PLANETARY ORBITS, FORCES, AND MASS ATTRACTION In the 15th century, Isaac Newton was aware of the thoughts
of both Copernicus and Kepler which postulated that the Sun remained stationary in space, and all motion of the planets relative to the Sun was therefore attributed entirely to the planets.
Newton postulated that planets in orbit about the Sun must be experiencing a centrifugal force outward along the radial line, away from the Sun. He recognized that there must be some inward directed radial force opposing the centrifugal force for the planets to remain in orbit. Based on mathematical procedures, the outward centrifugal force should be directly proportional to the product of the radial distance times the angular velocity squared, and the centrifugal force should also be directly proportional to a force referred to as the weight of the object if that object were stationary on the surface of the Earth. Newton therefore searched for a source of a force which would be equal in magnitude, but opposite in direction from the mathematical value equal to the centrifugal force.
The answer to his question may have been before his eyes if
he had considered another discovery of his own at that moment. This other discovery involved an actual observation then when two celestial bodies are in mutual rotation, both bodies revolve around a center that is located along an imaginary line between them. And the ratio of the radial distances of the two bodies from that common center of rotation is inversely proportional to what would be called their weight if they were located on the surface of the Earth. (R1/R2 = W2/W1). Both celestial bodies rotate around their common center of rotation with equal angular rates of motion, on opposite sides of the common center of rotation.
It must follow that the centrifugal force existing on the two bodies is exactly equal in magnitude, but opposite in direction. For that to be so, the two celestial bodies in mutual rotation must have the characteristics of a single physical object rotating on a common axle which is located such that the radial forces at the axle are balanced. The centrifugal force acting on one body is simply balanced by the centrifugal force acting on the other body. And the net force of the two body 'system' is zero.
Unfortunately, Newton did not see that obvious answer because he did not incorporate his own
observation about the reality of the center of rotation of a two body system. Rather, he carried forward Copernicus concept of a fixed Sun about which the planets rotated. As a result, he based his values for centrifugal force on the wrong radius of rotation, and failed to realize that the motion of two celestial bodies results in zero net force. He then set out to create an imaginary new force that he referred to as 'mass attraction' or 'gravity'.
The concept of 'mass' and 'mass attraction' were both purely imaginary - and mathematically incorrect. Onward to SIGNIFICANCE
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