PDA

View Full Version : Is There Such a Thing as a Circular Orbit?

Fiery Phoenix
2015-Dec-19, 11:28 PM
In practice, is it actually possible to achieve a circular orbit, where the eccentricity is exactly zero? Why or why not?

I know of no such phenomena in our solar system. Triton is probably the winner, though, having an eccentricity of only 0.000016, which is more or less circular. But still not quite uniformly circular.

Hornblower
2015-Dec-20, 02:13 AM
In practice, is it actually possible to achieve a circular orbit, where the eccentricity is exactly zero? Why or why not?

I know of no such phenomena in our solar system. Triton is probably the winner, though, having an eccentricity of only 0.000016, which is more or less circular. But still not quite uniformly circular.

To achieve and maintain a perfectly circular orbit, we would need a 2-body system free of all external gravitational perturbations. In principle "there ain't no such animal", but we could get a very close approach with a binary system out in an intergalactic void somewhere. Even getting well away from the Sun would do for a very close pair of bodies.

Jens
2015-Dec-20, 02:31 AM
If you think about it, an exact circle if one of an infinite possible ellipses, so the chance of one being perfect would be infinitely small, and it wouldn't stay that way.

antoniseb
2015-Dec-20, 03:17 AM
There can't be any perfectly circular orbits because they are only possible in a two-body universe, but they can be circular enough that we can't measure the difference.

DaveC426913
2015-Dec-20, 05:57 AM
Triton is probably the winner, though, having an eccentricity of only 0.000016.
That's a difference of less than 6 kilometres over 355,000 km. Not bad.

To plot this on a screen, you would need a monitor with a pixel rez of 60,000 x 60,000 (that's about 52 feet corner to corner) to see a single pixel deviation in the circle.

slang
2015-Dec-20, 12:40 PM
There can't be any perfectly circular orbits because they are only possible in a two-body universe, but they can be circular enough that we can't measure the difference.

How circular would the photon-sphere around a black hole be?

antoniseb
2015-Dec-20, 01:11 PM
How circular would the photon-sphere around a black hole be?
I don't know how to calculate the impact of a nearby star on the shape of a photon sphere around a black hole, but it would have an effect.
One other side note about things orbiting other things. If they both have mass, they give off gravitational waves (and energy), and will spiral in, so the orbit would not be exactly circular, but it wouldn't be elliptical either.

Fiery Phoenix
2015-Dec-20, 03:30 PM
That's a difference of less than 6 kilometres over 355,000 km. Not bad.

To plot this on a screen, you would need a monitor with a pixel rez of 60,000 x 60,000 (that's about 52 feet corner to corner) to see a single pixel deviation in the circle.
Yes, that's pretty impressive, especially when you consider that it's (probably) a captured trans-Neptunian object.

George
2015-Dec-20, 08:10 PM
If you think about it, an exact circle if one of an infinite possible ellipses, so the chance of one being perfect would be infinitely small, and it wouldn't stay that way. That's a great way to look at it. There is nothing to force an orbiting object into a circular object. Other than in math, is there anything that makes a perfect circle? We did once have this math prof. once who accidentally, in < 2 seconds, drew a large, perfectly-looking circle. We all laughed and began clapping; it had never been done before. :)

DaveC426913
2015-Dec-20, 08:27 PM
That's a great way to look at it. There is nothing to force an orbiting object into a circular object.
There is. Tidal effects of the two bodies will decrease the ellipticity of an orbit over time.

Here's a pretty succinct description of the process:
http://yarchive.net/space/orbits/tidal_circularize.html

I would hazard to say it is a much bigger effect than the influence of external third bodies.

Fiery Phoenix
2015-Dec-20, 09:05 PM
There is. Tidal effects of the two bodies will decrease the ellipticity of an orbit over time.

Here's a pretty succinct description of the process:
http://yarchive.net/space/orbits/tidal_circularize.html

I would hazard to say it is a much bigger effect than the influence of external third bodies.

George
2015-Dec-21, 07:26 PM
There is. Tidal effects of the two bodies will decrease the ellipticity of an orbit over time.

Here's a pretty succinct description of the process:
http://yarchive.net/space/orbits/tidal_circularize.html That's a good point; tidal action would more often than not reduce eccentricity, but even when the moon/planet ratio is high, which is the case for Earth, it doesn't give us a true circular orbit. Once tidal lock comes around (so to speak), then I assume this reduction ends.

