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Owen217a
2007-Nov-04, 11:35 AM
According to the Newton's Mechanics, always:

As it is known, the astronomic observations on the advance of the perihelion of planet Mercury produce a value of D = 574"./century.

According to the study of L. Verierr (1835), the sum of the perturbative forces of all other planets (Venus, Earth, Mars….. Pluto) on planet Mercury produce a value of D' = 531"./century.

Thus, there is a difference of:

δ = D - D' = 574''/century - 531''/century = 43''/century.

L. Verierr, in his study, considered that the center of mass of the Sun and the center of mass of the Solar System coincide (namely they are in the same position).

But this is wrong because these two mass canters do not coincide, see:

http://astro.berkeley.edu/~eliot/Astro7A/Gravity.pdf

Also, as it is known, the Sun and the planets rotate around the center of mass of our solar system and not around the center of mass of the Sun .

Consequently, if, in our calculations, we take into account the Sun's and the planets' rotation around the center of mass of the Solar System and not around the center of mass of the Sun (as it has been happening until today) then we once again have the same difference:

δ = D - D' = 574.''/century - 531''/century = 43''/century

as it is claimed by L. Verierr in his study?


This was my question.


Also,As appears on:

http://astro.berkeley.edu/~eliot/Astro7A/Gravity.pdfpict.3

The average distance (radius) R of the Sun's rotation around the center of mass of the solar system is:

R = 2.4 Rs

Where Rs is the radius of the Sun.



Consequently, the center of mass of the Solar system is located outside of the mass of the Sun!!!


Following the above, I would like to ask from the physicists of this forum to let me know the relevant bibliography where it is mentioned whether, from the age of Le Verrier (1835) to nowadays (2007), it has been taken into consideration the rotation of the Sun around the center of mass of the solar system for the calculation of the perihelion advance δ = 43"/century of planet Mercury.




Regards,

Tony

antoniseb
2007-Nov-04, 12:38 PM
I am moving this to Q&A, this is really not an ATM idea.

antoniseb
2007-Nov-04, 12:42 PM
Also, as it is known, the Sun and the planets rotate around the center of mass of our solar system and not around the center of mass of the Sun .


Is that true? It might be close to true for Jupiter and the Kuiper belt objects, but I don't think it is true for Mercury, Venus, Earth, or Mars.

Laguna
2007-Nov-04, 01:58 PM
The the center of mass of the Solar system is sometimes located above the suns surface. It depends on the planets positions. Taken the case that Jupiter and Saturn are standing in opposite directions the center of mass would be below the suns surface.
Here (http://www.surf2000.de/user/f-heeke/figure1.html) you can see the movement of the suns center of mass in relation to the solar systems center of mass from 1968 to 2013

frankuitaalst
2007-Nov-04, 04:32 PM
The planets in general evolve around the sun , beeing the most solid body of the solar system , but are disturbed by the others . The nearer a planet is to the sun the more it evolves around the sun . Planets further away may be considered as evolving aroud the center of mass . But both assumptions are first order approximations .
Hereunder is a picture of a simulation of our solar system .
X and Y axis represent the location of the sun to the center of mass of the solar system , related to the radius of the sun , being : 0.696E+9 meters.
Simulation started at 01/02/2007 and was run for 103 years from now.
It's clear that the center of the solar system is not always "inside" our sun .
Simulation was done with the GravitySimulator on www.orbitsimulator.com

frankuitaalst
2007-Nov-04, 07:35 PM
Quote :Following the above, I would like to ask from the physicists of this forum to let me know the relevant bibliography where it is mentioned whether, from the age of Le Verrier (1835) to nowadays (2007), it has been taken into consideration the rotation of the Sun around the center of mass of the solar system for the calculation of the perihelion advance δ = 43"/century of planet Mercury.
As far as I know the positions of the planets are now calculated by solving the n-body problem . This means the forces between each body individually are calculated as : m.dr/dt²= Sum ( -Gm.mi / rij²) . This gives for our solar system 11*3 differential equations . These equations can be solved numerically . Also the Sun is treated as a body .
The result of such calcultions is then often represented as referenced to the sun ( which has also a proper motion ) .

snowflakeuniverse
2007-Nov-04, 11:43 PM
Hi Owen 217a

The predicted advancement of the perihelion of Mercury is touted as one of the justifications of General Relativity.

It is interesting to note that by properly adjusting for the center of mass of the solar system, the advancement of the perihelion of Mercury is predicted with out resorting to general relativity.

There is one other author I know who is currently writing on this topic. Carlo Santagata

http://www.journaloftheoretics.com/Links/Papers/gravi.pdf

The above link is one of many articles that are linked to the name of Carlo Santagata.

