First post ever. Be Kind. Solar orbit questions

[Johio]

Hello, total layman here. I have some questions & ideas, but no one to discuss them with, so here I am.

1. In the continuum between a completely circular orbit, and a maximally elliptical orbit, what characteristics of the orbital body and the gravitational source are the prime determinants of the degree of ellipticality?

2. As the orbit becomes more and more elliptical, wouldn't the speed of the body increasingly vary? (ie. Speed up as it "falls" towards the sun and slow down once it slingshots past and is recaptured by gravity - much in the pattern of a comet falling from the Oort cloud...)

3.1 Is it true that everything in the universe is in (to some degree) circular/spiralic motion around something else? In other words, as with fractals; on a micro scale, electrons orbit the nuclei in all known matter, and on a macro scale, planets orbit around a sun, and so on up the scale?

If so, is our solar system in rotation around something? Is it the Sirius cluster?

3.2 If that is true, do we know what the length (in time) of the cycle is?

3.3. Also, do we know the degree of ellipticality of the orbit? (Is it more like a cometary orbit, or more like a planetary orbit?

3.4 Assuming for a moment that the orbit surpassed some threshold of ellipticality that would then cause some level of speed up and slowdown, would we have solar-system solstices and equinoxes? In other words, would there be critical points where the motion changed from "coming" to "going"? Or even more extremely, a "crack of the whip"?

4. If there is some degree of ellipticality in the Solar System's grand orbit, at the point closest to the "gravity well", could matter, or even space/time compress to some degree?

Please coach me up if I am using inappropriate or inaccurate terminology. Thanks !

 

[dacruick]

Hello, total layman here. I have some questions & ideas, but no one to discuss them with, so here I am.

Hi there, I don't think I can answer all of your questions, but some of them for sure.

1. In the continuum between a completely circular orbit, and a maximally elliptical orbit, what characteristics of the orbital body and the gravitational source are the prime determinants of the degree of ellipticality?

I would say that the answer to this is the mass of each of the bodies, as well as the speed and angle at which the orbiting mass entered the gravitational field of the source of mass. I'm honestly not completely sure about this one. I would imagine that there is always an equilibrium orbit which maybe most of the planets in our solar system have reached already. I'd like confirmation on this myself

Also, a maximally elliptical orbit is something called hyperbolic, in which it isn't much of an orbit. It actually just means that the 'orbiting mass' whips around the gravitational source and goes way out into space again.

This could be a helpful read. http://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion

2. As the orbit becomes more and more elliptical, wouldn't the speed of the body increasingly vary? (ie. Speed up as it "falls" towards the sun and slow down once it slingshots past and is recaptured by gravity - much in the pattern of a comet falling from the Oort cloud...)

Yes correct. The as the 'eccentricity' of the orbit increases (an eccentricity of 0 is a circular orbit), the difference between maximum speed and minimum speed also increases. (perihelion speed and aphelion speed respectively)

3.1 Is it true that everything in the universe is in (to some degree) circular/spiralic motion around something else? In other words, as with fractals; on a micro scale, electrons orbit the nuclei in all known matter, and on a macro scale, planets orbit around a sun, and so on up the scale?

This question is a bit over my head, but I guess I always assumed that this is the case.

I hope I helped, and I hope other fill in my void.

Cheers.

 

[D H]

1. In the continuum between a completely circular orbit, and a maximally elliptical orbit, what characteristics of the orbital body and the gravitational source are the prime determinants of the degree of ellipticality?

Energy, angular momentum, and mass. Closed orbits (circles and ellipses) result if the total mechanical energy is negative. A non-negative energy means the objects aren't in what most people think of as orbits. They are instead on an escape trajectory.

Given a fixed set of masses and a fixed energy, a circular orbit will arise only for one exact value for angular momentum. This means circular orbits never really happen in nature. There is always going to be some deviation between the ideal value and the real value. Everything else (assuming a negative energy) corresponds to an elliptical orbit. Eccentricity becomes one in the extreme of zero angular momentum. This is a radial orbit where the objects are moving in a straight line right toward one another.

Another reason circular orbits never occur in our solar system is that these circular orbits, elliptical orbits, parabolic orbits, and hyperbolic orbits only occur with two bodies that are gravitationally isolated from the rest of the universe. Our solar system is not an isolated 2-body system; those Keplerian orbits are an approximation of reality.

2. As the orbit becomes more and more elliptical, wouldn't the speed of the body increasingly vary? (ie. Speed up as it "falls" towards the sun and slow down once it slingshots past and is recaptured by gravity - much in the pattern of a comet falling from the Oort cloud...)

