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Thread: Do Orbits tend to go circular?

  1. #1 Do Orbits tend to go circular? 
    Forum Senior bill alsept's Avatar
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    I understand that all orbits are ecliptic and that a circle is kind of a special case for an eclipse. What I'm wondering is do ecliptic orbits tend to go more and more circular? If so what is the cause of this? Are there any good links to this subject?


    Last edited by bill alsept; February 17th, 2013 at 04:37 AM.
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    No, they don't tend to go circular, where did you get that idea from ? In order to go from a elliptical to a circular orbit you would have to change the orbital angular momentum of the body, meaning you would either have to apply an external force ( torque ), or somehow change the body's mass. In general the orbits are determined to good approximation by Kepler's laws, specifically the second law which gives us a relation between sector velocity and orbital angular momentum :



    The special case of a circular orbit can only occur if there is a very specific relationship between orbital radius and orbital velocity :



    wherein M is the mass of the central body; this velocity is of course constant.

    So in short - no, all other things being equal elliptical orbits do not tend towards circular ones, because this would violate the conservation of orbital angular momentum.

    Are there any good links to this subject?
    That would be Kepler's laws, if you want to stay within classical mechanics :

    http://en.wikipedia.org/wiki/Keplers_laws


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    Actually, tidal effects between the orbiting body and its primary do tend to reduce the eccentricity of the orbit. This is related to the tidal acceleration that is causing the Moon to recede. The strength of the tidal interaction varies with the radius of the orbit, and this has the effect of shifting the orbit into an more circular one.
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    Forum Senior bill alsept's Avatar
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    Quote Originally Posted by Janus View Post
    Actually, tidal effects between the orbiting body and its primary do tend to reduce the eccentricity of the orbit. This is related to the tidal acceleration that is causing the Moon to recede. The strength of the tidal interaction varies with the radius of the orbit, and this has the effect of shifting the orbit into an more circular one.
    Thanks do you know of a link that would explain this in more detail? So if this effect varies with the radius of the orbit wouldn't that mean that eventully the orbit would be circular. I assume the effect would be less and less the more circular the orbit became so this could take a while. What would the effect look like when the orbit was far from circular and the distance from the primary varied a lot?
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    Quote Originally Posted by Janus View Post
    Actually, tidal effects between the orbiting body and its primary do tend to reduce the eccentricity of the orbit. This is related to the tidal acceleration that is causing the Moon to recede. The strength of the tidal interaction varies with the radius of the orbit, and this has the effect of shifting the orbit into an more circular one.
    My guess, insofar as the Solar System is concerned, is that since the inter-planetary distances are changing constantly due to their orbital distances from the Sun, and their differing orbital velocities, the elliptical orbits are governed by, and kept fairly constant, by the gravitational forces exerted by all of them on one another. jocular
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    Forum Senior bill alsept's Avatar
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    Quote Originally Posted by jocular View Post
    Quote Originally Posted by Janus View Post
    Actually, tidal effects between the orbiting body and its primary do tend to reduce the eccentricity of the orbit. This is related to the tidal acceleration that is causing the Moon to recede. The strength of the tidal interaction varies with the radius of the orbit, and this has the effect of shifting the orbit into an more circular one.
    My guess, insofar as the Solar System is concerned, is that since the inter-planetary distances are changing constantly due to their orbital distances from the Sun, and their differing orbital velocities, the elliptical orbits are governed by, and kept fairly constant, by the gravitational forces exerted by all of them on one another. jocular
    I understand that the other planets, moons,etc have an influence on each other but I am interested in the isolated phanomena in which Jonas was referring to. One lone ecliptic orbiting body slowly changing to a more circular orbit.
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    Quote Originally Posted by bill alsept View Post
    One lone ecliptic orbiting body slowly changing to a more circular orbit.
    That is not what Janus said; he was referring to tidal interactions between a body and its primary moon. If there is no moon or other bodies, just one planet in isolation in otherwise free space will not change its orbit.
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by bill alsept View Post
    One lone ecliptic orbiting body slowly changing to a more circular orbit.
    That is not what Janus said; he was referring to tidal interactions between a body and its primary moon. If there is no moon or other bodies, just one planet in isolation in otherwise free space will not change its orbit.
    That's silly of course there would be two bodies involved how else would there be tidal forces. The orbiting body and the primary. I only referred to isolation for clearification after post five referred to all the other planets influencing and maybe being the cause of this eccentric orbit going circular. I was just trying to be clear that we where still talking about the phenomena that Janus was talking about. In post one I was looking for evidence that orbits tend to go circular. The second and third posts conflicted and that seems to be what I find as I do a search. Janus answer seemed vary reasonable and I am now narrowing my search in that area.
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    Quote Originally Posted by bill alsept View Post
    That's silly of course there would be two bodies involved how else would there be tidal forces. The orbiting body and the primary. I only referred to isolation for clearification after post five referred to all the other planets influencing and maybe being the cause of this eccentric orbit going circular. I was just trying to be clear that we where still talking about the phenomena that Janus was talking about. In post one I was looking for evidence that orbits tend to go circular. The second and third posts conflicted and that seems to be what I find as I do a search. Janus answer seemed vary reasonable and I am now narrowing my search in that area.
    Ok, so if you wish to account for tidal effects then disregard the material I have presented thus far, because Kepler's laws do not incorporate these. Instead you would be looking for something like this :

