Study of variation of gravitational constant (G) in very strong gravitational field

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Intenational Jounal of Astophysics and Space Science 13; 1(4): 56-6 Published online Octobe 3, 13 (http://www.sciencepublishinggoup.com/j/ijass) doi: 1.11648/j.ijass.1314.

1 Intenational Jounal of Astophysics and Space Science 13; 1(4): 56-6 Published online Octobe 3, 13 ( doi: /j.ijass Study of vaiation of gavitational constant (G) in vey stong gavitational field Dipo Mahto 1, Md Shams Nadeem, Umakant Pasad 3, Kumai Vineeta 4 1 Depatment of Physics, Mawai College, T.M.B.U. Bhagalpu-817, India Depatment of Physics, T.M.B.U. Bhagalpu-817, India 3 Depatment of Physics, T. N. B. College, T.M.B.U. Bhagalpu-817, India 4 Depatment of Education, S.M. College, Bhagalpu, India addess: dipomahto@hotmail.com(d. Mahto),msn.phy@gmail.com (M.S. Nadeem),umakant.pasad@gmail.com(U. Pasad) vineeta.piyadashi@gmail.com (K. Vineeta) To cite this aticle: Dipo Mahto, Md Shams Nadeem, Umakant Pasad, Kumai Vineeta. Study of Vaiation of Gavitational Constant (G) in the Vey Stong Gavitational ield. Intenational Jounal of Astophysics and Space Science. Vol. 1, No. 4, 13, pp doi: /j.ijass Abstact: In the pesent wok, we have deived the fomula fo the vaiation of the gavitational constant given by G/ 1 v / c in vey stong gavitational field of the compact bodies like supe massive black holes and neuton stas applying special elativity and Newton s law of gavitation fo two bodies whee v be the velocity of spinning compact bodies like black holes, neuton stas etc. and c be the velocity of light and calculated the vaiability of the gavitational constant (G) at diffeent speed of the spinning of the black holes, neuton stas and quasas to show the speed is also facto govening the foce of gavity addition to the mass. Keywods: Compact Body, Gavitational Constant, Black Hole and Neuton Sta 1. Intoduction Isaac Newton poposed Univesal law of Gavitation in 1687, which states that evey paticle in the univese exets a foce on evey paticle along the line joining thei centes. The magnitude of the foce is diectly popotional to the poduct of the masses of the two paticles and invesely popotional to the squae of the distance between them (Newton, 1687). In 1798, Cavendish measued G implicitly; using a tosion balance invented by the geologist Rev. John Michell and calculated implies a value fo G of m 3 kg 1 s - (Bush et al. 1). In 1915, Albet Einstein demonstated bette theoy of gavitation on the basis of geneal elativity, which has ovecome the limitations of Newton s law of univesal gavitation (Begmann, 1969). In Novembe 6, J. B. ixle et al. measued the Newtonian constant of gavity, G, using a gavity gadiomete based on atom intefeomety and epoted a value of G m 3 kg 1 s -, with a standad eo of the mean of ± and a systematic eo of ± m 3 kg 1 s - (ixle, 7).. Theoetical Discussion The gavitational constant (G) is an empiical physical constant involved in the calculation of gavitational foce between two bodies which appeas in Si Isaac Newton's law of univesal gavitation given by in the vectoial notation (Newton, 1687). Gm1m (1) whee m 1 and m ae the mass of any two bodies, be the distance between them and is the unit vecto. The negative sign indicates that the natue of gavitational foce is attactive. G denotes the gavitational constant and in Albet Einstein's theoy of geneal elativity, given by (Einstein,1915). R 1/( g R) κt () ik ik ik 4 Whee κ 8 πg/ c (3)

