Need some help

[Jzz]

When Einstein formulated his theory of General relativity and very accurately calculated the "precession of the perihelion" of the planet mercury. He explained a mystery that had puzzled scientists for centuries, "The precession of the perihelion of Mercury"
refers to the slow, gradual shift in the point of Mercury's closest approach to the Sun (perihelion) over time. This effect is thought to be primarily caused by the effects of general relativity, and was a key validation of Einstein's theory; this precession is not fully explained by Newtonian gravity alone, showing a small but measurable discrepancy that Einstein's theory perfectly predicted.

However, what was not known at the time and which must surely effect the result is the fact that Mercury’s core is partially liquid and that too not ordinary liquid but silicon which I suppose amounts to a semi-solid type of liquid. Maybe, just maybe, this circumstance of having a partially liquid or semi-solid core, is what causes a day on Mercury to be approx. 57 earth days long and a year to be 85 earth days long approximately or a ratio of 3:2 between its rotation on it axis and its orbit around the sun. This circumstance of a semi-solid liquid core must also surely affect the precession of the perihelion of Mercury as it orbits the sun.

An interesting (but unthinkable) corollary to this is the question of how did Einstein arrive at such accurate results? After all the precession of Mercury shows a difference of only 43 arcseconds every Century from the results arrived at by using purely Newtonian dynamics. For Einstein to make such delicate adjustments is truly remarkable especially when it is known that he did not know about Mercury’s semi-liquid core. Could he have been working backwards?

 

[Catastrophe]

Jzz

Please pardon a slight coorrection - hardly centuries. Nearer one and a half:

He explained a mystery that had puzzled scientists for centuries, "The precession of the perihelion of Mercury"

The first report of Mercury's perihelion anomalous precession was by Urbain Le Verrier in 1859, he found a discrepancy ~38" per century compared to newtonian gravitation. This value was updated to 43" in 1882 by Simon Newcomb.

Cat

 

[Helio]

The Sun to Mass ratio for Mercury is over 6 million to 1. His equations, like Newton's, only needs the total mass regardless of densities. Not knowing much about GR, I will assume the Sun's enormous mass would minimize any error for the mass of Mercury, if it wasn't known to great accuracy.

 

[Catastrophe]

Google Search

Google gives:

The equation that describes the precession of Mercury's orbit in Einstein's general theory of relativity is
d2u/dϕ2+u=GMj2+3GMc2u2d squared u / d phi squared plus u equals cap G cap M j squared plus 3 cap G cap M c squared u squared.
In this equation, r=1/ur equals 1 / u is the orbital distance,
ϕphi is the angle relative to perihelion,
j is the specific angular momentum, and
c is the speed of light.

[See original equation. 2 should be ^2 et cetera.]

Explanation
The equation models the motion of a body orbiting a much larger mass, like Mercury orbiting the Sun.

• The equation models the motion of a body orbiting a much larger mass, like Mercury orbiting the Sun.
• The quadratic term on the right side of the equation is responsible for the non-Newtonian precession of bound orbits.
• Einstein's theory of general relativity predicts the exact amount of precession observed in Mercury's orbit.
  
  Cat

 

[billslugg]

The composition of the mass has no effect on the orbital calculations. Mass is mass.

 

[Catastrophe]

The composition of the mass has no effect on the orbital calculations. Mass is mass.

That was the quotation referenced, in toto.

Where does it suggest that mass is represented in the equation?

Cat

 

[billslugg]

I was referring to an earlier comment referencing a liquid interior.

 

[Catastrophe]

I was referring to an earlier comment referencing a liquid interior.

Was that by Jzz in #1?

Cat :0

 

[Helio]

Where does it suggest that mass is represented in the equation?

It's hard to tell, but it looks like both masses are included in your equation, which makes sense if you want great accuracy.

 

[Helio]

Was that by Jzz in #1?

Cat :0

Yes, and I addressed it in my first post.

 

[Catastrophe]

It's hard to tell, but it looks like both masses are included in your equation, which makes sense if you want great accuracy.