John Kulick

AKA snowflake

grant hutchison
2007-Nov-05, 12:21 AM
Why would Mercury (or any other planet) revolve around the centre of mass of the solar system?
Mercury "sees" the mass of the Sun (big, close) and the mass of the other planets (smaller, farther away). It orbits around its common centre of mass with the Sun, and is perturbed by the recurring influence of the other planets.

If planets orbited around the centre of mass of the system, there would be no such thing as a stable orbit around one component of an equal-mass binary star system.

Grant Hutchison

tony873004
2007-Nov-05, 12:51 AM
With Mercury, you have to look at the Sun-Mercury barycenter. Jupiter tugs Mercury about as hard as it tugs the Sun, so Mercury won't care about the Sun's offset due to Jupiter, as it will have virtually the same offset.

Just to exaggerate the point, consider the Milky Way / Sun / Jupiter system. Jupiter doesn't orbit the center of this system.

I've simulated the solar system, including the masses of all the planets & Pluto. And I graphed the rate of Mercury's perihelion advance in arcseconds per century. I wanted to see what influence the time step would have. As the time step grew shorter, the advancement of Mercury's perihelion approached the value computed by the Newtonian model, which is no surprise since the simulation only accounted for Newtonian physics. So this should answer the OP's question, as the Sun in this simulation orbits the SS barycenter, and the gravity from each planet is modeled. Here's the graph:



http://orbitsimulator.com/gravity/mercuryperihelion.GIF

Ken G
2007-Nov-05, 01:04 AM
It could probably be said that Neptune orbits around the center of mass of the solar system, as its orbital period is longer than the rest so would tend to average over all those internal orbits. But yes, Mercury, orbiting much faster than Jupiter, would be dragged around the center of mass by the Sun-Jupiter system, while each of Mercury's orbits is clearly around the Sun.

Fortunate
2007-Nov-05, 03:59 AM
But yes, Mercury, orbiting much faster than Jupiter, would be dragged around the center of mass by the Sun-Jupiter system, while each of Mercury's orbits is clearly around the Sun.

Would you please clarify, for me, what you are saying here, Ken? Many thanks.:)

Celestial Mechanic
2007-Nov-05, 05:30 AM
Hi Owen 217a

The predicted advancement of the perihelion of Mercury is touted as one of the justifications of General Relativity.

It is interesting to note that by properly adjusting for the center of mass of the solar system, the advancement of the perihelion of Mercury is predicted with out resorting to general relativity.
Celestial Mechanicians of the 19th and early 20th centuries tried this very thing and lots of others, all of which came up wanting.

There is one other author I know who is currently writing on this topic. Carlo Santagata.
Santagata's works are rubbish, utter rubbish. And the Journal of Theoretics is good for lining bird cages and nothing else. I've critiqued the first half of one of Santagata's papers elsewhere at BAUTForum, I'll have to look for it.

I hope you aren't ruining your "gifted high-school student's" education with Santagata's tripe.

Celestial Mechanic
2007-Nov-05, 05:52 AM
As promised here are the links to my critique of this very paper in a thread started by snowflakeuniverse almost three years ago:

Part One (http://www.bautforum.com/against-mainstream/15757-precession-planets-santagata.html#post344450)
Part Two (http://www.bautforum.com/against-mainstream/15757-precession-planets-santagata.html#post344452)
Part Three (http://www.bautforum.com/against-mainstream/15757-precession-planets-santagata.html#post344453)

Also see my comment about the Solar System barycenter here (http://www.bautforum.com/against-mainstream/15757-precession-planets-santagata.html#post340265).

grant hutchison
2007-Nov-05, 08:46 AM
If planets orbited around the centre of mass of the system, there would be no such thing as a stable orbit around one component of an equal-mass binary star system.Or, to put it in perhaps a more compelling way:
If satellites of the Sun must orbit the solar system barycentre (the position of which is largely determined by the relative masses and positions of the Sun and Jupiter), then why aren't satellites of Jupiter constrained in the same way? Why are they all happily orbiting Jupiter?
It's physical evidence, in our own solar system, that proximity to one mass makes the satellite "choose" that mass as its orbital partner, by virtue of the inverse square law.

(And I think Ken's point is that Neptune is far enough out to "see" the whole inner part of the solar system as its orbital companion, so will make its orbit relative to the barycentre of that system.)

Grant Hutchison

tony873004
2007-Nov-05, 09:17 AM
I don't mean to advocate the Nemesis theory, but the barycenter of the solar system might not be where we think it is. It could be well beyond the orbit of Pluto, depending on what undiscovered objects might be orbiting the Sun from a distance.

