Computational modelling of the companion star and its interaction with Sol

tohuwabohu

Jedi Master
After reading some of the transcripts I found it interesting to model the influence of the companion star on the solar system. This will include the Oort cloud traversal and interaction with the asteroids. If the N-body problem will be implemented satisfactorily, I intend to implement some of the ideas of the electric universe if applicable to the problem presented.
 
As of now I will solve the problem in 2D but extension to 3D is always possible. The problem is a N-Body problem thus the 2D solution is always computationally cheaper and gives perhaps good initial approximation to what is going on. Moreover populating 2D space is easier compared to 3D space. Because this is a large scale problem, the view transformations (in 2D mostly scaling) are to be done in double precision on the CPU to prevent jittering and other viewing artifacts. Units used are kg, m, s, N (basic SI).

The first problem are the initial conditions.

It is not known to me where the companion is right now and what is its velocity vector. The size is unknown. This is the main problem. It is only known:
-that the semi-major axis is 1.7 LY
-the period is 28.2e6 years
-the perihelion should be close to pluto orbit
-the mass is 3.4 percent of the mass of the Sun

Regarding the Oort cloud, the total mass is unknown, it is speculated that it is somewhere between 40 to 80 times mass of the Earth but in my opinion this is underestimated.
It is known that:
-the mean distance is 820.76544e12 m which is roughly 5500 AU
-the asteroids fill a vast space between distance 1000AU and 10000 AU (so they say)
-the largest body has radius 724.2 km
-the number of bodies is variable but the numbers are unknown - it might be trilions
Statistical distribution of the mass and size is unknown


So the first thing I did is using the known values for the companion star I placed the companion in distance of 2*1.608324180338736e16-4436.82e9 m from Sun (aphelion), where the 1.6e16 m is roughly the semi-major axis and the 4436.82e9 m is perihelion distance of Pluto. Thus the orbit should be flat elliptic and the period should be 28.2e6 years. For the mass of the Sun was substituted 1.989e30 kg and companion 6.7626e28 kg.
The initial velocity of the companion at aphelion was estimated to be 1.2 m/s after trial and error so the perihelion is correct, for more than that the minimal distance increases and the conditions are not met. Also another uncertainty is that this should be the closest approach after the Oort cloud is already traversed and the trajectory might be changed. As of now the planets and asteroids are not present.

As can be seen in Figure 1, the orbit is flat elliptic, the minimum distance is rougly equal to mean distance of Pluto orbit (Fig. 2). The problem is that using only the mass of the Sun the companion is not accelerated quickly enough and thus its period is 35 million years (Fig. 1 at the bottom).
To satisfy the 28.2 million years period the companion would have to be placed closer, or there have to be more force exerted on him. So I included into the mass of the Sun also all planets which was not enough and actually it was clear that the Oort cloud acts on the companion with its mass and accelerates it. But as the total mass is unknown I experimented a bit and found that adding 50 percent of the mass of the Sun did the trick and the period is correct. Explicitly this would mean that the total mass of the Oort cloud is half the mass of the Sun (approximately) or there are other matters that are escaping me. The mean distance of the Oort cloud is depicted in Fig. 1 as a black circle around the Sun and indeed when the companion is far enough, the combined mass of the asteroids can be taken as a point mass which pulls the companion toward Sun.


The results are quite interesting. The velocity of the companion realtively to the Sun at aphelion is almost zero, whereas the maximum velocity at perihelion is close to 7 km/s. Whereas it takes for the companion some 2400 years to get to the Pluto orbit from the inner border of the Oort cloud, it takes only 60 years to cross the circle with radius given by maximum Pluto distance from the Sun. As some weird things are already happening in the solar system, it is safe to assume that the companion is pretty much somewhere near Pluto orbit. This is why I would like to implement also the electric ideas, but I am not good in electricity so any inputs are appreciated.
In the meantime I will try to find approximate positions and velocities of the planets.
 

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Something to keep in mind as a possible variable, according to Wal Thornhill over at the Electric Universe site, there may not be an Oort cloud; it was created as an explanation of the comets and asteroids entering the system, but if they are instead a result of interactions between the planets, there would not be an Oort cloud required.
 
Lost Spirit said:
Something to keep in mind as a possible variable, according to Wal Thornhill over at the Electric Universe site, there may not be an Oort cloud; it was created as an explanation of the comets and asteroids entering the system, but if they are instead a result of interactions between the planets, there would not be an Oort cloud required.