Fiery Phoenix
2015-Dec-21, 08:05 PM
That's a good point; tidal action would more often than not reduce eccentricity, but even when the moon/planet ratio is high, which is the case for Earth, it doesn't give us a true circular orbit. Once tidal lock comes around (so to speak), then I assume this reduction ends.
That's how I understand it as well. Once tidal locking is achieved, the system becomes stable and is no longer changing its orbital configurations.

George
2015-Dec-21, 09:29 PM
That's how I understand it as well. Once tidal locking is achieved, the system becomes stable and is no longer changing its orbital configurations. That is very likely true in a general sense, but things like libation and satellite orbital eccentricity may still have effects on a planet's orbit, though a large moon would also help stabilize it. These are guesses on my part.

DaveC426913
2015-Dec-21, 09:57 PM
That's a good point; tidal action would more often than not reduce eccentricity,
Pretty sure it only reduces eccentricity.

That is very likely true in a general sense, but things like libation and satellite orbital eccentricity may still have effects on a planet's orbit, though a large moon would also help stabilize it. These are guesses on my part.
Are you talking about the planet's eccentricity? We were talking about the moon's eccentricity.

George
2015-Dec-22, 03:42 PM
Pretty sure it only reduces eccentricity. My thought was for the case where the planet is rotating slowly and the satellite orbiting quickly. I only assume this would have the opposite effect on eccentricity?

Are you talking about the planet's eccentricity? We were talking about the moon's eccentricity. Yep, I'm still stuck on Earth. Oops. But it may not matter that much since the libation effects would effect both bodies, and a planet's eccentricity would impact the satellite's due to the tidal stress from the star.

Fiery Phoenix
2015-Dec-22, 04:29 PM
My thought was for the case where the planet is rotating slowly and the satellite orbiting quickly. I only assume this would have the opposite effect on eccentricity?
I know that would cause the satellite to approach the planet at a steady rate (as is the case with Phobos and Mars). Not really sure what it would mean for eccentricity, though.

Ken G
2015-Dec-23, 08:58 AM
In practice, is it actually possible to achieve a circular orbit, where the eccentricity is exactly zero? Why or why not?It is not possible to achieve a circular orbit, nor an elliptical orbit, nor an Archimedean spiral orbit, etc. The reason is because the word "orbit" can mean a lot of different things, and "achieving a circular orbit" incorrectly mixes those meanings.

For example, when we say a satellite "achieved orbit", we simply mean it made it out into space for a good long while, without either escaping Earth completely, or falling back down. That's pretty much all those words mean! They certainly don't mean it "achieved a definite one-dimensional geometric shape" as its motion, circular or otherwise! The reason is, when we talk about a "circular orbit", we actually are taking a very different meaning of "orbit" than the one I just gave. Now we are talking about a mathematical model, and we don't "achieve" mathematical models, we apply them. "Achieve" is simply the grammatically incorrect verb to use with "circular orbits"! That's why it's not possible, not because there is something special about circles, but simply because what we do with "circular orbits" is recognize they are mathematical models intended to be applied, not achieved. Achieving orbit uses a very different meaning of "orbit," something much more practical than an idealized mathematical model.

pindo
2015-Dec-23, 09:03 AM
It is not possible to achieve a circular orbit, nor an elliptical orbit, nor an Archimedean spiral orbit, etc. The reason is because the word "orbit" can mean a lot of different things, and "achieving a circular orbit" incorrectly mixes those meanings.

For example, when we say a satellite "achieved orbit", we simply mean it made it out into space for a good long while, without either escaping Earth completely, or falling back down. That's pretty much all those words mean! They certainly don't mean it "achieved a definite one-dimensional geometric shape" as its motion, circular or otherwise! The reason is, when we talk about a "circular orbit", we actually are taking a very different meaning of "orbit" than the one I just gave. Now we are talking about a mathematical model, and we don't "achieve" mathematical models, we apply them. "Achieve" is simply the grammatically incorrect verb to use with "circular orbits"! That's why it's not possible, not because there is something special about circles, but simply because what we do with "circular orbits" is recognize they are mathematical models intended to be applied, not achieved. Achieving orbit uses a very different meaning of "orbit," something much more practical than an idealized mathematical model.

So if something is moving around the earth (or some other such object) along a path that is nearly circular, what words do you use to describe that?