Ken G
2007-Nov-05, 03:54 PM
Would you please clarify, for me, what you are saying here, Ken? Many thanks.:)

Oh, I just mean that to be an "orbit", one must consider a complete cycle. Then if one asks "where is the mass that provided the force that produced that cycle", if the mass is itself in an orbit that occurs on a much shorter timescale, then that mass may not be said to be at the point it was at any moment in that orbit, but rather a kind of average, like the proverbial tiger chasing its tail around a tree until it turns into butter. One would then use the average location for the mass, the center of gravity, to solve the orbit of the outer planet. Of course one might also do a fully time dependent calculation, but then one is simply not making the orbital idealization-- for there is literally no such thing as an "orbit" in the solar system. I am elaborating on Grant's point-- the concept of "orbit" is really an idealization and can be successfully used only in two limits, where the period of the satellite is much shorter than that of what it orbits (as for Mercury), or much longer (as for Neptune). In between, one has a bit of a mess, and you get things like the Trojan asteroids.

Cougar
2007-Nov-05, 04:01 PM
That's a nice, well-researched question, Owen. Welcome to the forum.


Consequently, if, in our calculations, we take into account the Sun's and the planets' rotation around the center of mass of the Solar System and not around the center of mass of the Sun (as it has been happening until today) then we once again have the same difference:.... 43''/century....
Does this not indicate that the two methods of calculation yield equivalent answers and in fact are equivalent even though they approach the problem differently?

John Mendenhall
2007-Nov-05, 08:19 PM
Santagata's works are rubbish, utter rubbish. And the Journal of Theoretics is good for lining bird cages and nothing else. I've critiqued the first half of one of Santagata's papers elsewhere at BAUTForum, I'll have to look for it.

I hope you aren't ruining your "gifted high-school student's" education with Santagata's tripe.

Don't be so easy-going, CM. Tell it like it is.

Celestial Mechanic
2007-Nov-05, 08:42 PM
Don't be so easy-going, CM. Tell it like it is.
:clap:
If I really told like it is, I'd end up cooling my heels in the penalty box! ;)

Edited to add: "There is rubbish, and then there is rubbish. But the most rubbishy sort of rubbish are the papers of Carlo Santagata."

The above is a paraphase of a critic's comment. 50 bonus points if you can identify the original target!

antoniseb
2007-Nov-05, 09:09 PM
Hmmm. I don't think Owen217a is coming back to this thread. He started another one though...

snowflakeuniverse
2007-Nov-06, 01:56 AM
Dear Readers

Celestial Mechanics statement of that Santagata work is “rubbish” is unfair, and I hope others will follow the links he provided to review a more complete discussion of the work as discussed in this forum.

I tend to be inclined agree with Cougars insight/idea that somehow the two models (Keplerian/General Relativity) are the result of an underlying structure.

Owen posted his request as a question to see if others have derived results similar to L. Verierr (1835), work. I provided a link to Santagata’s work.

It may be easy to dismiss the work of one person, but when two people independently make the same observational /theoretical discovery, separated by over 100 years of time, it should certainly raise a certain level of curiosity and not condemnation.

It is important to note that I am not trying to rehash “old news”, I was simply responding to the request made as posted origionally in the ATM section.

John Kulick
AKA Snowflake

Celestial Mechanic
2007-Nov-06, 05:38 AM
Dear Readers:

Celestial Mechanic's statement of that Santagata work is “rubbish” is unfair, and I hope others will follow the links he provided to review a more complete discussion of the work as discussed in this forum. [Snip!]
By all means, follow the links, read the paper, draw your own conclusions.

Owen217a posted his request as a question to see if others have derived results similar to LeVerrier's (1835), work. I provided a link to Santagata’s work.
LeVerrier was a master of celestial mechanics; his work still stands to this day (apart from Vulcan, that is). His computations of the secular motions of the perihelia and nodes have been confirmed by later work by Newcomb and Hill (1895-1900), and the more recent theories known as VSOP82 and VSOP87. Santagata's paper is a muddled reworking of an obscure bit in Newton's Principia marred by numerous errors and inconsistencies in his own arguments. If you read Santagata, see if you can find the first error and the fatal flaw.

It may be easy to dismiss the work of one person, but when two people independently make the same observational /theoretical discovery, separated by over 100 years of time, it should certainly raise a certain level of curiosity and not condemnation.
For the reasons cited above, Santagata's "discovery" is not an independent discovery; in fact it is not really a discovery at all.