2 Intenational Jounal of Astophysics and Space Science 13; 1(4): The constancy fo G is expeimentally confimed in classical mechanics fo the bodies whee weak gavitational field is pesent, but theoies that violate the stong equivalence pinciple by allowing fo pefeed locations may pemit Newton s constant G vaies (Stais, 3). om equation (1), we have G / m1m (4) Obviously, the gavitational constant is defined as the foce of attaction acting between two bodies of unit mass placed at unit distance. om Newton s second law of motion, the foce is closely elated to the mass of the body as follow: ma (5) whee m is the mass of the body in classical mechanics. The vaiation of mass of a body due to change in velocity will affect the foce. This affect should be associated with the gavitational constant G in the vey stong gavitational field due to the compact bodies such as spinning black holes and neuton stas. Accoding to the classical mechanics, the mass of body emains the same duing eithe in motion o at the est, but accoding to special theoy of elativity, the mass of body vaies with velocity as follows: (Begmann,1969). m m Due to the vaiation of mass, the foce acting on the body will also vay and the vaiation of foce can be obtained by putting m instead of m and hence, we have m a Dividing eq n (7) by eq n (5) and solving, we have m m o vey low speed, v<<c o v/c<<1, (Begmann, 1969) then fom eq n (6), we have (6) (7) (8) m m (9) Putting the above value in equation (8), we have (1) o two bodies of mass m 1 and m placed at distance in the stong gavitational field & weak gavitational field, the foce of attaction is given espectively. m m (11) 1 Gm m 1 (1) Applying the eq n (11) and (1) into the eq n (1), we have m m mm G 1 1 Solving the above equation, we obtain G (13) (14) The equation (14) shows the vaiability of gavitational constant in the stong gavitational field like the gavitational field of black holes, neuton stas and quasas, depending upon the spinning velocity. E.S. Reich has shown gaphically in his pape that the spinning ate of the supe massive black holes begin fom about 5% of the speed of light to 99% of the speed of light and some supe massive black holes spin at moe than 9% of the speed of light, which suggest that they gained thei mass though majo galactic meges (Reich, 13). It is also clea fom the gaph that no supe massive black holes spin at ate below than 4% of the speed of light. On the basis of data egading the speed of supe massive black holes fom 1% to 98% of the speed of light, we calculated the vaiability of gavitational constant with the help eq n (14) in the table Data in suppot of vaiation of G Thee ae so many constants of natue in which the gavitational constant G has a vital ole in the study of gavitation. Accoding to Newton s law of gavitation, this G is constant thoughout the univese. A elative distance between the Eath and Mas was accuately measued by taking thousands of ange measuements between tacking stations of the Deep Space Netwok and Viking laundes on Mas. om a least squaes fit of the paametes of the sola system model to the data taken fom vaious ange measuements including those by Viking laundes to Mas fom July 1976 to July 198, a bound on G 1 1 is obtained: G/ G ( ± 4) 1 y (Hellings et al. 1983). om the analysis of the data fom 1969 to 199, a bound 1 1 G/ G (.1± 1.4) 1 y, on G is obtained: while fom the data fom 197 to 1994,

3 58 Dipo Mahto et al.: Study of Vaiation of Gavitational Constant (G) in vey Stong Gavitational ield 1 1 G/ G (1 ± 8) 1 y. Recent analysis using the data up Apil 4 yields G G 13 1 G/ G (4 ± 9) 1 y. The uncetainty fo / is impoving apidly since the sensitivity fo the obsevations depends on the squae of the time span (Chiba, 11). om the timing of the binay pulsa PSR , a bound on G is obtained: 11 1 G/ G (1. ±.3) 1 y (Damou et al. 1988). When the effect of the vaiation in the gavitational binding enegy induced by a change in G is taken into account, the above bound is somewhat weakened depending on the equation of state (Nodtvedt, 199). Jin Wang studied the astophysical bounds on the change of the gavitational constant with time and found that 1 1 G/ G < 1 y is the condition that has to be satisfied in ode not to cause a conflict with the obsevations (Wang, 1991). In geneal, vaiation in G ae expected to occu on the timescale of the age of the univese, such that 1 1 G/ G H.7 1 y, whee H is the Hubble constant and the stong equivalence pinciple violating time-vaiable G would be expected to alte the popeties of neuton stas and white dwafs and to affect binay obits(stais, 3). 4. Table Sl. No % speed of supe massive black holes, Neuton stas, Quasas of the speed of light Vaiability of Newton s constant in the stong gavitational field. Speed of Supe massive black holes, Neuton stas, Quasas (m/s) Newton s constant G (m 3 Kg -1 s - ). G 1 3.9x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x x1-11 (m 3 Kg -1 s - ).