Helio, it is Einstein's modified equation, not mine.

I cannot see any reference by me to mass in my posts, which are mostly posts.

Cat

 

[Classical Motion]

The length and phase of Mercury orbit. If Sol is still Mercury’s orbit has a certain length/time ratio.

If Sol is moving that ratio changes. And Mercury speeds up. Same time, more displacement length. And more momentum. More energy.

Our planets are constantly changing velocity. They cycle velocity. They accelerate up and down during the orbit.

Sol might be doing the same thing. Changing the phase of orbits. A length phase.

Same durations(periods) different lengths.

Same with earth. Our orbit length is more than just orbital circumference. It’s orbital circumference plus the lateral displacement of the sun. How much displacement length does that add in six months?

Is a parallax base line a true line?

And the same for stars in galaxies. We can’t see and measure all the motion. We don’t even measure earth’s true length displacement. All is referenced to a still Sol.

Just a motion supposition. For cubic space. And a set time.

 

[Helio]

Mass (M) is required in the equation, but I assume both masses are in the equation as is the case for Newton's equations, right?

 

[Catastrophe]

Mass (M) is required in the equation, but I assume both masses are in the equation as is the case for Newton's equations, right?

Helio, a Google ref gives:

The precession of Mercury's perihelion is directly proportional to the mass of the Sun.

Post #4 quote includes:

• The equation models the motion of a body orbiting a much larger mass, like Mercury orbiting the Sun.

Does this mean that the mass of Mercury is not needed? I don't know.
If mass of Mercury is small in comparison, can it be ignored?

Cat

 

[Helio]

Helio, a Google ref gives:



Post #4 quote includes:



Does this mean that the mass of Mercury is not needed? I don't know.
If mass of Mercury is small in comparison, can it be ignored?

I think the answer is yes, but Einstein wasn't looking for a fairly accurate result, he wanted to nail it to as many decimals as possible, IMO. So, he would use the mass of Mercury, perhaps.

It's an interesting question, and note that I've eschewed GR math at every opportunity.

 

[Catastrophe]

I think the answer is yes, but Einstein wasn't looking for a fairly accurate result, he wanted to nail it to as many decimals as possible, IMO. So, he would use the mass of Mercury, perhaps.

It's an interesting question, and note that I've eschewed GR math at every opportunity.

OK, but Mercury is 0.000000166 ... and both M terms on RHS are ^2 so 0.0277755556 etc.
squared 0.0277755556 x 10^-12 or about .03 in a trillion. How does this stack up with the other figures'accuracy?

The gravitational constant, G, is currently known with a relative uncertainty of around 47 parts per million (ppm), meaning the accepted value has a margin of error of about 0.00002 x 10^-11 m^3 kg^-1 s^-2; while considered relatively accurate, this is still considered low precision compared to other fundamental constants due to the difficulty in measuring it precisely.

There is no point insisting on better than .03/trillion if another factor is only 47/million?

Cat

 

[Helio]

His actually math when he solved it is probably in some museum somewhere. It was this solution that reportedly gave him heart palpitations for a week since it was his primary evidence that convinced him his GR theory was correct.

 

[Catastrophe]

Helio, are you really talking about Einstein???

Cat

 

[Helio]

Helio, are you really talking about Einstein???

Cat

Yes. I’ve seen it stated several times. Recall he worked on it for 10 years (1905 to 1915). He complained to his closest friend it was driving him mad. So, he was elated when his theory solved not only the Mercury mystery but explained what Newton could not — gravity.

 

[Jzz]

Jzz

Please pardon a slight coorrection - hardly centuries. Nearer one and a half:





Cat

True, That is a lesson in itself. Never indulge in hyperbole when physics is involved and even though this is a discussion about physics and not physics itself, it seems that it still matters . Interesting to learn a more in depth history on this topic.

 

[Jzz]

OK, but Mercury is 0.000000166 ... and both M terms on RHS are ^2 so 0.0277755556 etc.
squared 0.0277755556 x 10^-12 or about .03 in a trillion. How does this stack up with the other figures'accuracy?