Yes. One way to express this is via the vis viva equation,
v^2 = G(M+m)\left(\frac 2 r - \frac 1 a\right)
Google "vis viva equation" for more.

3.1 Is it true that everything in the universe is in (to some degree) circular/spiralic motion around something else? In other words, as with fractals; on a micro scale, electrons orbit the nuclei in all known matter, and on a macro scale, planets orbit around a sun, and so on up the scale?

No.
First off, the only thing electron orbitals have in common with planetary orbits is that both have the letters o-r-b-i-t in them. The model of electrons circling the nucleus as planets orbit the Sun was one of the earliest attempts to model the atom. It is demonstrably false.

Going down from stars to planets to moons, it is very hard for moons to have moons, and essentially impossible further down the scale. Moons are the end of the line for all practical purposes. Going up from stars, stars orbit about the galaxy in which the stars reside, groups of galaxies form clusters, groups of clusters form superclusters, but that's about it.

The concept of Keplerian orbits is not valid for galaxies and larger structures. There's no large central mass about which smaller masses orbit. Another problem, particular for those very large structures, is the expansion of space.

If so, is our solar system in rotation around something? Is it the Sirius cluster?

The solar system is a part of the Milky Way galaxy, which in turn is a member of the Local Group, which in turn is a part of the Virgo Supercluster.

3.2 If that is true, do we know what the length (in time) of the cycle is?

Yes, for the Sun about Milky Way. It's about 250 million years, but its a bit tough calling this an "orbit" in the sense you are thinking of. Larger structures: No. They just aren't orbits any more in the sense that you are thinking. Note: The Milky Way appears to be on a collision course with the Andromeda galaxy.

3.3. Also, do we know the degree of ellipticality of the orbit? (Is it more like a cometary orbit, or more like a planetary orbit?

None of the above. It's not even quite right to talk about eccentricity any more.

 

[Johio]

DH, and DACrucik, thanks for your prompt replies.
I appreciate the schooling.
I remember reading somewhere that our solar system has a cycle (orbit), within this solar arm , of 26,000 years. (Maybe this relates to the Procession of the Equinoxes, but I have not read up on that yet either) Is this possible? It may have been in a non scientific book...
I guess what I am looking to try and apply is a fractal way of thinking, patterns within patterns. While I can see the cycles that repeat within our solar system, I am wondering if there are far more massive cycles in which our solar system is merely a single body. The reason I asked about The Sirius cluster is that I have read that it contains over 250 suns in the same aprox. space as our solar system, which would make it a huge gravity well. Am I the victim of poor information?
If there are areas of space with that many concentrated suns, could the intense gravity compress space/time, or matter?

 

[D H]

I remember reading somewhere that our solar system has a cycle (orbit), within this solar arm , of 26,000 years. (Maybe this relates to the Procession of the Equinoxes, but I have not read up on that yet either) Is this possible? It may have been in a non scientific book...

You might have misread, or you might have read a bad book.

The precession of the equinoxes results from gravity from the Moon and Sun exerting a torque on the rotating Earth. You can see something analogous in a spinning top. If the top is not oriented vertically, gravity exerts a torque on the top that causes the top's rotation axis to rotate. Note: This torque does not slow the top down. The top slows because of friction with the surface on which it is spinning and with the air.

The best way to think of the spiral arms is that they are traffic jams. Traffic jams on a freeway can persist long after the original cause vanished. Sometimes they appear for no reason whatsoever. Just as cars eventually move through the traffic jam, only to be replaced by new ones arriving at the tail of the jam, stars eventually move through the spiral arms, only to replaced by other stars entering the arms.

I guess what I am looking to try and apply is a fractal way of thinking, patterns within patterns. While I can see the cycles that repeat within our solar system, I am wondering if there are far more massive cycles in which our solar system is merely a single body.

My advice: Don't get too caught up in fractals. Dynamic systems theory is one thing, fractals are another. Solar systems don't look like anything else.

The reason I asked about The Sirius cluster is that I have read that it contains over 250 suns in the same aprox. space as our solar system, which would make it a huge gravity well. Am I the victim of poor information?

You're looking for patterns that don't exist.

BTW, I suspect you are talking about the Ursa Major Moving Group. Sirius is not a member of it, nor is the solar system.

If there are areas of space with that many concentrated suns, could the intense gravity compress space/time, or matter?

Not really. The Ursa Major Moving Group is a weak collection of stars that probably used to be an open cluster. Except for the immediate vicinity of the central black hole, time dilation is pretty small even at the center of the galaxy.