4 Intenational Jounal of Astophysics and Space Science 13; 1(4): Gaph igue 1: The gaph plotted between vaiability of gavitational field G ' and % speed of supe massive black holes, neuton stas and quasas of speed of light. 6. Results and Discussion In the pesent wok, we have deived the fomula fo the vaiation of the gavitational constant given by G/ 1 / compact bodies like black holes and neuton stas applying special elativity and Newton s law of gavitation fo two bodies whee v be the velocity of spinning compact bodies like black holes, neuton stas etc. and c be the velocity of light. In the pesent wok, we have also calculated the vaiability of the gavitational constant (G) at diffeent speed of the spinning of the black holes, neuton stas and quasas. It has been obseved fom the table and gaph that the vaiability of the gavitational constant (G) inceases gadually with the incease of the speed of the black holes, neuton stas and quasas up to 8% of the speed of light and afte 85%, the vaiability of the gavitational constant (G) inceases apidly up to 1%. This shows that fo the supe massive black holes, neuton stas and quasas spinning almost equal to the speed of light gain maximum gavity. v c in vey stong gavitational field of the This means that the speed is also facto govening the foce of gavity addition to the mass, because new theoy of gavitation is dependent on the speed of bodies which states that the facto joining the whole Sola system and galaxies all in one piece would have to have highe speed than the velocity of light. At pesent, no highe speed is known than the velocity of light, thus the phenomenon ascibed to gavitation must have othe fom than that know cuently as the phenomenon of gavitational pull (Boowski, 1). 7. Conclusion In couse of the pesent eseach wok, we can daw the following conclusions such as: (i) The supe massive black holes, neuton stas and quasas spinning with almost equal to the speed of light gain maximum gavity than that of the gavity of supe massive black holes, neuton stas and quasas spinning with almost up to 8% of the speed of light. (ii) The speed is also facto govening the foce of gavity in addition to the mass (iii) The fomula G/ holds good fo the gavity of supe massive black holes, neuton stas and quasas spinning with the speed compaable to the speed of light.

5 6 Dipo Mahto et al.: Study of Vaiation of Gavitational Constant (G) in vey Stong Gavitational ield Acknowledgement The authos ae gateful to the efeee fo pointing out the eos in the oiginal manuscipt and making constuctive suggestions. The authos ae also gateful to D. (Pof.) Gopi Kant Jha, the fome H. O. D, Univesity Depatment of Physics, L. N. M. U. Dabhanga (India), D. Neeaj Pant, Associate Pofesso, Depatment of Mathematics, N. D. A. Khadakwasala, Pune and Pof. M.S.H. John, Pincipal & V. K. Misha, H.O.D. Physics, Mawai College Bhagalpu fo thei inspiation and motivation. Refeences [1] I. Newton,: The Pincipia (The mathematical pinciples of Natual knowledge), [] A. Einstein, Peuss, Akad. Wiss, Belin, Sitzbe, pp,778, 831, and 844 (1915). [3] Bush, Stephen G.; Holton, Geald James (1), Physics, the human adventue: fom Copenicus to Einstein and beyond, New Bunswick, N.J: Rutges Univesity Pess, p. 137, ISBN [5].J. B. ixle; G. T. oste; J. M. McGuik; M. A. Kasevich (7-1-5), "Atom Intefeomete Measuement of the Newtonian Constant of Gavity" Science 315 (588): 74 77, Doi:1.116/science PMID , 7. [6] Jin Wang: Astophysical constaints on the gavitational constant, Astophysics and Space Science, 184, 31-36(1991). [7] Ingid H. Stais: Testing Geneal Relativity with Pulsa Timing. Living Reviews in Relativity, 3. [8] Tomasz Boowski: The new theoy of gavitation epesenting the movement of planets. Intenational Lettes of Chemisty, Physics and Astonomy 1 (1) 1-5. [9] Eugenie Samuel Reich: Spin ate of black holes pinned down. Natue, Vol.5,p-135, Macmillan Publishing limited, Aug 13. [1] Takeshi Chiba: The Constancy of the Constants of Natue: Updates. Pogess of Theoetical Physics, Vol.16, No. 6, Dec. 11. [11] K. Nodtvedt: Physical Review Lette, 65, (199),953. [1] T. Damou, G.W. Gibbons and J. H. Taylo, Physical Review Lette,61, (1988), [4] P.G. Begmann,: Intoduction to the Theoy of Relativity. Pentice Hall of India, New Delhi (1969).

Determining solar characteristics using planetary data

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