Many comments here are to the effect that it is only the mass that matters in calculating orbits and precession. But is this really true?

In actual fact a solid sphere and a sphere filled or partially filled with liquid would rotate differently on their axis because the liquid inside the sphere will not rotate as a single unit like the solid material, leading to a larger moment of inertia for the liquid-filled sphere, meaning it will resist rotational acceleration more than the solid sphere, making it spin slower for the same applied torque. This is why I had made the reference to Mercury’s partially semi-solid core being responsible for its slower rate of rotation on its axis (i.e., a day on Mercury would take approx. 57 earth days). In order to vary by 43 arc seconds a Century, the precession would have to be something like 1.3 x 10^-8 arc seconds per second.

The above example shows that often it is best to check things out for oneself; a partially solid and partially liquid core would have to rotate and orbit differently from a purely solid mass. Also, a silica type gel surrounding the core would probably give the perfect fit necessary to explain the precession of mercury, since as has been demonstrated this is very slight. Personally, I feel that the precession of Mercury based on the partially liquid composition of its core, is a far more acceptable explanation than to think that space and time bend to bring such a phenomenon about.

Lastly anyone can try this experiment at home, spin a solid sphere and then spin a liquid filled sphere on a table and the difference would immediately be apparent. It might even be possible to build a model of Mercury and its precession using this method.

 

[Catastrophe]

The composition of the mass has no effect on the orbital calculations. Mass is mass.

billslugg, what is your estimation of post #21 then, please?

Does the composition of Mercury appear in the equation in post #4?
*d²u/dφ² + u = GM/h² + (3GM/c²)u²;

Cat

Jzz, can you see where composition appears in the equation?

Cat

 

[Catastrophe]

billslugg, what is your estimation of post #21 then, please?

Does the composition of Mercury appear in the equation in post #4?
*d²u/dφ² + u = GM/h² + (3GM/c²)u²;

Cat

Jzz, can you see where composition appears in the equation?

Cat

The following is NASA information which provides interesting comparisons between the cores (solid and liquid) of Mercury and Earth. This suggests to me that the effects suggested on Mercury precession would be much more noticeable for Earth. Is this the case? If not, are they significant for Mercury?

Genova and his team put data from MESSENGER into a sophisticated computer program that allowed them to adjust parameters and figure out what the interior composition of Mercury must be like to match the way it spins and the way the spacecraft accelerated around it. The results showed that for the best match, Mercury must have a large, solid inner core. They estimated that the solid, iron core is about 1,260 miles (about 2,000 kilometers) wide and makes up about half of Mercury’s entire core (about 2,440 miles, or nearly 4,000 kilometers, wide). In contrast, Earth’s solid core is about 1,500 miles (2,400 kilometers) across, taking up a little more than a third of this planet’s entire core.

Source:

A Closer Look at Mercury’s Spin and Gravity Reveals the Planet’s Inner Solid Core - NASA

NASA Scientists found evidence that Mercury’s inner core is indeed solid and that it is very nearly the same size as Earth’s inner core.

www.nasa.gov

Cat

 

[Jzz]

Jzz, can you see where composition appears in the equation?

Jzz, can you see where composition appears in the equation?

Cat

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 agree that earth also has what could be considered to be a practically liquid core, but other factors are present that make it a more cohesive solid than Mercury is. What is fascinating is that these differences can result in such slight changes in the precession of Mercury. No I don't see any reference to mass, or composition in the GR equations, which is why the answer might have been found by working backwards towards observations.

 

[Catastrophe]

It is assumed (though not stated in this post, as far as I am aware) that M is mass (of the Sun or of Sun plus Mercury):

d²u/dφ² + u = GM/h² + (3GM/c²)u²

This equation needs (imho) to be treated with dimensional analysis to clarify this point.

Cat


Addendum:
For any unfamiliar with dimensional analysis, it is based on the obvious fact that both sides of an equation must reduce to the same dimensions. You cannot have mass/length on the LHS and length/time on the RHS, for example.