It is important to note that I am not trying to rehash “old news”, I was simply responding to the request made as posted originally in the ATM section.
Unfortunately you responded with misinformation. :(

John Mendenhall
2007-Nov-06, 03:34 PM
For the reasons cited above, Santagata's "discovery" is not an independent discovery; in fact it is not really a discovery at all.

(

Owens and CM, although on opposite sides of this issue, have given a fine example of a recurring problem in analysis. Let me put on the lecture hat and cite some others.

When the Stealth Fighter appropriation was before Congressional committee, one of the members of the committee commented "It's no longer stealthy when you turn on the aircraft's target aquisition radar." The irritated response was "Do you think we didn't think of that already?" Without violating security, you know after that comment that the Stealth Fighter has one dandy stealth radar to go along with it.

The message is, for many of these subtle issues, lots and lots of bright and capable people have looked at them already, and poked, and prodded, and reviewed the observations and the theory quite thoroughly.

Since Mercury is where we expect it to be, when we expect it to be there, using the relativistic mechanics, then it’s probably correct. Especially if the best people in astronomy have all gone over the material again and again, for SR about 100 years now, and agree on the results.

edit: It occurs to me that a good subtitle for this post would be "Let's NOT build another Space Shuttle."

Ken G
2007-Nov-06, 04:13 PM
If you read Santagata, see if you can find the first error and the fatal flaw.


I don't know if it's the "fatal flaw" of which you speak, but I got as far as equation (14) and discovered that this result is false because it was derived from considerations of bodies in an orbiting frame and applied to non-orbiting bodies. If he could not get through 14 freshman-physics equations without such an error, the rest of the paper is hardly worth my time. At what point something counts as "rubbish" is not so clear, but at what point it is unreliable is eminently clear.

John Mendenhall
2007-Nov-06, 06:39 PM
If he could not get through 14 freshman-physics equations without such an error, the rest of the paper is hardly worth my time.



Yes. "Stuck in Freshman Physics" is a good descripition of a lot ATM and Q&A.

Celestial Mechanic
2007-Nov-06, 08:26 PM
[Snip!] The message is, for many of these subtle issues, lots and lots of bright and capable people have looked at them already, and poked, and prodded, and reviewed the observations and the theory quite thoroughly.
And if amateurs would do their research better, they would see that this is true. Since many of the amateurs that show up at this portal do not do this research, it is necessary to point out that it has been done.

Since Mercury is where we expect it to be, when we expect it to be there, using the relativistic mechanics, then it’s probably correct. Especially if the best people in astronomy have all gone over the material again and again, for SR about 100 years now, and agree on the results. [Snip!]
And indeed I pointed to the work of LeVerrier, Newcomb, Hill and the folks who gave us VSOP82 and VSOP87. Unfortunately there is a lot of misinformation out there, and highlighting and debunking this misinformation is part of the mission of Bad Astronomy.

I am currently doing a bit of study to see if I can calculate the perihelion motion due to the other planets and present it here at a level similar to my Precession Dialogues. Precession is another topic that comes up here frequently and it is useful to have this presentation handy to link to when the need arises. And it will continue to arise.

BTW, anybody figure out the original target of "There is rubbish, and then there is rubbish. But the most rubbishy sort of rubbish are the papers of Carlo Santagata."?

HINT: The original target had the same initials, but scientific papers were not the target. :D

Owen217a
2007-Nov-07, 07:59 AM
THE SOLUTION

The difference of 43´´/century with astronomic observations as regards the advance of Mercury’s perihelion is not attributed to the curvature of space-time around the Sun, as the Theory of Relativity erroneously maintains.
The 43´´/century of the advance of Mercury’s perihelion (as demonstrated above) are due to the revolution of the Sun around the center of mass of our Solar system, a fact that until today has never been taken into account when calculating the advance of Mercury’s perihelion.

The proof, see:

http://www.tsolkas.gr/english/document1/proof-perihlion/proof-perihlion.html

Tony

Owen217a
2007-Nov-07, 08:06 AM
THE SOLUTION

The difference of 43´´/century with astronomic observations as regards the advance of Mercury’s perihelion is not attributed to the curvature of space-time around the Sun, as the Theory of Relativity erroneously maintains.
The 43´´/century of the advance of Mercury’s perihelion (as demonstrated above) are due to the revolution of the Sun around the center of mass of our Solar system, a fact that until today has never been taken into account when calculating the advance of Mercury’s perihelion.


Tony

tony873004
2007-Nov-07, 08:23 AM
... a fact that until today has never been taken into account when calculating the advance of Mercury’s perihelion.[/B]

This certainly is taken into account. I posted the results of a simulation that agree with the Newtonian model, and it takes the Sun's motion into account. It would be hard not to take that into account. It would actually take more work to ignore it. What's your source for claiming that until today this wasn't accounted for?

