One of the first observations suggesting the existence of an invisible dark matter came in 1933 when astronomer Fritz Zwicky noticed that galaxy clusters were more energetic than they should be, according to the mass of visible stars in them, and he proposed dark matter to explain the discrepancy. Later observations of galaxies (by Rubin & Ford, among others) showed that the galaxies’ edges were rotating as fast as the insides of the galaxies, even though acceleration is supposed to decrease with radius.
While dark matter is still the most popular explanation for this and other problems, there have also been many proposed alternative explanations. Most recently, Michael McCulloch of Plymouth University in the UK, who specializes in geomatics (the mathematics of positioning in space), has proposed that a new model that modifies a galaxy’s inertial mass may account for the faster-than-expected rotation at a galaxy’s outer edges, even though this model violates Einstein’s famous equivalence principle.
McCulloch’s paper on the model of modified inertial mass is published in Astrophysics and Space Science, and is also posted at arXiv.org.
In general, there are two ways to calculate the mass of any object. One way involves comparing the force of gravity on an object of unknown mass to the force of gravity on an object whose mass is known. This method, which the bathroom scale is based on, gives an object’s gravitational mass. The second method, which gives inertial mass, involves applying a known force to an object of unknown mass, measuring the resulting acceleration, and calculating the mass using Newton’s Second Law (m = F/a).
In 1907, Einstein proposed that gravitational mass and inertial mass are always equal, which is known as the equivalence principle and serves as a fundamental concept of general relativity. Although tests of the equivalence principle have verified that Einstein is correct to many decimal places of accuracy, some scientists have been willing to violate the equivalence principle in attempts to explain the galactic rotation problem without invoking dark energy. More here Dark matter effect might be explained by modified way to calculate inertial mass.