The C´s talked about the Oort Cloud:

August 3, 1996 Frank, Laura, Terry, Jan

Q: (T) They know, but don't talk about it. So, we may have, in this theory, a dark star orbiting...
A: And what would happen if you did?
Q: (L) Well...
A: And it, like, comes and goes?
Q: (T) Like every 3600 years?
A: Maybe.
Q: (T) And maybe this dark star also has some planets orbiting it?
A: Ok, change of direction: Oort cloud and comet cluster and sun twin occasionally passing through the former like a bowling ball through pins.
Q: (L) How does the dark star passing through the Oort cloud relate to the comet cluster?
A: Cause and effect.
Q: (L) So, the comet cluster is caused by the dark star smashing through the Oort cloud? (T) Well, not necessarily smashing, but passing close enough for its gravity to change things... (L) But they said "like a bowling ball through pins." (T) The gravity of that star would cause the comets to be flung in all directions. (J) Is the earth like a pin? A bowling pin? (L) No, that's the Oort Cloud.
A: Explain what the Oort Cloud is, Laura.
Q: (L) Does everybody know what the Oort Cloud is? (J) I don't. [explanation of Oort cloud.] Okay, so we are looking at something...
A: Now, think of how your Biblical prophecies speak of a very terrififying period, followed by an apparent renewal of normalcy, followed by the "End."

July 4, 1998 Frank, Ark, Laura

Q: (L) What is the closest it could come to earth... (A) Solar system... (L) Yes, but which part of the solar system? We have nine planets... which one? (A) I understand that this brown star will enter the Oort cloud... (L) I think they said it just brushes against it and the gravity disturbs it...
A: Passes through Oort cloud on orbital journey. Already has done this on its way "in."
Q: (A) You mean it has already entered the Oort cloud?
A: Has passed through.
Q: (A) So, it will not approach...
A: Oort cloud is located on outer perimeter orbital plane at distance of approximately averaged distance of 510,000,000,000 miles.
Q: (L) Well, 510 billion miles gives us some time! (A) Yes, but what I want to know... this Oort cloud is around the solar system, so this brown star, once it has passed through... (L) It must already be in the solar system? (A) No, it could have passed through and may not come closer. Is it coming closer or not? Is it coming closer all the time?
A: Solar system, in concert with "mother star," is revolving around companion star, a "brown" star.
Q: (A) So, that means that the mass of the companion star is much...
A: Less.
Q: (A) Less?
A: They are moving in tandem with one another along a flat, eliptical orbital plane. Outer reaches of solar system are breached by passage of brown companion, thus explaining anomalies recently discovered regarding outer planets and their moons.
Q: (A) But I understand that the distance that the distance between the sun and this brown star is changing with time. Eliptical orbit means there is perihelion and aphelion. I want to know what will be, or what was, or what is the closest distance between this brown star and the sun? What is perihelion? Can we know this, even approximately. Is it about one light year, or less or more?
A: Less, much less. Distance of closest passage roughly corresponds to the distance of the orbit of Pluto from Sun.
Q: (A) Okay. Now, this closest pass, is this something that is going to happen?
A: Yes.
Q: (A) And it is going to happen within the next 6 to 18 years?
A: 0 to 14.


Mod's note: Changed the name of one of the attendees to what it is in Laura's public transcripts. This seems to be from a pirated version of the sessions in which those people did not care about the privacy of others. Maybe it would be best not to copy/paste from this version since it is pirated.
 
tohuwabohu said:
After reading some of the transcripts I found it interesting to model the influence of the companion star on the solar system. This will include the Oort cloud traversal and interaction with the asteroids. If the N-body problem will be implemented satisfactorily, I intend to implement some of the ideas of the electric universe if applicable to the problem presented.

Hi Tohuwabohu,

This is a very interesting project you've undertaken. I'd urge you (if you haven't already) to look into the literature on Nemesis' orbital parameters and stability. Here's a link to an ADS search with some relevant papers:

_http://adsabs.harvard.edu/cgi-bin/basic_connect?qsearch=nemesis+orbital+stability&version=1

Here's Richard Muller's website on Nemesis:

_http://muller.lbl.gov/pages/lbl-nem.htm

The take-away is that he's adamant that a) the orbit will not be perfectly stable, however b) it is stable enough over the last few billion years to explain the 26 Myr extinction periodicity.