Nereid
2007-Nov-07, 09:10 AM
This certainly is taken into account. I posted the results of a simulation that agree with the Newtonian model, and it takes the Sun's motion into account. It would be hard not to take that into account. It would actually take more work to ignore it. What's your source for claiming that until today this wasn't accounted for?[Moderator note]

It's in the post above the one you were reading; it was held, awaiting mod review, as it contains a link and Owen217a is a new BAUT member.

[/Moderator note]

Owen217a
2007-Nov-07, 09:35 AM
What's your source for claiming that until today this wasn't accounted for?

see e.g: study by L. Verrier, http://www.math.toronto.edu/~colliand/426_03/Papers03/C_Pollock.pdf), General Relativity by A.Einstein,.......etc...etc...etc.


Tony

Halcyon Dayz
2007-Nov-07, 09:41 AM
Didn't we discuss Tsolkas' ideas before?

Ah, here (http://www.bautforum.com/against-mainstream/40893-tsolkass-problem.html).
With Tsolkas himself.

It was cut short, though.

EDIT: And here (http://www.bautforum.com/against-mainstream/43912-great-error-einstein-proof.html) too.

Owen217a
2007-Nov-07, 09:50 AM
What's your source for claiming that until today this wasn't accounted for?


see e.g: study by L. Verrier, C. Pollock, General Relativity by A.Einstein,.......etc...etc...etc.


Tony

frankuitaalst
2007-Nov-07, 07:45 PM
I haven't read the article of Tsolkas fully , but stopped reading at the first page .....when I saw Tolkas used for each planet a radius in order to calculate the center of gravity of our solar system . One can hardly imagine all planets re in a circular orbit !
If he would have used an elliptical orbit for each planet and also would have taken into account the inclination of each planet I would have read furher on ...
I rather prefer good simulation programs in order to get a result than this kind of pages.

tony873004
2007-Nov-07, 08:00 PM
Thanks for the links. In http://www.math.toronto.edu/~collian...C_Pollock.pdf it seems they are advocating relativity as the source. Just read the conclusion. Ctrl+F and look for "barycenter" or "center of mass". These terms are not used in this paper.

In the link http://www.tsolkas.gr/english/document1/proof-perihlion/proof-perihlion.html he does state that

"The 43´´/century of the advance of Mercury’s perihelion (as demonstrated above) are due to the revolution of the Sun around the center of mass of our Solar system, a fact that until today has never been taken into account when calculating the advance of Mercury’s perihelion."

But what is his source for this? It's obviously not true because he never asked me. I ran the experiment 2 years ago and I did take the Sun's motion into account, and I got results that were consistent with the Newtonian predictions, and shy of the observed value.

I believe his mistake is when he says distance R´1 separating the Sun from planet Mercury constantly changes (periodically), as a function of time. See Fig. 2
Since for simplicity he's assuming a circular orbit, this statement would only be true if Mercury were orbiting the solar system barycenter, rather than directly orbiting the Sun. The other planets tug the Sun and Mercury as a system. So his figure 2 should look more like this:
http://orbitsimulator.com/gravity/images/bc1.GIF
Also worth noting: in Pic.1 he shows the Sun drifting as much as 4 solar radii from the barycenter, when it reality, its maximum distance is only around 2 solar radii.

Nereid
2007-Nov-07, 09:33 PM
Wondering about Owen217a? Check out this post (http://www.bautforum.com/about-baut/30979-baut-banned-posters-log-11.html#post1107513).

grav
2007-Nov-07, 09:34 PM
This thread has really caught my curiosity. Quite a while back, I found a distinct mathematical relationship between the spin of the sun and precession, which gave accurate results for each of the planets, but I was unable to identify a model that accounted for the Doppler shift for all points of mass within the sun while it spins, but only indirectly across its equator, so it may have just been coincidence. I also tried to apply it to the gravity of an equatorial bulge for the sun, but the results of that were inconclusive, and the oblateness of the sun is already accounted for with the precession anyway. Now I'm wondering if there might not be some kind of tidal lock between the sun and the planets which might cause it to spin at the same rate at which it revolves, as offhanded as that sounds, but I'm still curious.

tony873004, your program does indeed account for the motion of the sun as well as that of the planets while orbitting, there can be no question about that, but I'm wondering what your parameters were for the sun in the initial conditions. I mean, if one starts the sun off stationary in respect to the planets, and then attempts to measure the precession of Mercury within a few dozen orbits or so, the pure massiveness of the sun would keep it from varying too much from its original position and speed, so the results would be about the same as if the sun were held in place. If the initial conditions of the sun are unknown, as far as the direction and speed relative to the orbits of the planets, or barycenter of the solar system or whatever, one would probably have to run the iteration at a moderate speed for a while to get the sun to eventually move as it would in unison with the orbits of the planets. Then, after enough time has passed to be satisfied that the sun is moving as it should, the program can be slowed down to measure the precession of Mercury.

