**Rotational curve of galaxy and modification of newtonian gravity**

Amala Joseph

Teacher, Department of Physics, Sree Sankara College Kalady, Ernakulam,Kerala, 683574

Dr. Rathin Adhikari

Center for Theoretical Physics, Jamia Millia Islamia, Jamia Nagar, Okhla, New Delhi,110025

## Abstract

The universe is a bundle of mysteries. It amuses us in its own ways. Dark matter remains one of such interesting mysteries. In this project, we do a study on dark matter, whether it exists or some other idea can replace this mystery. The plot of velocity versus radial distance from the center of galaxy is the rotation curve. The rotation curves of different galaxies have an interesting peculiarity. After a peak value of velocity at a particular radial distance it decreases and after that it remains almost a constant. It is different from the theoretical plot based on Newton's law of gravitation. For rotational motion having axial symmetry if a velocity is a constant then the mass enclosed should be directly proportional to the radial distance. But as per the spectroscopic and optical data collected by scientists they have found that the density of optical bodies decreases as radial distances increases. So the possible assumptions are: 1) There will be some invisible mass which contributes to the fact that mass is directly proportional to the radial distance. Scientists named this invisible matter as dark matter. Or the other possibility is that, 2) There may be some more additional terms in gravitational force that causes the velocity to remain a constant after a particular radial distance. Even though the concept of dark matter is introduced a long time ago, no proof has been obtained yet, to authenticate its presence. No real elementary particles of dark matter is invented. So in this project we are trying to find out the additional terms in gravitational potential which may replace the concept of dark matter. This additional term have a prominent role only after a particular distances,so that the gravitational force remains as per Newton's equation at normal cases. Further , we stimulate a mathematical plot of rotational curve which is provided by gravitational potential having that additional terms and verify its effect. We shall explore the role of gravitational potential which is different from Newton's.

**Keywords**: rotational curve, dark matter, gravitational potential

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