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Orbital Planes (Astrophysics)
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Mick Harper
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I need some technical guidance. Imagine a binary star. Assume they're roughly the same size. Draw in their respective orbits. Now theoretically, these two orbits can lie in the same plane or two different planes. However, if they are two different planes, how can Newton's equal-and-opposite law apply? In other words does a binary system have to adopt a flat plain? Plane? I wish I could work out what spelling applies too.
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Ishmael


In: Toronto
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This is something Dan and I covered (or was it Komorikid? Or Brian? --have to look it up again) in the discussion of my work.

I'd rather not go into it all publicly at this time but the short answer is, "Yes." Bodies in orbit around the same primary must eventually adopt the same plane of orbit due to the interaction of (what are currently termed) "Tidal Forces" (I've a better and, I believe, more accurate terminology for the process involved).
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Mick Harper
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This business of "tidal forces" comes later. What I want to know now is whether two bodies can orbit one another and not have both orbits in the same plane. I am having difficulty envisioning it but surely if you tilt one orbit away from the other, then the common centre of gravity won't be equidistant between them in a straight line -- which as I understand Newton, it has to be.
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Ishmael


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Mick Harper wrote:
This business of "tidal forces" comes later. What I want to know now is whether two bodies can orbit one another and not have both orbits in the same plane. I am having difficulty envisioning it but surely if you tilt one orbit away from the other, then the common centre of gravity won't be equidistant between them in a straight line -- which as I understand Newton, it has to be.

Ok Mick. I obviously didn't understand your question.

If you only have two bodies, they must orbit one another in the same plane, by definition. You can have two (or more) objects orbiting in different planes only if a third body is involved.

Earth's orbital plane, with respect to the Sun, differs from its orbital plane with respect to the Moon (by 5 degrees I think), which is why we don't have Solar Eclipses every other day or so. Thus, the Earth and Moon orbit the Sun through different planes but they still orbit one another through a common plane.

But I don't want to overly complicate things. The simple fact is that two ends of a bar-bell cannot revolve around their common center of gravity on separate planes of orbit. The common plane of orbit is defined by the bar that separates the weights at each end and binds the two weights together.
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Mick Harper
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Good, that's what I thought. Though it's interesting that "cartoon" illustrations of binary stars always show them in orbits that are at anything up to ninety degrees apart so this fact has clearly not reached the popular mind. And as we all know, "cartoon images" are significant even after children have grown up to be astronomers. Did you yourself have to work this out? I had to send imaginary balls round imaginary offset orbits and still couldn't quite work out whether it was possible to have centres of gravity shifting about. But, yes, it did seem impossible.

Now onto the next bit. Is it true (since we see the Milky Way overhead as a strip) that our Solar System orbital plane is at right angles to the plane of the galaxy?
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Ishmael


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Mick Harper wrote:
Though it's interesting that "cartoon" illustrations of binary stars always show them in orbits that are at anything up to ninety degrees apart so this fact has clearly not reached the popular mind.

I don't think I have been exposed to cartoons of that sort.

Did you yourself have to work this out?

I've been confused by a lot of simple things for sure -- but not this one.

Is it true (since we see the Milky Way overhead as a strip) that our Solar System orbital plane is at right angles to the plane of the galaxy?

Yes. I believe it is. Not quite 90 degrees but it's definitely toward the perpendicular.
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Mick Harper
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Yes. I believe it is. Not quite 90 degrees but it's definitely toward the perpendicular.

So...tidal forces have had no effect in several billion years...interesting.
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Ishmael


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Mick Harper wrote:
Yes. I believe it is. Not quite 90 degrees but it's definitely toward the perpendicular.

So...tidal forces have had no effect in several billion years...interesting.


I wouldn't put it that way.

Whenever sufficient time has been available for a force to work its effect, we must assume that the force has, in fact, already worked.

Now if the current state is at variance with what must have worked within the time available, then something else must have worked subsequently to alter conditions.

There's an AE principle right here I've been trying to work out. Something like, "If anything should have happened by now, it has."

In your specific case, AE tells us that, once upon a time, Sol's revolutionary axis was aligned with its orbital plane (with respect to the galactic core). Something must have occurred relatively recently to change this natural situation.

Mind you...orbital physics on the galactic level is beyond me. From my layman's perspective, the spiral form of the Milky Way should be unsustainable. I've yet to be exposed to a proper explanation as to how the stars farthest from the galactic core can orbit the center at the exact same rate as do the stars closest in.

I still currently assume such an explanation exists -- though disappointed so many times before. I would not be surprised at this point to find there is no explanation.
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Mick Harper
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I think I'll stick to a different AE principle: where's there's no observable relationship, there may be no observable relationship. (No 1445 in your handbook.)

