Part VI.   Why is the Relativity of Gravity Correct?
JJ.   What Should Be the New Formulae for Two-Body Systems?

Let us now answer the question: How does the natural law of the Relativity of Gravity change the current Newtonian algebraic equation for gravitation? Since the modern Newtonian equation says nothing about mass ratios or about relative gravitational accelerations based on the relative mass-ratio of opposing masses, we must express these concepts as follows, with specific reference to the Earth/Moon system, as an example:

Where m1, a1 and F1 and are respectively the inertial mass (inertial resistance), the relative gravitational acceleration, and the relative intensity of gravitational force in all directions of the Earth; where m2, a2 and F2 are respectively the inertial mass (inertial resistance), the relative gravitational acceleration, and the relative intensity of gravitational force in all directions of the Moon; and where d2 is the square of the distance between their centers.

Based on the above example, the remaining specific formulae are as follows:

Thus, Galileo’s first approximation—the equality of gravitational accelerations of unequal masses—was not correct. It only appeared that way because the relatively similar masses of two relatively tiny objects (unequal cannonballs), as compared to the enormous mass of the Earth, fell (accelerated) toward the Earth in what appeared to be equal times. Based on the above postulates, observations, and similar causations, a priori it turns out that Galileo’s smaller cannonball actually fell (accelerated) relative to the Earth faster than his larger cannonball. We shall explore the specific reasons for this conclusion in the next sections.