The page on the stability of the orbit contains this interesting little anecdote:

"Bailey goes on to characterize Hut's paper as "a near retraction"!!!! Hut considered his paper to be a vindication of the original Nemesis paper. He contacted Bailey to find out how Bailey could be so wrong in his understanding, and Bailey told Hut that he never wrote those words! "Near retraction" had been inserted by the editor at Nature!"

One wonders if the Nature editor was under some pressure to do what he could to discredit the work?

Now, as to EU concepts ... here, you're undertaking something quite large, I think, as these are difficult to work with, and the theory in general is still in very early stages, still far more qualitative that quantitative. Also, you must ask, what is it you hope to learn from the model?

With those caveats, here are some very quick notes I made on the subject:

Implementing EU ideas
- will probably need to go to 3D to do this, although perhaps 2D can work with some assumptions
- basic concept is that Nemesis interrupts Galactic current feeding the Sun, causing the Sun to discharge
- need to know:
o voltage drop between photosphere and heliopause
o electric field gradient within heliosphere
o magnitude and (ideally) direction of electric current into and out of the Sun
- none of these are known directly, however, educated guesses can be made based upon proxies e.g. magnetic measurements
- IBEX data => orientation of Galactic magnetic field + plasma density in the circumheliospheric region => with assumption that Galactic current is field-aligned, this gives direction + magnitude of the current outside the heliopause
- Electric field gradient within heliosphere: essentially unconstrained, however, a reasonable assumption is that the gradient is very low throughout the heliosphere, but quite steep inside the heliopause (i.e. a double layer).
- Current interruption will presumably happen only when Nemesis enters the heliosphere => Need to locate heliopause: when/where does Nemesis cross this region?
- Magnitude of disruption will depend upon Nemesis’ charge. This is wholly unconstrained.
- Electric star model: basically, a star is fed by a polar current column, and discharges through an equatorial current sheet. Heliospheric current sheet is well-constrained, but the polar column is undiscovered (no one’s bothered looking for it!), however its properties can be estimated by energy conservation requirements, roughly P_in = P_out, where P_out = (Solar luminosity) + (energy loss through current sheet).
- Precisely how much current is required to power the Sun can be estimated via either I = V/R, where V is the voltage drop between the heliopause and the photosphere, and R is the total resistance of the Sun; or via I = sqrt (P / R). Since V is wholly unconstrained, the latter equation is probably safest; however, need to calculate R, which is non-trivial, as it will depend on a) the resistivity of photospheric plasma and b) the geometry of the electric currents. Neither is known precisely, however a) can be calculated via MHD considerations (density and temperature of the plasma), and b) can be approximated by examining the magnetic topology. Of course, the magnetic field structure of the Sun is extremely complicated.
- The value of I obtained should of course be checked for plausibility against what is actually available in the circumheliospheric environment
- Of course, with I and R, V can also be calculated
- Once plausible values of I, R, V, and P have been obtained, can begin modeling the interaction, although this will necessitate assumptions about grad(E) (i.e. the double layer)
- Since the electric charge acquired by Nemesis while in interstellar space is unknown, multiple models would need to be run, trying out various values.
- Model could perhaps make the assumption that the solar luminosity will remain unchanged (as empirically, the Sun has not dimmed). Thus the main difference would be in the discharge rate of the Sun i.e. changes in the current sheet.
 
Thank you guys for the comments and Psychegram for the links and problem analysis.

I read some articles about n-body systems and oort cloud and also nemesis, and I understand that there are some sophisticated models with lot of stars and molecular clouds etc, but I want to start simple and see where it will lead me.
I was thinking that maybe the electric interaction can be compared to fluid flow except that instead of the fluid some electrically charged particles are going to form the currents and resistance can be a resistive force in their path similar to viscosity in fluids. Then it would only be necessary to estimate charges of all space bodies and assume that each body emits particles with equivalent or proportional charge. As the particles meet, they will interact so as to form some kind of equilibrium, like for example in the heliopause the particles from sun are in equilibrium with the particles from outer universe, and similarly on the Earth magnetosphere where the Sun's particles are repulsed by the force of emitted particles from Earth. Thus if this model is valid, it can be simulated using n-body theory and moreover the nemesis can be simulated with negative charge so as to vacuum all the surrounding particles and when it comes close to sun, form some kind of funnel through which a discharge might occur.
This is only my very simplified idea how to start but as I said the model can be improved over time and things can be added to it.