Measuring the precession of Mercury this way probably wouldn't be an easy task, so I won't ask you to do that, but since you're already set up and are experienced with your program, I was wondering if you could start your program with some normal initial conditions for the orbits of the planets with a pinpoint for an originally stationary sun. Then zoom in on the original coordinates of the sun and run it for some time until it picks up some kind of steady general motion over time, perhaps using a different color for after every few years pass, or every hundred thousand years, whatever the case may be, depending upon the period of repeat for those general motions, if there is any. I think your program does most of this already.

I am just curious as to what those general motions for the sun would end up being. If it draws out some kind of regular orbit, that would be very interesting, and I would like to know the period and size of that orbit. I had assumed the motions of the planets would just perturb the sun slightly this way and that as their positions in their orbits change, and would probably just average out the same as for a stationary sun, and that may be the case, but then, that isn't the case with Mercury, but its precession due to the planets seems pretty precise after all, although that might be because Mercury has a steady orbit to begin with or something, and the sun might not, I don't know. Anyway, it would be interesting to see, to me anyway, if you could post an image of something like that here. Thanks in advance. :)

tony873004
2007-Nov-07, 10:59 PM
The planets positions and velocities are originally set relative to the Sun, so the Sun is originally at r=0,0,0 v=0,0,0, but it is free to drift which it immediately begins doing as soon as iterations are performed. The position and velocity vectors are from JPL Horizons. I query for positions and velocities relative to the Sun. But if I wanted to, I could query for positions and velocities relative to the Solar System barycenter, in which case the Sun would have non-zero initial values.

Here’s an image of the “point-sized” Sun tracing its path around the SS barycenter over the course of about 1 century. I photoshopped in the solar disk for scale. 100 thousand years would be too much, as all the gaps would fill in and the end result would be a big yellow circle about 2 solar diameters wide. I doubt you’d see any repeating patterns no matter how long you ran it. A pattern would suggest that all of the planets are in resonance with each other.

The Sun doesn’t need any time to pick up speed and start moving, since the image is centered on the barycenter, and the Sun’s initial R and V are not zero wrt the barycenter.
http://www.orbitsimulator.com/BA/ssBarycenter.GIF

In post #9 of this thread I show a graph comparing the size of the time step to the precession of Mercury. It shows that I need a small time step of only 1 or 2 minutes for the simulation to approach the accepted answer, as the numerical method introduces a reverse precession that is stronger with larger timesteps. At timesteps greater than 2048 seconds, Mercury actually precesses backwards due to the numerical errors. To produce this graph, I let the simulation run for 10 thousand years for each trial. At slow time steps it can take up to a day of real time to simulate 10 thousand years. You’re right, it would be hard to get good data from just a few Mercury orbits.

grav
2007-Nov-08, 12:30 AM
Cool. Thanks, tony. That's a pretty neat graph. :) It looks like the path of the sun is a little irregular, but not as much as I might have thought it would be. Would that look the same if it were positioned on the original coordinates for the center of the sun instead of the barycenter, that is, r=0,0,0 at all times, or does the barycenter move as the planets move? Does the program tell how many complete loops, regardless of size, the sun makes on average per given time?

tony873004
2007-Nov-08, 01:07 AM
If I locked the Sun to the middle of the screen, then you would see no motion. It would still be moving, but with each graphic update, the entire system would be recentered on the Sun's position making it appear stationary.

To an outside observer, the Sun would appear to wobble around the barycenter (this is how exosolar planets are found), but the barycenter would have a smooth path through space as the solar system orbits the galaxy.

Keep in mind, this is the barycenter of the Sun + 9 planets system (Pluto included). If there happen to be undiscovered massive planets in the Oort Cloud, the this would shift the barycenter quite a bit.

The program won't directly tell you how many loops are made. But it will be one loop for each orbit of each object orbiting the Sun. So in reality, it's a high number if you count all the small loops produced by asteroids and stuff. As it is now, you can't see the loop produced by Pluto. It's too small for this screen resolution to show it.

