In order to properly answer this question, let us begin with a few obvious empirical examples that are unquestionably observed. We observe binary star systems where two stars orbit around their combined “center of mass.” If the orbits of the two binary stars are equal or the same, this phenomenon is much like two children of equal weight (mass) who balance each other at equal distances on a seesaw (Figure 24). Both this binary star system and the children’s seesaw system have an equidistant common center of mass.
In this example, the two binary stars have equal masses, thus they attract each other’s mass (equal inertial resistance) with equal intensity and with an equal quantity of gravitational force of attraction, and each equal mass accelerates (falls) relative to the other mass in an equal manner. This is a perfect and obvious example of Newton’s three laws of motion at work, in combination with his law of gravitational attraction. The gravitational forces (both intensity and quantity received), the inertial resistances, and the gravitational accelerations of the two binary stars are equal, and their motions of action and reaction are also equal. But not every binary star system is so idyllic.
Let us now assume that one star mass m2 is situated 4.5 times further from the center of mass of the binary star system than is star mass m1 (Figure 25). Empirically, as stated by Professor Zeilik, “[T]hat means that m1 has 4.5 times the mass of m2.” How do astronomers know the relative magnitude of the above star masses? Strangely enough, “We use the [relative] accelerations of two stars orbiting one another to find their masses,” stated Zeilik. In other words, if m2 accelerates 4.5 times faster and farther in t time than m1, we know that m1 has 4.5 times the mass of m2. “In a binary system each star orbits the center of mass at a distance inversely proportional to its mass,” concluded Zeilik.
This unequal binary star scenario is also a perfect example of Newton’s law of gravitational attraction at work, in combination with his three laws of motion. The pulling force received by and acting upon each pulled binary star’s different inertial resistance is equivalent, thus the gravitational acceleration of each different pulled binary star is inversely proportional to its own mass. The action (motion of acceleration) which the smaller binary star creates on the mass of the larger star (the larger star’s smaller orbit) is equivalent to the reaction (motion of acceleration) created on its own smaller mass (the smaller star’s larger orbit), and vice-versa. This result is similar to where a 45 kg boy sits 4.5 meters from the fulcrum of a seesaw and counter balances a 202.5 kg man who is sitting 1 meter from the fulcrum (their combined center of mass) (Figure 25). In both scenarios—unequal masses of binary stars and unequal masses of people on a seesaw i.e., the mass-ratio of the opposing bodies—is 4.5:1.
Other obvious examples of this center of mass concept are also observed throughout our solar system; for example with the Sun-Earth gravitational system. The Sun-Earth system exemplifies extremely unequal masses, where the Sun’s mass is 330,000 times larger than the Earth’s mass (Figure 16). Similarly to the unequal binary star system, the center of mass between the relatively very massive Sun and the relatively tiny Earth is located 330,000 times closer to the Sun’s physical center than it is to the physical center of the Earth. In fact, both theoretically and empirically, the center of mass of the Sun-Earth gravitational system is located at a point within the sphere of the Sun itself, and only about 455 km from the Sun’s physical center.
Also like the unequal binary star system, both the Sun and the Earth orbit around this common center of mass. But because of their vastly unequal masses, the Sun’s theoretical annual radial orbit of 455 km relative to the Earth is normally not even noticed. On the other hand, the Earth is observed to orbit this center of mass from a radial distance of approximately 93 million miles (about 150,000,000 km), which radius is approximately 330,000 times greater than the theoretical 455 km radius of the Sun’s orbit relative to the Earth. Each second the Earth accelerates (falls) in its elliptical solar orbit toward the Sun about 330,000 times faster and farther than the Sun falls in its tiny theoretical orbit relative to the Earth. This, again, is a perfect example of Newton’s law of gravitational attraction at work, in combination with his three laws of motion, and for the reasons as previously stated.
If Galileo’s equal gravitational acceleration of unequal masses result and conclusion was really correct, then we should expect the extremely unequal masses of the Earth and the Sun to fall (accelerate) equally toward each other (Figure 21B). In other words, they would equally orbit around each other (Figure 26B). But this obviously does not happen. In the Sun-Earth system, each vastly different pulled mass accelerates or falls toward the other pulling mass with a motion which is extremely inversely proportional to the mass of each pulled body, just as predicted by Newton’s second and third laws, and as stated by Feynman:
“…a body reacts to a force by accelerating, or by changing its velocity every second to an extent inversely as its mass…”