Review of Modified Gravity: Gravitational force without dark matter

We have derived a new modified gravitational force that is an extension of Newton’s force of gravity. It shows that the observed velocity of stars inside galaxies (flat rotation curve) does not require dark matter. The new force produces logarithmic potential energy. This force is comparable to those of Gravitomagnetic force and Weber’s gravitational force. It is derived from Einstein’s general relativity by taking into consideration the velocity of a gravitating mass. This law treats the gravitational field as a fluid surround a gravitating mass in agreement of Maxwell assumption about the electromagnetic field. The fluid surrounding massive objects provide a background that acts like dark matter and dark energy partaking in cosmic expansion. Three modified laws of gravitation have been studied and are shown to give a velocity distribution profile in agreement with observations.