If f(r, v) is Busack's correction, the inverse-square
It comes from the second edition of the Principia and is essentially a defensive position, designed to force the issue that we must accept the empirical evidence that there is an inverse-square
interaction quite apart from whether we even attempt any detailed picture of how that action is transmitted: "It is enough that gravitation actually exists and acts according to the laws we have exposed.
Maybe when gravity gets very weak, as it does on cosmic scales, quantum effects come into play and cause it to deviate from the usual inverse-square
I will also describe two equivalence experiments and a test of the inverse-square
law of gravitation.
Any extra dimensions affecting gravity would alter Isaac Newton's inverse-square
law, which holds that objects attract each other with a force inversely proportional to the square of the distance between them.
Test of Newton's Inverse-Square
Law in the Greenland Ice Cap, Physical Review Letters, 1989, v.
According to Isaac Newton's well-tested inverse-square
law, gravity's strength falls off with the square of the distance.
Now, Robert Hooke, secretary to the Royal Society, contends that Newton did not himself invent the notion that an inverse-square
force law governs planetary motion.
All three of these types of experiments--G measurements, Equivalence Principle and inverse-square
law tests--however, are static measurements in the sense that the test masses were not free to move beyond a small distance compared to the size of the source mass.
In 1981 Israeli physicist Mordehai Milgrom conceived a way to avoid the need for dark matter: modify Newton's inverse-square
law of gravity over very large distances.
and Kepler's third law to arrive at the inverse-square
This result would disqualify proposed explanations such as dark matter in the solar system, the pull of Kuiper Belt objects, and alterations to Newton's inverse-square
law over long distances, key to a theory known as Modified Newtonian Dynamics.