How did Newton spin rotation into orbits
Published by admin May 7th, 2008 in Physics, Newton, Kepler, MoonIn Definition 5 Newton defines a new word to describe a new species of force he just invented: centripetal force. Centripetal force is a force that seeks a center. Newton gives four examples of this force: Terrestrial heaviness with which bodies tend to the center of the Earth; iron seeking loadstone; the force holding planets in their orbits and the sling motion. In the case of the sling, the centripetal force manifests itself as the tension on the string, and the stone stretches the string “the more strongly the more swiftly it revolves.”
Newton then projects the properties of the sling rotation to planetary orbits. These properties are radial acceleration, the “endeavor” to fly off and the tension on the string dubbed “force.” According to Newton all orbits are rotational and have the same properties as the sling motion.
Newton’s claim that orbits are rotational is wrong. Either Newton goofed, or more likely, he was spin doctoring rotation in order to make his occult force the cause of planetary orbits. Rotation and revolution are ruled by different rules and orbital motion is free of the tension on the radius. The tension in the string exists because radius is constrained. In orbital motion such a radial constraint does not exist and therefore, Newtonian force does not exist.
Rules for rot and rev Rotation Revolution
Rotation is ruled by radian motion, Θ = S/R or S = R Θ. According to this rule, for a given radius R, increasing Θ by turning the sling faster, will increase S and consequently, the radius R will want to increase proportionately, but since R is constrained and kept constant by the string, that additional motion belonging to R will manifest itself as tension on the string. The increase in S will be a measure of this tension.
Newton, on the other hand, interprets the sling motion in terms of the force he just defined. As the sling rotates, the stone stretches the string and endeavors to fly off and the centripetal force draws the stone back toward the hand to make the orbit happen. Newton hereby defines force as the cause of the sling orbit. Then Newton claims that the same mechanism creates all orbits because “all bodies endeavor to recede from the centers of their orbits.” For example, the Moon is a body in orbit, and just like the sling, it must be hurled by something, and in this case, that something is “the hand of God” or gravity. And like the sling, the Moon, too, endeavors to fly off along the tangent but it is held in its orbit by the centripetal force acting instantaneously.
Newton’s attempt to describe planetary orbits as rotational motion fails. The Moon’s orbit is not described by the radian rule. Increasing R does not increase the orbital arc the Moon describes in unit time. On the contrary, the Moon obeys Kepler’s rule and moves according to the rule S :: R^-1.5. Unlike the sling motion, increasing R decreases S.
In orbital motion the integrity of the radius is not respected because there is no material radius connecting the mover and the moved. In fact, there is no mover. Newton ascribes material qualities to orbital radius which is nothing more than distance created by the orbit. The orbital radius is not constrained because it does not exist. Without the sling the string will continue to exist but without the orbit there will be no radius. Therefore, in orbital motion, there is no radial or “centripetal” acceleration and there is no “endeavor” to fly off. Orbits are inertial, i.e., geometric and Keplerian, and not dynamical and Newtonian. This is proved by the fact that all of the rotational elements Newton projected to orbital motion by turning them into occult qualities must be eliminated in order to describe orbits.
These Newtonian elements, force F, mass m, and acceleration a, are always eliminated from orbital computations.1 This cannot be otherwise because orbits do not obey the radian rule, orbits obey Kepler’s rule. Newton defined his centripetal force to define orbital motion as rotational motion. But Newton’s force fails to describe orbits and consequently it is eliminated from computations of orbits. Yet, following Newton blindly, physics textbooks still enforce Newton’s absurd explanation of orbital motion.
- Keplerian part of acceleration, that is, R/T^2 = radius/period^2, remains, what is eliminated is the Newtonian label acceleration. [↩]
F and m get eliminated because neither of these can be measured; as you’ve said before, it is F/m = a that is measured. But acceleration cannot be eliminated; it can be measured and it is included, implicitly, in Kepler’s laws.
To get acceleration in Kepler’s laws, you have to deal with a law that relates time with orbits. That would be the 2nd law, the one that says the line connecting the planet and the sun sweeps out equal areas in equal times. Turning this into a statement about acceleration might be arduous but should be possible.
Either that or Kepler’s laws do not fully describe the orbit.
My personal opinion is that R/T2 is the only quantity that is measured. The way I see it Newton’s a is eliminated along with F and m. They must be eliminated because orbital motion is independent of mass and force. If we write a =F/m and call it the measured quantity we would still claim that F and m are orbital quantities. The way I interpret the orbital motion, that is not the case. Orbit knows only R/T2, not F, and not m. Maybe I didn’t understand what you mean correctly?
I think that Kepler’s second law supports the claim made in the post that orbits are not sling-type rotations created by hurling objects and keeping the radius constant as assumed by Newton. For circular orbits Kepler’s second law is an assertion of uniform motion. But still, increasing R will keep the areas proportional by the third law, as far as I understand. If we have two orbits s, r and S, R then R^2/r^2 = s^2 r/S^2 R. I would appreciate comments/corrections.
Re “R/T2 is the only quantity that is measured.”
For circular orbits, my recollection is that “R/T^2 = k a” where “k” is a constant, maybe “(2 pi)^2″.
Thanks, Carl. My mistake. I should have said “the only orbital parameters that are measured are R and T” or something to that effect.
Regarding the constant terms, I believe that they are units necessary for measurement and I perceive them as units not as orbital quantities.
I was thinking that in F/M = a something strange happens. Both F and M are eliminated, so, if F/M = a were to be a ratio a should vanish with them, but it doesn’t. There is hidden in a the ratio R/T^2, which to me, is not the Newtonian acceleration but density at R, because T is not time but period.
So, the sling-type rotational “acceleration” that Newton projected to Keplerian orbit cancels because there is no such acceleration in the orbit but R/T^2 remains because it is not the “centripetal acceleration” supposed by Newton but density at R. I’m still trying to understand this, so, I appreciate the comments.