A fun thing to do is to run the simulation on your computer, and set some planet masses to 0 to see what effect they were having. Setting Jupiter's mass to 0 removes the largest loop you see. The Sun's path shrinks, and you'll want to zoom in a little more. This will give you a good feel for how this pattern is produced.

grav
2007-Nov-08, 01:55 AM
If I locked the Sun to the middle of the screen, then you would see no motion. It would still be moving, but with each graphic update, the entire system would be recentered on the Sun's position making it appear stationary.

To an outside observer, the Sun would appear to wobble around the barycenter (this is how exosolar planets are found), but the barycenter would have a smooth path through space as the solar system orbits the galaxy.

Keep in mind, this is the barycenter of the Sun + 9 planets system (Pluto included). If there happen to be undiscovered massive planets in the Oort Cloud, the this would shift the barycenter quite a bit. I was asking about centering the graph on the original coordinates for the sun but then allowing the sun to move, but then I guess it would still need something to move relative to, and that would just be the barycenter after all, I suppose. I was wondering if the barycenter itself might move around with the changing positions of the planets, but I was thinking more in terms of individual barycenters between every two bodies, although I suppose that is not too far off either, since that is how all of the little loops are produced, basically just loops inside loops. That last statement you made is very interesting to me, although probably natural to you and most people on here, but I never really thought it about that way, as far as a multi-body system goes, anyway, and so I guess if the barycenter is smooth around the galaxy, then that just makes it the overall center of gravity for the entire system, which doesn't change or oscillate in a closed system such as our solar system as the positions of the planets change during their orbits, and so is the one stable point at all times, right? So every time something moves around in the solar system, everything else in it also readjusts in such a way that the barycenter for all of the mass remains stable?


The program won't directly tell you how many loops are made. But it will be one loop for each orbit of each object orbiting the Sun. So in reality, it's a high number if you count all the small loops produced by asteroids and stuff. As it is now, you can't see the loop produced by Pluto. It's too small for this screen resolution to show it.

A fun thing to do is to run the simulation on your computer, and set some planet masses to 0 to see what effect they were having. Setting Jupiter's mass to 0 removes the largest loop you see. The Sun's path shrinks, and you'll want to zoom in a little more. This will give you a good feel for how this pattern is produced.That is very interesting also, and I've learned a lot from your post. Now that you've described things the way you have, I can visualize the mechanics of the entire system much more clearly now. I figure from your last statement that all of the bodies would undergo similar loops in regard to every other body in the solar system, then, and the largest loops for the planets would just become that of their orbits, in respect to the largest mass, the sun (depending upon distance too, of course). Neat. Thanks for putting things in a better perspective for me. :D

frankuitaalst
2007-Nov-08, 04:56 PM
I think there can be a long term cycle in the solars orbit around the barycenter . If we omit the small planets as Mercury, Venus , Earth , Mars and Pluto there are 4 big planets left which have all their own proper period . If there is no resonance between them and the orbital periods are Tj,Ts,Tu and Tn then we should get after Tj*Ts*Tu*Tn years the same configuration again . A quick calculation yields a period of more than 2 million years . Hard to notice for us of course .

Ken G
2007-Nov-08, 05:49 PM
But the same configuration of those planets does not imply that the Sun must be the same. I doubt there is any strictly periodic behavior in these orbits over any time scale. What you are talking about is more a good way to track how the planets affect each other, given a constant Sun, rather than a way to figure out what will happen to the Sun's orbit.

frankuitaalst
2007-Nov-08, 07:33 PM
But the same configuration of those planets does not imply that the Sun must be the same. I doubt there is any strictly periodic behavior in these orbits over any time scale. What you are talking about is more a good way to track how the planets affect each other, given a constant Sun, rather than a way to figure out what will happen to the Sun's orbit.
I think if the allignment of the planets is the same after some time also the position of the sun will be the same as a result of the conservation of momentum .
If mp is the mass of the planets and rp is the postion of the planets we can write : Sum(mp*rp)+mSun*rsun=ct .
Suppose this is the position at the beginning . After several years the Sum(mp*rp) becomes equal again , so the position of the sun must be the initial position as we have the relationship above .
The time for a new "alligment" is about 4.8 million years .

tony873004
2007-Nov-08, 08:48 PM
I think there can be a long term cycle in the solars orbit around the barycenter . If we omit the small planets as Mercury, Venus , Earth , Mars and Pluto there are 4 big planets left which have all their own proper period . If there is no resonance between them and the orbital periods are Tj,Ts,Tu and Tn then we should get after Tj*Ts*Tu*Tn years the same configuration again . A quick calculation yields a period of more than 2 million years . Hard to notice for us of course .

