Share This Article:

Four Poission-Laplace Theory of Gravitation (I)

Abstract Full-Text HTML XML Download Download as PDF (Size:413KB) PP. 1195-1206
DOI: 10.4236/jmp.2015.69124    2,238 Downloads   2,609 Views   Citations

ABSTRACT

The Poisson-Laplace equation is a working and acceptable equation of gravitation which is mostly used or applied in its differential form in Magneto-Hydro-Dynamic (MHD) modelling of e.g. molecular clouds. From a general relativistic standpoint, it describes gravitational fields in the region of low spacetime curvature as it emerges in the weak field limit. For non-static gravitational fields, this equation is not generally covariant. On the requirements of general covariance, this equation can be extended to include a time-dependent component, in which case one is led to the Four Poisson-Laplace equation. We solve the Four Poisson-Laplace equation for radial solutions, and apart from the Newtonian gravitational component, we obtain four new solutions leading to four new gravitational components capable (in-principle) of explaining e.g. the Pioneer anomaly, the Titius-Bode Law and the formation of planetary rings. In this letter, we focus only on writing down these solutions. The task showing that these new solutions might explain the aforesaid gravitational anomalies has been left for separate future readings.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Nyambuya, G. (2015) Four Poission-Laplace Theory of Gravitation (I). Journal of Modern Physics, 6, 1195-1206. doi: 10.4236/jmp.2015.69124.