Since our orbital plane is neither parallel to nor (precisely) at right angles to the plane of the galaxy, I shall work on the assumption that there is no relationship. Or better still, since the whole of the galaxy does have such a relationship, I shall assume that our Solar System is so recent in formation that the relationship hasn't had time to kick in.
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DPCrisp


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Now theoretically, these two orbits can lie in the same plane or two different planes.

You mean you can draw (cartoons of) rings in one plane or two, yes. But whether these rings can then represent orbits is another matter. This is the problem we struggled with before: you can't necessarily go with intuition and common-sense where gravity and orbits are concerned.

If you only have two bodies, they must orbit one another in the same plane, by definition.

Careful with that "by definition": it's powerful medicine. Seems obvious, don't it? But then why do people, not just Mick, struggle with it? Definitions are used in training, the siblings of assumptions and paradigms. How often do we (need to) check that they are sound?

I have a paper here, How Newton's Laws lead to elliptical orbits, which says in paragraph 1 "this is a 2-dimensional problem since it's possible to prove that the orbit will be in a plane". And with one leap we are free!

What comes off the top of my head now that I try to think about (explaining) it is that it must be all in one plane since we only have two dimensions: the position and the velocity of the one body with respect to the other one.

Try looking at it this way: there is a line from body A to body B; some short time later, B has gone a short distance in whatever direction it's travelling at the moment; from this new position, the force/acceleration is back towards A. These are 3 sides of a triangle, which is a 2-dimensional shape. (By definition!) The position, velocity and acceleration are always in the same plane because ex hypothesi the force of gravity is the only thing causing the velocity to change.

I'm not sure that that helped.
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DPCrisp


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But I don't want to overly complicate things. The simple fact is that two ends of a bar-bell cannot revolve around their common center of gravity on separate planes of orbit. The common plane of orbit is defined by the bar that separates the weights at each end and binds the two weights together.

Don't over-simplify things either: don't forget that the distance between the objects does not have to remain constant.

Yes. I believe it is. Not quite 90 degrees but it's definitely toward the perpendicular.


So...tidal forces have had no effect in several billion years...interesting.

Well, the galaxy appears to be flattened, so the tidal forces appear to have done a lot of work; but Solar System in the galactic plane and Solar System aligned with the galactic plane are different propositions.

Whenever sufficient time has been available for a force to work its effect, we must assume that the force has, in fact, already worked.

Do we have any idea how long it should take to orient all stellar systems into the same plane? Since the tidal forces are all about differences in force from one side of an 'object' to another, getting the Solar System into the galactic plain probably works best if we're at right angles. Maybe the fact that we're still at right-angles is a dead give-away to our having come from somewhere off the plane: only the stellar systems that started out near the plane have had time to orient themselves towards it too.
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DPCrisp


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the spiral form of the Milky Way should be unsustainable. I've yet to be exposed to a proper explanation as to how the stars farthest from the galactic core can orbit the center at the exact same rate as do the stars closest in.

At the first approximation, they can't: the arms spiral-in precisely because the inside rotates faster than the outside. The shapes we see must be transitory on a galactic scale, but this fleeting glimpse will last... who knows how many million/billion years?

'Smooth' star clusters are reckoned as 'young', perhaps partly because they haven't had time to develop much structure... The more exotic shapes presumably come with age...

At the nth approximation, it may be that the force of gravity varies with the distribution of mass: stronger, say, where stars are more tightly packed. This alone might explain away 'Dark Matter': maybe Newton's constant, G = 6.674-blah-blah, is only the local, not the universal, gravitational constant. Maybe no-one knows what the galactic-scale physics is that we have to get our heads round!
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Ishmael


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DPCrisp wrote:
At the nth approximation, it may be that the force of gravity varies with the distribution of mass: stronger, say, where stars are more tightly packed. This alone might explain away 'Dark Matter': maybe Newton's constant, G = 6.674-blah-blah, is only the local, not the universal, gravitational constant. Maybe no-one knows what the galactic-scale physics is that we have to get our heads round!

As soon as you start saying "maybe" you are in the realm of special pleading. In AE, we are forced to make sense of the universe only with the established rules we have at hand and, by those rules, it would appear that our Galaxy must be very young or has only recently been transformed into its spoked form. Two or three rotations should be more than enough to turn our spiral into a wheel (well....we should find out how many it should take -- which should not be too hard!).

