American Journal of Astronomy and Astrophysics 2014; 2(4): 42-46 Published online September 20, 2014 (http://www.sciencepublishinggroup.com/j/ajaa) doi: 10.11648/j.ajaa.20140204.12 Variation of gravitational constant w. r. t. the spinning velocity of super dense stars in very strong gravitational field Md Shams Nadeem 1 , Dipo Mahto 2 , Kumari Vineeta 3 , Krishna Murari Singh 2 1 Department of Physics, T. M. B. U. Bhagalpur-812007, India 2 Department of Physics, Marwari College, T.M.B.U. Bhagalpur-812007, India 3 Department of Education, S. M. College, T.M.B.U. Bhagalpur, India Email address: msn.phy@gmail.com (M. S. Nadeem), dipomahto@hotmail.com (D. Mahto), vineeta.priyadarshi@gmail.com (K. Vineeta), kmsinghphy@gmail.com (K. M. Singh) To cite this article: Md Shams Nadeem, Dipo Mahto, Kumari Vineeta, Krishna Murari Singh. Variation of Gravitational Constant w. r. t. the Spinning Velocity of Super Dense Stars in Very Strong Gravitational Field. American Journal of Astronomy and Astrophysics. Vol. 2, No. 4, 2014, pp. 42-46. doi: 10.11648/j.ajaa.20140204.12 Abstract: Mahto et al. have derived the formula for the variation of the gravitational constant given by G  =    /  in very strong gravitational field of the compact bodies like super massive black holes and neutron stars (2013). In this paper, we have extended this work to show that the variation of gravitational constant in the strong gravitational field with respect to the spinning velocity of super dense stars is directly proportional to its spinning velocity. Keywords: Gravitational Constant, Black Hole and Neutron Star 1. Introduction In 1687, Isaac Newton proposed the universal law of gravitation which states that every particle in the universe exerts a force on every particle along the line joining their centres. The magnitude of the force is directly proportional to the product of the masses of the two particles and inversely proportional to the square of the distance between them (Newton 1687 & Mahto et al.2013). In 1915, Albert Einstein demonstrated better theory of gravitation on the basis of general relativity, which has overcome the limitations of Newton’s law of universal gravitation (Bergman1969 & Mahto et al.2013). In, 1951, Papapetrou first derived the equations of motion for a spinning test particle in a gravitational field. After this work, several people have considered the problem of the motion of spinning bodies in the gravitational field of a black hole or some other compact object such as a neutron star by means of post-Newtonian approximations (Ma & Wang, 2014). In November 2006, J. B. Fixler et al. measured the Newtonian constant of gravity, G, using a gravity gradiometer based on atom interferometry and reported a value of G = 6.693 × 10 –11 m 3 kg −1 s -2 , with a standard error of the mean of ±0.027 × 10 –11 and a systematic error of ±0.021 × 10 –11 m 3 kg −1 s -2 (Fixler, 2007 & Mahto et al.2013). Mahto et al. have proposed a relation for the variation of the gravitational constant given by 2 2 ' / 1 / G G v c = - in very strong gravitational field of the compact bodies applying special relativity and Newton’s law of gravitation for two bodies where v be the velocity of spinning compact bodies like black holes, neutron stars etc.(Mahto et al. 2013). In the present research paper, we have extended the above work to show that the variation of gravitational constant in the strong gravitational field with respect to the spinning velocity of super dense stars is directly proportional to its spinning velocity. 2. Theoretical Discussion The constant of proportionality (G) called gravitational constant/universal constant is one of the fundamental constants of nature. As the precision of measurements increased the disparity between the values of G, gathered by different groups, surprisingly increased. This unique situation was reflected by the 1998 CODATA decision to increase the relative G uncertainty from 0.013% to 0.15 % (Mohr & Taylor, 2001). The repetitive measurements of the