Dark Energy Attenuation Based Modification of Newton’s Law of Gravity: A Theoretical Support to Milgrom’s MOND Concept

The Concept of MOND (Modifying Newtonian Dynamics) was proposed by Mordehai Milgrom as a possible way to reconcile the difference between the experimentally observed high values and the calculated values using Newton’s Law of Gravity for the dynamical parameters of orbiting stars in a galaxy, without having to introduce the concept of dark matter. Milgrom’s MOND concept challenges the need for dark matter to account for the above difference. The experimentally observed velocity rotation curves of stars in a galaxy show that for small values of r (distance of the star from the centre of the galaxy), the velocity observed (V_O) for the orbiting star fairly agrees with values (V_N) calculated using Newton’s law of gravity. But as r increases, the difference between V_O and V_N gradually increases. For very large values of r, V_O increases with a constant slope. Finally, V_O becomes fairly constant with distance. The above features of V_O cannot be explained by Newton’s law of gravity. Milgrom successfully showed that the above features can be explained by modifying Newton’s law of gravity as $F=\frac{GMm}{r^2\mu }$ where μ is a function just added by Milgrom without a supporting theory behind and is assumed to have certain special properties to suit the purpose. In this paper, it is shown that when the attenuation of dark energy by the space medium is taken into account, Newton’s law of gravity gets modified with a correction term in it. This correction term surprisingly gives rise to the required properties of the function μ added by Milgrom to the existing conventional law of gravity. The work presented here therefore can be considered as a theoretical support for the successful phenomenological scheme proposed by Milgrom.