Ken G
2015-Dec-23, 09:52 AM
So if something is moving around the earth (or some other such object) along a path that is nearly circular, what words do you use to describe that?If people understand what you mean, you can say it in any number of ways, including using the words "followed a nearly circular orbit", even though they are formally incorrect. Formally, if we say it is "in orbit", we mean it is not escaping and not falling down without being powered-- anything doing that is "in orbit". But since you also want to compare that motion to some kind of mathematical model (such as saying a "nearly circular path"), you could more precisely say its motion can be approximated by a circular orbit, since now you have invoked the other meaning of "orbit"-- a mathematical model. We often get away with an awkward mixing of the practical meaning and the mathematical model all the time, the distinction doesn't matter so much because we generally wish to draw a parallel anyway-- we wish to say that objects that aren't escaping, and aren't falling back down, can be approximately described by invoking a mathematical model (such as what Kepler did). But it's still formally wrong to mix the two, like in the movie "the Fly", and end up with "the object followed a nearly circular orbit." In practice, however, this creates no problems-- we know what we intend to mean, a simultaneous reference to two different meanings of "orbit," one something the object is said to be doing, the other a mathematical model we are invoking like a template to understand what the object is doing by placing these two meanings in juxtoposition.

That's an intersection that we take so for granted we can easily forget there are two quite different usages of the word "orbit" going on there. The distinction normally doesn't enter-- it only appears when you see questions like "is it possible to achieve a circular orbit."

Hornblower
2015-Dec-23, 03:41 PM
We could argue until doomsday about the meanings of "orbit" and "achieve", and in my opinion it would be pointless for the purpose of this thread. It is my sincere opinion that if we are not overthinking it, most of us can see that Fiery Phoenix is simply asking if it is possible to set gravitationally bound bodies in inertial motion that keeps their separation constant. Quantum-mechanical constraints may make it meaningless to try to determine this constancy or lack thereof beyond a certain level of precision.

Fiery Phoenix
2015-Dec-23, 03:54 PM
We could argue until doomsday about the meanings of "orbit" and "achieve", and in my opinion it would be pointless for the purpose of this thread. It is my sincere opinion that if we are not overthinking it, most of us can see that Fiery Phoenix is simply asking if it is possible to set gravitationally bound bodies in inertial motion that keeps their separation constant. Quantum-mechanical constraints may make it meaningless to try to determine this constancy or lack thereof beyond a certain level of precision.
Yes, this is it. I get that such terms can have different connotations depending on the specific topic. Nonetheless, I thought it was pretty obvious where I was coming from ;)

Ken G
2015-Dec-23, 04:45 PM
Yes, this is it. I get that such terms can have different connotations depending on the specific topic. Nonetheless, I thought it was pretty obvious where I was coming from ;)Well you did ask if eccentricity could be exactly zero, did you not? So that's what calls for interpretation of the question. I guess I should have paid closer attention to when you said "practically speaking", so I think what you were really asking is "what is the smallest eccentricity we could ever expect to measure in any real system," i.e., a question about the practical end of measuring quantities, not the abstract mathematical models. To that question, you've had a lot of good answers.

But even so, the answers you got, though they addressed your question, did bump into the problem of mistaking what can be said from an observation with what is an attribute of an abstract mathematical model. I'm not being critical of these answers, I totally get what they were saying, but there is a problem with them, which is they did run into this confusion. I'm not saying we always have to make the distinction between what we can say is true based on observations, and what is an attribute of a mathematical abstraction, I'm just saying that we can run into problems if we so routinely mix that kind of language that we forget we are doing it. The question can be answered more precisely by first untangling that distinction. But you are saying you weren't looking for so precise an answer as that, so that's fine.

Fiery Phoenix
2015-Dec-23, 05:12 PM
Well you did ask if eccentricity could be exactly zero, did you not? So that's what calls for interpretation of the question. All I'm saying is that sometimes scientific words get their meaning from practical observations (the measured separation between Io and Jupiter, etc.), and other times they get their meaning from abstract mathematical models ("circular orbits"), and only the latter could ever use the word "exactly". We rarely bother to keep those two approaches to meaning in science separate, but when the word "exactly" gets used, it is not clear if we are bumping into this disconnect or not. I agree that we get away with ignoring these differences most of the time, but when we use words like "exactly", it starts to sound like maybe that's what the question is about. It's more clearly an issue for questions like "is the universe really infinite", and so on.
Point taken!

Ken G
2015-Dec-23, 05:20 PM
(Stepping off soapbox...)

DaveC426913
2015-Dec-23, 05:34 PM
Note that a circular orbit isn't special in this sense. An orbit with any eccentricity is going to be measurable only to a certain degree of precision, and will only hold it for an arbitrary length of time.

In this regard e=0.0000 is no more special that e=0.5000 or e=0.9999 or any other value between 0 and 1.