As of now I implemented some more functionality into the application and added the planets. I found the positions on the jpl ephemerides site yesterday and had to approximate it into 2D positions. It is pretty close and I observed period of each planet and it agrees good with informations available on the web. The only thing is that pluto gets harassed a lot by neptune, because their orbits do intersect in 2D and in reality pluto's orbit is out of alignment with ecliptic which can't be modelled in 2D.

The planets compared to the system are extremely small so I had to scale their dimensions so they are now much more bigger than in reality (depending on scale) but this is only for visualisation purposes.

In the attachment there is the application and in the picture the controls are explained.

Additional controls: mouse wheel - zoom in/out
mouse middle button (click and hold) - move around

The Sun is initially at the origin but it will move towards the companion and also one can see how the Sun's motion is perturbed by the motion of planets, mainly Jupiter as that planet is gigantic. When the application starts it is paused so it is necessary to hit the run/pause button.
Companion is lurking just outside the future Oort cloud at 10,000 AU. It takes some 72000 years for him to come near Pluto. I determined the initial position and velocity form the previous simulations.

One note of advice - there is used semi-implicit Euler integrator with constant stepping, so be careful with the timestep, increasing it too much causes instability in the simulation and the planets will fly away.

The CPS (cycles per second) simply shows how many time per second the system is forwarded in time, the higher the number, the better (more powerful computer).

Have fun.
 

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Hi tohuwabohu,

Sorry to be a bit slow to react. You stated in Reply # 1:

-the mass is 3.4 percent of the mass of the Sun

I have a problem with that because I've found a quote out of Session July 11, 1998 which states that the mass of the companion star is 56% of the mass of the sun.

That snippet is quoted in the thread Some transcripts about dark companion and comet cluster which can be found here:
http://cassiopaea.org/forum/index.php/topic,8401.0.html

Q: (A) […] First, about this companion star: where is it now; which part of the zodiac?
A: Libra Constellation.
[…]
Q: (A) So, we have the idea. Next question concerning this companion star; we were told that its mass is less than the sun, can we have a figure on how much less?
A: 56 percent of the mass of the sun.
Q: (A) Okay, if this is really so, then when it really starts to approach the solar system, and they rotate in tandem, it means that the sun will really start to feel its gravity, and because of this, the solar system will start to move with respect to other stars, so all the constellations will shift, is this correct?
A: More like a slight "wobble" effect.
Q: (L) Will that be perceptible to us here on the Earth?
A: Only through measurements.

This session is not yet officially transcribed according to the list here http://cassiopaea.org/forum/index.php/topic,13581.0.html

Nevertheless, it can be read completely here: http://web.archive.org/web/20030219132949/http://www.cassiopaea.org/sessions/980711.html
 
Hi Palinurus, I think tohuwabohu is working from a more recent transcript:

_http://cassiopaea.org/forum/index.php/topic,15927.0.html

(Ark) Oh, it's predictable on a more or less... I mean, they are small anomalies, not big anomalies. I want to ask about my numbers. So, I put numbers. We were asking for these numbers years ago, you were evasive, and you even admitted that you are evasive for a good reason. Nevertheless, I did calculations with what I could - of course garbage in/garbage out as everyone knows. So, I put for the period 26 million years. Is it approximately true?

A: Very close 28.2 million years.

Q: (Ark) Then I had to put another number which was not told to us. I was asking about the mass of this companion star, and I was told that it was "much less than the sun". So, in my calculations, I put half a percent of the mass of the sun. Is it approximately true?

A: 3.4, closer

Q: (Ark) 3 percent?! And not half a percent?? That would mean that when it approaches, it will induce perturbation of the solar system.
 
Thanks psychegram for filling me in so promptly on tohuwabohu's used source. In that session you mentioned, Ark references the 1998 sessions while starting his more recent series of questions. That's partly how I knew where to look.

Still, I think the rather large discrepancy between the two numbers should give us pause to reconsider which one would be the more probable one to use. I myself haven't the faintest idea how to explain the difference between them or how to reconcile these two very distinct indications.
 
Palinurus said:
Thanks psychegram for filling me in so promptly on tohuwabohu's used source. In that session you mentioned, Ark references the 1998 sessions while starting his more recent series of questions. That's partly how I knew where to look.

Still, I think the rather large discrepancy between the two numbers should give us pause to reconsider which one would be the more probable one to use. I myself haven't the faintest idea how to explain the difference between them or how to reconcile these two very distinct indications.

