Anomalous Concept of Barycenters
How would you react if something may not be possible according to physics but somebody may furnish a mathematical proof that may falsify it, as has happened in the case of the concept of barycenters?
As explained by NASA in its post https://spaceplace.nasa.gov/barycenter/en/ taking the example of a seesaw using the following diagram, barycenters are imaginary points about which it should be possible for a star to balance its planets in the same way as two persons swinging on a seesaw may balance each other if the values of the torques exerted by them at the fulcrum of the seesaw may be same.
Though according to this post, the barycenter of a star and its planet is supposed to behave just like the fulcrum of a seesaw, you would be surprised — such a view does not go well with the basic principles of physics.
They could have balanced each other only if they exerted torques in opposite directions in the same way as the torques the persons swinging on a seesaw exert at the fulcrums of the seesaws.
But if you looked at the star and the planet shown in the above diagram from the top — it is not, at all, difficult to make out that both the star as well as the planet, are exerting an anticlockwise torque at the barycenter while in the case of seesaws, the person sitting on the left side of the seesaw exerts anticlockwise torque at the fulcrum of the seesaw and the person sitting on the right side of the seesaw exerts a clockwise torque at the fulcrum of the seesaw.
In the case of the stars — the gravitational force exerted by them on its planets acts along the line connecting the star and the planet as shown in the following diagram.
So the distance between the barycenter and the gravitational force acting on the planet is zero.
Since this distance is zero — obviously, not only the torque created by the gravitational force at the barycenter is zero; the torque exerted by the centrifugal force (acting on the planet) at the barycenter is also zero which implies that they don’t exert any torques at their barycenter.
Besides it, a torque is exerted at the fulcrum by the persons swinging on a seesaw, only because both persons sit on a wooden or a steel plank of the seesaw, which rests on a fulcrum — which, in turn, rests on the ground.
But in the case of the star and the planet, neither the star nor the planet sits on anything that may look like the plank of a seesaw.
Nor does any such thing physically, rests on any terra firma in such a manner as has been shown in the following diagram.
But in the case of the persons swinging on a seesaw, while the person sitting on the left side of the fulcrum of the seesaw exerts anticlockwise torque at the fulcrum; the person sitting on the right side of the fulcrum exerts a torque in an opposite direction. So we can say — they may balance each other if the value of the torques exerted by them may be the same.
So any comparison between “how a star and a planet may balance each other” and “how two persons sitting on a seesaw may balance each other” is anomalous.
Such comparison could have made some sense if we, mentally, removed the plank on which the star and the planet rest (as shown in the second diagram) and pushed the star downward; the torque supposed to have been exerted by it at the barycenter may push the planet upward, but is it not true — the planet shall not rise even a wee bit upward?
The fact is — if the star and the planet are not seated on anything akin to the plank of a seesaw, neither can the star exert any torque at the barycenter nor can the planet exert any torque at the barycenter.
Therefore this simile turns out to be, altogether, a fallacious simile.
Just because we can explain why the Sun does not keep on revolving around the same point forever — to assume that the stars and their planets may be revolving around their barycenters, is quite myopic because this phenomenon may be explained even in such a way as has been shown by me, through the following diagram.
The Sun gets posited at a place where all gravitational forces exerted by it on its all planets may get balanced.
Since the distances of the planets from the Sun keep on varying because all orbits are elliptical, the values of the gravitational forces acting on various planets also keep on changing and, accordingly — the position of the Sun also keeps on changing in the same manner as though the Sun was expected to be revolving around a point which could have been about 2R☉ away from its geometrical center between 2020 and 2023, it is expected to revolve around a point which may be about 0.5R☉ away from its geometrical center during 2029–2030 as per https://astronomy.stackexchange.com/a/40914, R☉ being the radius of the Sun.
Therefore it seems to be fallacious to assume that the planets of any star may be revolving about their barycenters, as has been shown in the case of Mercury and the Sun in the following diagram.
Since according to physics, it is not possible for a star to balance its stars about their barycenters, it should not be possible to prove even mathematically to be possible.
Therefore does it not surprise how it should have been possible for Minoru Matsuda, a Japanese scientist should have been able to prove mathematically that the stars and their planets may balance each other about their barycenter in the paper “Barycenters and extreme points” [1] presented by him to the Mathematical Society of Japan in the year 1977 [1 ].
It, definitely, gives us a hint that there may be some catch in the method employed by him to prove it.
ACCORDING TO PHYSICS, THOUGH THE STARS MAY REVOLVE AROUND THE POINTS WHERE THE GRAVITATIONAL FORCES EXERTED BY THEM ON THEIR PLANETS MAY POSIT THEM AS EXPLAINED BY ME; THE PLANETS OF THE STARS ARE SUPPOSED TO REVOLVE AROUND THEIR STARS ONLY — NOT AROUND THE POINTS AROUND WHICH THE STARS REVOLVE.
_________________________
Math. Soc. Japan, Vol. 29, №4, 1977