Need some help

[Catastrophe]

According to https://vixra.org/pdf/1103.0060v1.pdf

M is solar mass M, and h is angular momentum ML^2. u is orbital distance.

Cat

 

[Helio]

Here is a five year intensive study by Cornell University that shows that a partially liquid core plays a large role in (Mercury's) orbit.

I don't see that they address orbital relationships with cores. It is about spin. It's an interesting paper that shows Mercury likely formed much farther out then migrated inward. This is consistent with theories like the Grand Tack model where Jupiter migrated inward and wiped out the early planets, but then was pulled outward by Saturn, allowing new ones, fortunately for us, to form.

Core densities will alter their migration rate, in or out, due to angular momentum exchanges due to different rotation-revolution rates. But Mercury is tidally locked so I doubt there is much change in the orbit at this time.

Orbits and trajectories require energy or mass exchanges outside of itself. Spin is internal.

 

[Helio]

According to https://vixra.org/pdf/1103.0060v1.pdf

M is solar mass M, and h is angular momentum ML^2. u is orbital distance.

Cat

Wow. That's heavy duty!

Remember that to determine the angular momentum the mass of the body (ie Mercury) is required. So I would guess some mass value is needed for the equation, though a slight error may not have much effect as you note earlier.

 

[Catastrophe]

Wow. That's heavy duty!

Remember that to determine the angular momentum the mass of the body (ie Mercury) is required. So I would guess some mass value is needed for the equation, though a slight error may not have much effect as you note earlier.

Angular momentum is included as h? h= angular momentum in d²u/dφ² + u = GM/h² + (3GM/c²)u²

 

[Helio]

Yes. It’s more obvious in Newtonian physics.

Swinging a cannonball round and round has more angular momentum than swinging a Nerf ball. The only difference is mass, assuming the rope length and swing period are the same.

 

[Jzz]

There appears to be a basic dichotomy going on. The difference between the manner in which a solid and a liquid object spin, is part of human mythology, it has been used to tell apart boiled eggs from raw eggs for literally Millenia. Some particularly gifted persons can even tell apart well boiled eggs from partially boiled eggs by the act of spinning them. The point is that the difference in spins between objects with a solid core and those with a liquid core is based on observable, discernible, measurable, empirical facts. The question that then arises is this; when there is a choice between two options; one based on empirical facts and the other based on reasoned but invisible and (essentially) undetectable facts; which option is preferable? It has been reasoned here in this thread, that given the comparative mass of the sun and mercury, it is only the mass of the sun that determines the orbit of mercury. Obviously, this is not true for were it true, Mercury’s orbit would have been far less elliptical than it is, other unknown but ponderable reasons must be responsible for Mercury’s orbit. As regards its precession it appears that there is a general ignorance of the magnitudes involved. One arcsecond amounts to 1/3600 th of a degree. That is small, to say that a variation of 43 arc seconds per century is incredibly small is therefore no exaggeration. Given that this is so, isn’t it possible, if not probable, that this difference in the precession of the perihelion of Mercury is due to the movement of the partially solid core rather than to some fantastically complicated calculation involving the bending of space and time. Further, it should be considered, that this fact about Mercury’s core being partially liquid has only recently come to light through sophisticated probes and calculations and was not known at the time of Einstein’s General relativity explanation in 1915. n.b. Many thanks for link posted by Helio

 

[Helio]

Jzz, I think you are referring to Cat's link.

Your challenge to GR will require some powerful math to show how core densities can solve the old orbital puzzle, which was solved by GR to, eventually, everyone's satisfaction.

Newton had already shown how mass can be treated as a point location (center of gravity), which eliminates all density issues. This, I'm confident, is held to be true in GR.

But the math must be understandable even if it requires oversimplification as a precursor to the larger math model. Math that shows how an orbit can change due to internal activity (ie density changes) will be key, I suppose.

The only change I can imagine to an orbit due to internal behavior would come from the orbital shift in mass. Since energy is equated to mass, then if an object is internally heated, then it will lose "mass" with radiation.

 

[Catastrophe]

Jzz, I think you are referring to Cat's link.

Your challenge to GR will require some powerful math to show how core densities can solve the old orbital puzzle, which was solved by GR to, eventually, everyone's satisfaction.

Newton had already shown how mass can be treated as a point location (center of gravity), which eliminates all density issues. This, I'm confident, is held to be true in GR.

But the math must be understandable even if it requires oversimplification as a precursor to the larger math model. Math that shows how an orbit can change due to internal activity (ie density changes) will be key, I suppose.

The only change I can imagine to an orbit due to internal behavior would come from the orbital shift in mass. Since energy is equated to mass, then if an object is internally heated, then it will lose "mass" with radiation.

Helio, you are correct in your confidence! Albeit with slight adjustment (for centre "space").

Google Search

however, there are ways to define a similar concept based on the distribution of mass and the resulting spacetime curvature, which is often referred to as a "center of mass line" in more complex calculations related to extended bodies in general relativity.

Cat