Well, a mass on the order of 0.5 M_Sun would imply a red dwarf star, which is self-luminous and hence, should have already been detected. A mass of around 0.03 M_Sun would be consistent with a brown dwarf star, which is not self-luminous (at least at optical wavelengths, infrared is a different story) which could quite plausibly remain un-detected (although it should show up in the Widefield Infrared Survey Explorer data).

As to the discrepancy, in general, I think the accuracy of the transcripts has likely increased with time, as Laura et al. have increased their own receivership potential and, simultaneously, taken efforts to screen out pathological types from the sessions.
 
Thanks for your explanation, psychegram. :cool:

It excludes the possibility of a typo (i.e. 56% would really be 5.6%) and the more general gist of improving receivership capability and so on seems to me to be in line with actual developments on a number of interrelated fields. So thanks again and sorry for the noise I may have made.
 
Palinurus said:
Thanks for your explanation, psychegram. :cool:

It excludes the possibility of a typo (i.e. 56% would really be 5.6%) and the more general gist of improving receivership capability and so on seems to me to be in line with actual developments on a number of interrelated fields. So thanks again and sorry for the noise I may have made.

Or perhaps, 0.56%? As I think that's the value Ark was originally working with. You're right though, I wasn't thinking of typos.

I didn't hear any noise ... just honest questions, and we're here to learn :)
 
Yes Psychegram you are right I used the information from the new transmissions in hope that with time the accuracy of them gets better. Some of the missing pieces I got from various papers so that might not be so accurate.

Nonetheless I created random asteroid generation in the application so that the Oort cloud gets populated. The distribution should be random using gauss distribution. The radius of the asteroid is what is generated in interval <0, 724> km and then the mass is calculated assuming spherical shape and average density of 1200 kg/m^3.

The distance from the Sun is in range 1000 to 10,000 AU also randomly generated. So I tried 100,000 asteroids and 1 million asteroids and found that the total mass of the Oort cloud for them is 2.38e25 kg and 2.38e26 kg respectively. So not even close to the half of the mass of the Sun which I used to accelerate the companion to meet the required period. Given that the relation of the total mass to the number of asteroids is linear the theoretical number of asteroids have to be over 4 billion to reach the required mass (half of the Sun). I include pictures so one can see how the density of the cloud is for 100,000 (Fig. 1) and for 1 million asteroids (Fig. 2).

It is evident that even for 1 million the density is rather sparse and the real density should be higher. The problem is that to calculate the forces acting on the asteroids in naive way costs O(N^2) operations where N is the number of asteroids. I found that for 10,000 asteroids the force evaluation takes 12 seconds which is unacceptable.
So last day I tried to implement the tree structure which could reduce the cost to O(NlogN) and indeed the speed improved but not that much how I would like to. For 100,000 asteroids the speed was like few cycles per second (1 to 5 CPS). So this is much better but still not good enough because it would take months to do the simulation.

Now I am trying to implement an O(N) algorithm that is close to multi-grid methods. It will cost more memory but the speed should be linear with N so the improvement can be substantial. I will see how that goes. I am not giving up yet even though it is clear to me that for large simulations with billions of asteroids a supercomputer would be a necessity.
 

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Hi Tohuwabohu, this is really excellent work you're doing on this project.

Combinatorial complexity is a problem that bedevils every large N-body simulation. Why don't you try using a smaller number of particles, with a larger mass for each particle? There will be some loss of accuracy with this method, but it might still help to get a general idea of how the overall system behaves. I don't think it's necessary to compute the trajectories of billions of cometary bodies ... we can generalize from the behaviour of a few hundred thousand, I should imagine, and simply scale up.

As to the mass problem, two comments:
1) what about dust? Perhaps the mass of dust might be comparable to the cometary mass ... I don't know, to be honest. Of course even if there's 10 times the mass of comets in dust, that still leaves a huge gap since you're orders of magnitude away from 0.5 M_Sun.
2) in your second post you raise the possibility of more force being exerted than can be accounted for using purely Newtonian physics. Perhaps this is an EU effect? For instance, the relative charge of the companion and the Sun results in a stronger overall attraction between them. The Pioneer anomaly comes to mind here ... EU theorists have suggested that the small extra acceleration towards the Sun experienced by the probes might be an electrical effect. If this is the case, it would stand to reason that a body moving in the opposite sense would also experience anomalously strong acceleration.

This might be sometime to ask the C's about.
 

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