Ken G
2015-Dec-23, 07:15 PM
Exactly-- any ellipse is a mathematical idealization, very useful in understanding orbits, but not the same thing as a practical orbit. There really are two very different meanings of an "orbit", what the object is doing, and how we create mathematical idealizations to understand what the object is doing. (If I say those are just two different types of models, we'll get into that long thread that we don't want to get into, so I'll instead stress the differences there.) The OP question has been clarified as asking, if we are to use mathematical idealizations to understand orbits, how small are we likely to ever need the eccentricity to be in practical problems? That's an interesting question, the answer seems to be something along the lines of "very very small, but never smaller than our ability to measure if we get a good enough look at it," for all the reasons given above.

Jens
2015-Dec-25, 12:17 AM
It is not possible to achieve a circular orbit, nor an elliptical orbit, nor an Archimedean spiral orbit, etc. The reason is because the word "orbit" can mean a lot of different things, and "achieving a circular orbit" incorrectly mixes those meanings.

I'm not meaning to nitpick, but couldn't you also say that all orbits are precisely elliptical, as long as you look at what the object is doing at any exact time? At least in Newtonian physics, it is following a path that it "thinks" is elliptical, so at that precise point in time it is essentially tracing a path that follows the mathematical formula. Of course, the conditions change all the time so that elliptical path is never the same from moment to moment.

Ken G
2015-Dec-25, 12:34 AM
I'm not meaning to nitpick, but couldn't you also say that all orbits are precisely elliptical, as long as you look at what the object is doing at any exact time? I would say that even a piece of an ellipse is still not something an object does, it is a mathematical abstraction we use to understand what objects do. In other words, it is a kind of mathematical template we hold next to the object, and say, "wow, that's really close, so close we can say we understand something here." But it's never exact, not even a piece of an ellipse. There's always a measurement we could do, if accurate enough, that will find a discrepancy.

At least in Newtonian physics,Exactly-- "Newtonian physics." Is that something that objects do, or a mathematical abstraction we use to understand what objects do?

DaveC426913
2015-Dec-25, 01:15 AM
I'm not meaning to nitpick, but couldn't you also say that all orbits are precisely elliptical, as long as you look at what the object is doing at any exact time? At least in Newtonian physics, it is following a path that it "thinks" is elliptical, so at that precise point in time it is essentially tracing a path that follows the mathematical formula. Of course, the conditions change all the time so that elliptical path is never the same from moment to moment.
At any given moment, (in a Newtonian universe) the object is pulled in a direction that is a vector sum of every massive body around it. So it knows nothing about any ellipse. It would only happen to have been tracing out an ellipse if the only influence had been a central massive body over some arbitrary time span.

Er....

The body knows nothing about a path it might be following; it simply responds at any given moment to the sum of influencers.

Fiery Phoenix
2015-Dec-25, 02:41 AM
I would say that even a piece of an ellipse is still not something an object does, it is a mathematical abstraction we use to understand what objects do. In other words, it is a kind of mathematical template we hold next to the object, and say, "wow, that's really close, so close we can say we understand something here." But it's never exact, not even a piece of an ellipse. There's always a measurement we could do, if accurate enough, that will find a discrepancy.
At the risk of derailing my own thread, how transferable is this assertion? Could everything we do in science be described as an 'abstraction' from which it is easier to draw satisfactory conclusions?

I understand that that's pretty much exactly what Newtonian physics is all about, but I'm curious as to the generalizability of the concept.

Ken G
2015-Dec-26, 02:29 AM
At the risk of derailing my own thread, how transferable is this assertion? Could everything we do in science be described as an 'abstraction' from which it is easier to draw satisfactory conclusions? I would say any individual is free to believe that science does more than that, but can never demonstrate scientifically that it ever does anything more than that! After all, I am aware of no scientific demonstration anywhere that it does more than that, and we can see lots of examples of it doing just that, but it is fair to say a lot of scientists do choose to believe it does more. (I don't really know why-- for me personally, the process of learning Newton's laws, and then unlearning them, was a process I only had to go through once to get the gist of how this goes!)

DaveC426913
2015-Dec-26, 07:13 PM
At the risk of derailing my own thread, how transferable is this assertion? Could everything we do in science be described as an 'abstraction' from which it is easier to draw satisfactory conclusions?

I understand that that's pretty much exactly what Newtonian physics is all about, but I'm curious as to the generalizability of the concept.

All theoretical physics is about producing models of nature. The more accurate they are, the more useful.

We don't see spacetime curving, but our Einsteinian model of space and time predicts things that we then observe in nature. This makes for a successful model.

But they are merely models.