References

[1] Nyambuya, G.G. (2010) Monthly Notices of the Royal Astronomical Society, 403, 1381-1391.
http://dx.doi.org/10.1111/j.1365-2966.2009.16196.x
[2] Nyambuya, G.G. (2015) Monthly Notices of the Royal Astronomical Society, 451, 3034-3043.
http://dx.doi.org/10.1093/mnras/stv1100
[3] Nyambuya, G.G. (2010) Research in Astronomy and Astrophysics, 10, 1137-1150.
http://dx.doi.org/10.1088/1674-4527/10/11/006
[4] Nyambuya, G.G. (2010) Research in Astronomy and Astrophysics, 10, 1151-1176.
http://dx.doi.org/10.1088/1674-4527/10/11/007
[5] Nyambuya, G.G., Makwanya, T., Tuturu, B.A. and Tsoka, W. (2015) Astrophysics and Space Science, 358, 1-12. http://dx.doi.org/10.1007/s10509-015-2394-4
[6] Zinnecker, H. and Yorke, H.W. (2007) Annual Review of Astronomy and Astrophysics, 45, 481-563.
http://dx.doi.org/10.1146/annurev.astro.44.051905.092549
[7] Zinnecker, H. (2004) From Massive Stars to Planets. In: Garca-Segura, G., Tenorio-Tagle, Franco G.J. and Yorke, H.W., Eds., From Massive Stars to Planets, Revista Mexicana de Astronom’a y Astrof′sica (Serie de Conferencias), 22, 77.
[8] Bonnell, I.A., Bate, M. and Zinnecker, H. (1998) MNRAS, 298, 93. http://dx.doi.org/10.1046/j.1365-8711.1998.01590.x
[9] Yorke, H.W. (2002) ASP Conference Series, 267, 165.
[10] Yorke, H.W. and Sonnhalter, E. (2002) Astronomical Journal, 569, 846-862.
http://dx.doi.org/10.1086/339264
[11] Wolfire, M.G. and Cassinelli, J.P. (1987) The Astrophysical Journal, 319, 850.
http://dx.doi.org/10.1086/165503
[12] Yorke, H.W. and Krügel, H. (1977) Astronomy & Astrophysics, 54, 183.
[13] Lason, R.B. (1972) Monthly Notices of the Royal Astronomical Society, 156, 437-458.
http://dx.doi.org/10.1093/mnras/156.4.437
[14] Williams, J.G., Turyshev, S.G. and Boggs, D.H. (2014) Planetary Science, 3, 1-9.
http://dx.doi.org/10.1186/s13535-014-0002-5
[15] Williams, J.G., Boggs, S. and Schillak, D.H. (2009) The Astronomical Unit Now. In: Williams, J.G., Boggs, S. and Schillak, D.H., Eds., Transits of Venus: New Views of the Solar System and Galaxy, Number 196 in Proceedings of 16th International Workshop on Laser Ranging, Space Research Centre, Polish Academy of Sciences, Warsaw.
[16] Williams, J.G., Turyshev, S.G. and Boggs, D.H. (2004) Physical Review Letters, 93, Article ID: 261101. http://dx.doi.org/10.1103/PhysRevLett.93.261101
[17] Standish, D.W. and Kurtz, E.M. (2005) The Astronomical Unit Now. In: Standish, D.W. and Kurtz, E.M., Eds., Transits of Venus: New Views of the Solar System and Galaxy, Number 196 in Proceedings IAU Colloquium, IAU, Cambridge University Press, Cambridge, 163-179.
[18] Krasinsky, G.A. and Brumberg, V.A. (2004) Celestial Mechanics and Dynamical Astronomy, 90, 267-288.
http://dx.doi.org/10.1007/s10569-004-0633-z
[19] Lense, J. and Thirring, H. (1918) Physikalische Zeitschrift, 19, 156-163.
[20] Iorio, L. (2012) General Relativity and Gravitation, 44, 719-736.
http://dx.doi.org/10.1007/s10714-011-1302-7
[21] Pugh, G.E. (1959) Proposal for a Satellite Test of the Coriolis Prediction of General Relativity. Number 11 in WSEG Research Memorandum, The Pentagon, Washington DC.
[22] Schiff, L.I. (1960) American Journal of Physics, 28, 340. http://dx.doi.org/10.1119/1.1935800
[23] Schiff, L.I. (1960) Physical Review Letters, 4, 215-217. http://dx.doi.org/10.1103/PhysRevLett.4.215
[24] Zeldovich, Y.B. (1965) Journal of Experimental and Theoretical Physics Letters, 1, 95.
[25] Vladimirov, Y., Mitskievic, N. and Horsky, J. (1987) Space Time Gravitation. University of Chicago Press, Mir, Moscow, 91.
[26] Cohen, J.M. and Mashhoon, B. (1993) Physics Letters A, 181, 353-358.
http://dx.doi.org/10.1016/0375-9601(93)90387-F
[27] Lichtenegger, H., Iorio, L. and Mashhoon, B. (2006) Annalen der Physik, 15, 868-876.
http://dx.doi.org/10.1002/andp.200610214
[28] Iorio, L. and Lichtenegger, H.I.M. (2005) Classical and Quantum Gravity, 22, 119-132.
http://dx.doi.org/10.1088/0264-9381/22/1/008
[29] Iorio, L., Lichtenegger, H.I.M. and Mashhoon, B. (2002) Classical and Quantum Gravity, 19, 39-49.
http://dx.doi.org/10.1088/0264-9381/19/1/303
[30] Iorio, L. (2001) International Journal of Modern Physics D, 10, 465-476.
http://dx.doi.org/10.1142/S0218271801000925
[31] Iorio, L. (2001) Classical and Quantum Gravity, 18, 4303-4310.
http://dx.doi.org/10.1088/0264-9381/18/20/309
[32] Mashhoon, B., Iorio, L. and Lichtenegger, H.I.M. (2001) Physics Letters A, 292, 49-57.
http://dx.doi.org/10.1016/S0375-9601(01)00776-9