 

[Johio]

DH, I really appreciate the time you are giving to replying to my questions. You are saving me from a lot of previous inaccurate information & premises, which led me to theorize toward a wrong headed conclusion. Thanks for your service.
Now, I have some reading to do. :D

 

[Ken G]

First off, the only thing electron orbitals have in common with planetary orbits is that both have the letters o-r-b-i-t in them. The model of electrons circling the nucleus as planets orbit the Sun was one of the earliest attempts to model the atom. It is demonstrably false.

That is certainly a generally correct remark, but I think it leads us to abandon classical analogs that can still be quite useful in quantum mechanics. So if someone says "everything orbits something else" in some general way, that's not really entirely untrue even at the level of electrons bound inside atoms. You are certainly right that the classical analogy can be taken too far, leading to all kinds of misconceptions that no doubt you see all the time. But it can also not be taken far enough, and abandoned too soon without benefiting from its potential uses.

Now, I agree that classical analogs provide little or no insight into quantum mechanical systems without first including the key surprise of quantum mechanics: the principle of superposition. (Superposition means that any two states that are possible can be combined in an arbitrary linear combination, and you end up with a new state that is also possible.) The new state is not one or the other of the old ones, it is a bizarre form of combination that has no classical analog. But adding this non-classical idea to classical concepts like orbits is often all that is needed to be able to carry over a lot of useful classical notions into quantum mechanics. (This is often done, for example, in the deBroglie-Bohm interpretation of quantum mechanics, but I just mean it in a much more informal way of making pictures that can still help us understand quantum mechanics using classical analogs.)

The way this could work in the context of orbits and atoms is that if we imagine that the electron is not in a classical orbit around the nucleus, but instead in a superposition of classical orbits, we get much of what we need to understand quantum mechanics. For example, each of those classical orbits that is being superimposed to create a quantum state will individually obey the "virial theorem", so on average will have half as much (positive) kinetic energy as they do (negative) potential energy, just as is true of classical gravitational orbits. So when we make superposition states, we expect that attribute to continue to hold, and sure enough it does-- quantum mechanical bound states have, on average, half as much kinetic energy as potential energy.

How about orbital angular momentum? This is a big problem if we don't include superpositions, because a planet in orbit around a star always has orbital angular momentum, but an electron in an "s" orbital has zero orbital angular momentum. But before we conclude that classical angular momentum has no bearing on atomic orbitals, all we really need is the concept of superposition. If we superimpose classical orbits that are oriented in all directions, like the Oort cloud of comets, we recover the concept of an "s" orbital-- the superposition has zero angular momentum. But if we want to treat a "p" orbital, which does have angular momentum, we can superimpose classical orbits that go around more one way than the other.

Now, I won't claim that all of quantum mechanics can be obtained this way (without adding all the baggage of the deBroglie-Bohm interpretation, which is a lot of trouble to go through to preserve the classical pictures), there's a reason quantum mechanics is considered its own theory with very different kinds of building blocks. I'm just saying that many classical analogies can still be used to help us understand quantum mechanical language, as long as we first get clear on the all-important superposition principle. I hate to give up too early on classical analogies, because with care, they are still quite helpful. After all, we all have much more experience with classical systems, in our daily lives, than with quantum ones!

 

[D H]

So if someone says "everything orbits something else" in some general way, that's not really entirely untrue even at the level of electrons bound inside atoms. You are certainly right that the classical analogy can be taken too far, leading to all kinds of misconceptions that no doubt you see all the time.

That's true, but you need to remember the context of the question, which was fractals.

Even if the one of those old planetary models of the atom was correct, it still would not be valid to use this as an argument for a fractal view of orbits. Systems that have a fractal nature have to look more or less the same at all scales. There are instead tiny ranges where one can say “Yep. If I look at it right I can say there are orbits at this scale,” but those are intermingled amongst huge, huge voids where one must say “Nope. There are no orbits at this scale.”

 

[Ken G]

Yes, there is certainly a danger of thinking "it's turtles all the way down" when it comes to orbits. Something changes quite fundamentally when you go from a planetary orbit to an electron orbit, or even from a planetary orbit to a galactic orbit (dark matter comes into play), or from galactic orbits to the motions of the universe (dark energy comes into play). It's not a fractal, but there certainly are repeating patterns in more general terms. (What's also interesting is the huge gaps in scales that make physics possible-- vast amounts of empty space between stars allow us to have solar systems, vast spaces between planets let's us imagine we orbit the Sun, then things get pretty crowded on biological scales which gives us the complexity we need for life, but then scales separate again when we get to atoms. Very convenient that it's not a fractal-- fractals would make the reductionist approach of physics awfully tough!)