Solar System Synchronicity
This post is essentially just an interesting bit of trivia. It also presents a possible challenge.
Kepler's Third Law of Planetary Motion is the epitome of a geocentric equation, Its units are the year and AU; both are defined by the Earth's motion with our defined values.
From Wikipedia: "The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit."
Because this equation works for all the bodies in the solar system, one can conclude all bodies move around the Sun just like the Earth even though all have a different mass.
This equation is not a behavior driven explicitly by gravity, the force proportional to the two masses which are not included.
However all bodies have the solar system barycenter, or the system's instantaneous center of gravity, at the ellipse focus not the Sun.
Using Excel I entered the orbit parameters for every substantial body (no comets).
This included all the planets, 20 named asteroids (out of 700K), 14 TNO and Pluto.
The two most distant TNO (from the lists) are:
55565 AW197 T= 325.79yr, R= 47.347 AU
Sedna T= 12059.0yr, R=525.86 AU
Neither has been observed for one complete orbit.
All bodies, whether close to the Sun or distant, conform rather closely.
Excel was working correctly. Initially some results were off but after fixing each entry error, those were also fixed.
I was honestly surprised Sedna conformed at its extreme distance.
I also found Earth's quasi-satellite Kamo'oalewa conforms but at 1.002yr at 1.0011 AU this result for the NEO is expected.
The trivia: I don't know if anyone bothered to check all the bodies for conformance; they do.
The inevitable question:
Can the EU explain this synchronicity of all bodies in the solar system, regardless of the individual mass, using an electromagnetic behavior which mimics the gravity behavior of the barycenter?
The Sun carries a positive electric charge of 77 Coulombs.
"Earth has a charge of -1.6×10^-19C."
Several bodies have measured magnetic fields, including Earth and Sun.
One could expect these electric and magnetic fields having an effect on the synchronicity but by observation they do not.
I added the following as a separate comment:
Please ignore the challenge at the end.
EU does not replace gravity which remains 1 of the 3 fundamental forces. I see no issue with the barycenter.
The Sun is a positive charge but the solar wind contains electrons to provide a negative charge to all the bodies in orbit including the Earth.
I expect the result is all bodies slightly repel another which approaches. Earth, Mars, Venus had charge differentials during their encounters with the result observed by our ancestors.
However I expect the negative charged bodies could have a small repulsion counter to gravity but we never observe that.
The only time EU is obvious is an asteroid becoming a comet with its electrical discharge and coma which sometimes occur far from the Sun.
Comet C/2017/K2 has a coma as large as Jupiter but it is still beyond Saturn.
All the asteroids can maintain their orbits despite so many others moving around but their electric fields are probably negligible.
I brought up a meaningless challenge.
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