[33] Everitt, C.W.F., DeBra, D.B., Parkinson, B.W., Turneaure, J.P., Conklin, J.W., Heifetz, M.I., Keiser, G.M., Silbergleit, A.S., Holmes, T., Kolodziejczak, J., Al-Meshari, M., Mester, J.C., Muhlfelder, B., Solomonik, V.G., Stahl, K., Worden, P.W., Bencze, W., Buchman, S., Clarke, B., Al-Jadaan, A., Al-Jibreen, H., Li, J., Lipa, J.A., Lockhart, J.M., Al-Su-waidan, B., Taber, M. and Wang, S. (2011) Physical Review Letters, 106, Article ID: 221101. http://dx.doi.org/10.1103/PhysRevLett.106.221101
[34] Ginzburg, V.L. (1959) Scientific American, 200, 149-160.
http://dx.doi.org/10.1038/scientificamerican0559-149
[35] Cugusi, L. and Proverbio, E. (1978) Astronomy & Astrophysics, 69, 321-325.
[36] Ciufolini, I. and Pavils, E.C. (2004) Nature, 431, 958-960. http://dx.doi.org/10.1038/nature03007
[37] Iorio, L. (2006) Classical and Quantum Gravity, 23, 5451-5454.
http://dx.doi.org/10.1088/0264-9381/23/17/N01
[38] Iorio, L. (2009) The Astronomical Journal, 137, 3615-3618.
http://dx.doi.org/10.1088/0004-6256/137/3/3615
[39] Iorio, L. (2010) Central European Journal of Physics, 8, 509-513.
http://dx.doi.org/10.2478/s11534-009-0117-6
[40] Iorio, L. (2012) Solar Physics, 281, 815-826. http://dx.doi.org/10.1007/s11207-012-0086-6
[41] Iorio, L., Lichtenegger, H.I.M., Ruggiero, M.L. and Corda, C. (2011) Astrophysics and Space Science, 331, 351-395. http://dx.doi.org/10.1007/s10509-010-0489-5
[42] Iorio, L., Ruggiero, M.L. and Corda, C. (2013) Acta Astronautica, 91, 141-148.
http://dx.doi.org/10.1016/j.actaastro.2013.06.002
[43] Renzetti, G. (2013) New Astronomy, 23, 63-66. http://dx.doi.org/10.1016/j.newast.2013.03.001
[44] Renzetti, G. (2013) Central European Journal of Physics, 11, 531-544.
http://dx.doi.org/10.2478/s11534-013-0189-1
[45] Renzetti, G. (2014) New Astronomy, 29, 25-27. http://dx.doi.org/10.1016/j.newast.2013.10.008
[46] Will, C.M. (2006) Living Reviews in Relativity, 9, 3.
[47] Will, C.M. (2009) Space Science Reviews, 148, 3-13. http://dx.doi.org/10.1007/s11214-009-9541-6
[48] Will, C.M. (2014) Living Reviews in Relativity, 17, 4.
[49] Einstein, A. (1915) Sitzungsberichte der Preussischen Akademie der Wissenschaften (Berlin), Part 2, 844-847.
[50] Nyambuya, G.G. (2011) On the Resolution of the Azimuthally Symmetric Theory of Gravitation’s λ-Parameters. http://vixra.org/abs/1101.0054
[51] Nyambuya, G.G. (2014) Journal of Modern Physics, 5, 1-35.
[52] Nyambuya, G.G. (2014) Journal of Modern Physics, 5, 1733-1766.
http://dx.doi.org/10.4236/jmp.2014.516173
[53] Brownstein, J.R. and Moffat, J.W. (2006) Classical and Quantum Gravity, 23, 3427-3436.
http://dx.doi.org/10.1088/0264-9381/23/10/013
[54] Minguzzi, E. (2006) New Astronomy, 12, 142-145.
[55] Moffat, J.W. (2004) Modified Gravitational Theory and the Pioneer 10 and 11 Spacecraft Anomalous Acceleration. http://arxiv.org/abs/gr-qc/0405076
[56] Anderson, J.D., Laing, P.A., Lau, E.L., Liu, A.S., Nieto, M.M. and Turyshev, S.G. (2002) Physical Review D, 65, Article ID: 082004. http://dx.doi.org/10.1103/PhysRevD.65.082004
[57] Sanders, R.H. (2006) Monthly Notices of the Royal Astronomical Society, 370, 1519-1528.
[58] Sanders, R.H. (1984) Astronomy & Astrophysics, 136, 21-23.
[59] Anderson, J.D., Schubert, G., Trimble, V. and Feldman, M.R. (2015) EPL (Europhysics Letters), 110, 10002. http://dx.doi.org/10.1209/0295-5075/110/10002
[60] Bovaird, T. and Lineweaver, C.H. (2013) Monthly Notices of the Royal Astronomical Society, 435, 1126-1138. http://dx.doi.org/10.1093/mnras/stt1357
[61] Chang, H.-Y. (2010) Journal of Astronomy and Space Sciences, 27, 1-10.
[62] Poveda, A. and Lara, P. (2008) La Revista Mexicana de Astronomía y Astrofísica, 44, 243-246.
[63] Nyambuya, G.G. (2014) Journal of Modern Physics, 5, 1902-1909.
http://dx.doi.org/10.4236/jmp.2014.517185
[64] McDonald, K.T. (1997) American Journal of Physics, 65, 1074. http://dx.doi.org/10.1119/1.18723
[65] Mould, J. and Uddin, S.A. (2014) PASA—Publications of the Astronomical Society of Australia, 31, 1-5.
http://dx.doi.org/10.1017/pasa.2014.9
[66] Nyambuya, G.G. (2014) Journal of Modern Physics, 5, 2111-2124.
http://dx.doi.org/10.4236/jmp.2014.518207
[67] Milne, E.A. (1935) Relativity, Gravity and World Structure. Oxford University Press, Oxford.
[68] Dirac, P.A.M. (1937) Nature, 139, 323. http://dx.doi.org/10.1038/139323a0

  
comments powered by Disqus

Copyright © 2019 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.