This should be easy enough to check. Delete Neptune and Uranus too to reduce your configuration period, and see if you get a repeating pattern after 11.862615 * 29.657 296 = 351.813084 years.

frankuitaalst
2007-Nov-08, 10:57 PM
Quote ( This should be easy enough to check. Delete Neptune and Uranus too to reduce your configuration period, and see if you get a repeating pattern after 11.862615 * 29.657 296 = 351.813084 years. )
Thanks for the hint :
simulating the Sun - Jupiter - Saturn system for more than 700 years with the GravitySimulator gives the following result :
The picture herunder shows in pink the relative motion in the x-direction of the suns center relative to the barycenter of the whole system .
The blue line gives the same motion , but for the next "cycle" .
Pink and blue lines follow the same pattern if the period is set to 355.0 years .
This means the solars motion has a cycle of 355.0 years in the Jupiter / Saturn system .
I don't have an explanation why this doesn't match the 351.81 years .

tony873004
2007-Nov-09, 05:15 AM
If there is no resonance between them and the orbital periods are Tj,Ts,Tu and Tn then we should get after Tj*Ts*Tu*Tn years the same configuration again . A quick calculation yields a period of more than 2 million years.

Thinking about it a little more, I don't think its this easy. For example, imagine you have two planets with periods of 1 and 2 years 1*2=2 years. But express it in days instead: 365*(2*365)=266450 days or 730 years. If this method worked, you should get the same results no matter what unit of time you used.

grav
2007-Nov-10, 02:00 AM
Thinking about it a little more, I don't think its this easy. For example, imagine you have two planets with periods of 1 and 2 years 1*2=2 years. But express it in days instead: 365*(2*365)=266450 days or 730 years. If this method worked, you should get the same results no matter what unit of time you used.Yes, that's true. It would have to be taken in ratios where one planet is considered T=1, say Tj=1. If we figure that each orbit is an ellipse, then they would have to complete a full integer number of orbits each to be in the same configuration again in respect to the solar system's barycenter.

So let's say Ts=3.5 Tj. So after 3.5 orbits of Jupiter, Saturn will have completed 1, but Jupiter will be only halfway around according to the .5, so Saturn will have to complete 2 full orbits to (3.5)*(2) = 7 for Jupiter before they realign, in order to give an integer number of orbits for both of them. But now let's say it is Ts=Tj * 3.454545... That would be 3.45454545... = 3 + 1/2.2 = 3 + 1 / (2 +1/5), run out until the last inverse is an integer, which means Jupiter would have to complete (3.454545...)*(2.2)*(5) = 38 orbits to 38 / 3.454545... = 11 (or (2.2)*(5) = 11) for Saturn before they can realign in the same way. The ratio for the time of Saturn's orbit to Jupiter's can be any arbitrary number whatsoever, though, and if the fractional part is irrational, and probably is, then the sequence I ran above will never end, and therefore an integer number of orbits for both can never be found, and so they will never quite line up in exactly the same way again.

frankuitaalst
2007-Nov-10, 06:21 PM
Right ...
We have to consider an integer number of revolutions . In the example of Tj=11.86 years and Ts=29.46 years , we should get both periods to an integer :
T100j=1186y and T100s=2946 years.
If we calculate then the smallest common multiplication of both we get 1746978 years . In this period of time J makes 147300 revolutions and S makes 59300 revolutions . Both are integer . That means both planets will get at the same position after all this years. So 1.746.978 years may be the period after which the planets are alligned again.
I think this time period is much to large to get an exact alligment again , as the interaction of both planets will change their position .
So I guess Tony is right saying each configuration is unique and there will be no repeating patterns.

Writing this I realised that we can devide the period with 100 , giving 1473 J revolutions and 593 S revolutions giving a period of 17.469,78 years , still long , so that mutual interactions can have an influence .
Adding a third planet to the system increases of course the period , also reducing the odds to have an alligment

Celestial Mechanic
2007-Nov-12, 05:16 AM
[Snip!] BTW, anybody figure out the original target of "There is rubbish, and then there is rubbish. But the most rubbishy sort of rubbish are the papers of Carlo Santagata."?

HINT: The original target had the same initials, but scientific papers were not the target. :D
Still no takers? OK, the answer is: the music of Camille Saint-Saens. I'm not sure who the author was, I think it was either Philip Hale or Olin Downes, noted American music critics of the late 19th and early 20th centuries. My source is The Lexicon of Musical Invective by Nicholas Slonimsky, a book that I highly recommend, but haven't seen in almost 20 years. :)

Edited to add: I like the music of Saint-Saens. I do not consider it rubbish.