There are only two ways to sustain a spiral form. Either throw off the stars or suck them in. Either way, we must have a large fuel supply -- either internal (in the first case) or external (in the second). Perhaps the universe is filled with black, potential stars that are constantly being sucked into whirlpools, whereupon they ignite into fiery balls just before plunging down the black hole at the center. Or perhaps there is a veritable inexhaustible fuel supply at the center of the galaxy spinning rapidly and throwing off all the stars into deep space -- stars that go dark on the outer rim of the spiral.

It's one way or the other.

Now as I understand it, conventional science has it both ways and neither. There's no external fuel supply but all the stars that do exist are orbiting around a black hole at the galactic core. This scenario, however, by all the laws of physics as I understand them, is incompatible with the spiral form of our galaxy.
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Ishmael


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Ishmael wrote:
Perhaps the universe is filled with black, potential stars that are constantly being sucked into whirlpools, whereupon they ignite into firey balls just before plunging down the black hole at the center.

Imagine the universe is full of invisible energy -- energy through which light can pass without effect. But some sort of energy. Let's call it ether.

This ether is not pure energy -- for it does have mass -- but it takes a lot of it to weigh up to much of anything. Nevertheless, it fills all of space.

The ether tends to pool, which results in giant globules of mass all moving around one another, exposing the rest of the ether to the influence of multiple opposing forces. The result of these contrarian forces is whirlpool disturbances in the ether, which continually flows in from the infinite void to fill the deep recesses dug by its own weight. The fingers of these whirlpools stretch far out into the deepest reaches of the imaginable cosmos. Invisible to us.

But as the ether approaches the deepest depths of each whirlpool, it is exposed to incredible forces (forces which we actually take for granted and think of as normal space time). Under the massive strain, the ether ignites! Forming stars. Stars which convert the nearly pure energy of the ether into the nearly pure matter of iron.

The converted ether continues its swirling sink toward oblivion, plunging down the whirlpool until reaching.....what?

If the model parallels what we see in water, the matter must somehow sink into an underworld, beneath the three dimensions we know, to rise back upward again as ether -- and the cycle is renewed.
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DPCrisp


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In AE, we are forced to make sense of the universe only with the established rules we have at hand...

I'm somewhat surprised at you saying this, Ish, given that the intuition, common sense and experience us mortals have to hand is in general not applicable to planetary dynamics; while what the exalted astros have established are ill-founded rules in an unknown state of corruption, with false paradigm alarm bells going off all over the place.

Two or three rotations should be more than enough to turn our spiral into a wheel (well....we should find out how many it should take -- which should not be too hard!).

OK, for small objects in near circular orbits around a big one, velocity varies with distance from the centre according to the equation...

Wait a minute. Are they in near circular orbits? We can't watch any for long enough to see... Our nearest neighbours are going in all different directions, so they're no help... What if stars are as a rule on highly elliptical orbits around the centre of the galaxy? Are there any statistical models that show the different shapes we are just what you get if you happen to take snapshots at different times? Can it be shown that the various shapes can't be different stages in the same sequence?

Even if stars in spiral galaxies are generally going in circles, the speed-at-a-given-distance is given by the universal gravitational constant, G, and the mass of stars, etc., M, in the centre of the galaxy.

M is controversial already: that's what Dark Matter is all about. What they see stars doing does not match the maths. So which is wrong, what they think they're seeing or the equations they think should describe it?

And G is a funny one. It's natural for Newton, but I always wondered why Einstein used it. It's related to "scale invariance", which has been an issue for decades and a 2002 paper, Scale invariant gravity and the quasi-static universe, Robin Booth, Imperial College, London says things like

Einstein's General Theory of Relativity... stands alone amongst field theories in that it is not scale invariant. For example, the differential form of Maxwell's equations, which elegantly describe the electromagnetic field, do not define any intrinsic scale. Conversely, Einstein's field equations, which describe the way that matter curves spacetime, are linked to an apparently arbitrary scale determined by the Newtonian gravitational constant, G.

and

The replacement of Newton's gravitational constant in the quasi-static model by a scale-dependent re-normalisation factor is also able to account for a number of astronomical observations that would otherwise require ad-hoc explanations.

and

It can be seen that by adopting this modified form for the gravitational field equations, that the space-time curvature arising from a given body of matter will depend on its scale relative to the Universe as a whole, and not solely on its mass.

Even if we reject Einsteinian Relativity, the Newtonian gravitational field has curvature... and we might wonder whether the curvature in a region of space is affected by all the nearby masses, rather than 'gravitiness' uniformly "emanating" from a mass in the way Newton suggests. In effect, G might be a function of M, not a constant.

So, should it be too hard to work out how the shape of a galaxy evolves with each turn and how many turns it has had time to complete?
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