An erfc metric. Results Phys. 9, 456–462 (2018)
11. R. Plamondon, Solar system anomalies: revisiting Hubble’s law. Phys. Essays 30(4), 403–411
(2017)
12. J.A. Wheeler, K.W. Ford, Geons, black holes, and quantum foam: a life in physics (W. W.
Norton & Company, New York, 2000)
13. W.J. Lindeberg, Eine neue Herleitung des Exponential-gesetze in der Wahscheinlichkeitsrechnung. Math Zeit 15, 211 (1922)
14. A. Einstein, Die Grundlage der Allegemeinen Relativitatstheorie. Ann. Phys. 49, 769 (1916)