    http://www.dspace.cam.ac.uk/bitstrea...1/1/thesis.pdf

    This is pretty advanced stuff so far as classical mechanics go, so you need to make sure first your maths knowledge, specifically so far as vector calculus and differential equations is concerned, is up for the job. The basic idea is simple though - the tidal interactions produce a net gravitational torque on the body, thus altering its orbital angular momentum over time. The energy difference goes into tidal heating ( through deformations ) of the two bodies. There are also other effects related to the intrinsic angular momentum of the body, and of course interactions of the magnetic fields.

    That's silly of course there would be two bodies involved how else would there be tidal forces.
    I meant a planet without moons. Obviously you still need a central body.
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by bill alsept View Post
    That's silly of course there would be two bodies involved how else would there be tidal forces. The orbiting body and the primary. I only referred to isolation for clearification after post five referred to all the other planets influencing and maybe being the cause of this eccentric orbit going circular. I was just trying to be clear that we where still talking about the phenomena that Janus was talking about. In post one I was looking for evidence that orbits tend to go circular. The second and third posts conflicted and that seems to be what I find as I do a search. Janus answer seemed vary reasonable and I am now narrowing my search in that area.
    Ok, so if you wish to account for tidal effects then disregard the material I have presented thus far, because Kepler's laws do not incorporate these. Instead you would be looking for something like this :http://www.dspace.cam.ac.uk/bitstrea...1/1/thesis.pdfThis is pretty advanced stuff so far as classical mechanics go, so you need to make sure first your maths knowledge, specifically so far as vector calculus and differential equations is concerned, is up for the job. The basic idea is simple though - the tidal interactions produce a net gravitational torque on the body, thus altering its orbital angular momentum over time. The energy difference goes into tidal heating ( through deformations ) of the two bodies. There are also other effects related to the intrinsic angular momentum of the body, and of course interactions of the magnetic fields.
    That's silly of course there would be two bodies involved how else would there be tidal forces.
    I meant a planet without moons. Obviously you still need a central body.
    Thanks for the article it looks interesting. Are you agreeing that obits do tend to go circular? If so then I was also wondering how this effect would look on a graph. I assume the effect would be much stronger when the bodies where close but wouldn't this effect continue even at the farther distances? More specifically if there were two identical bodies with similar ecliptic orbits. One with an average distance as close as Murcery's and the other like Pluto's. Would the two graphs show both orbits eventully going circular but with a completly different curve on the graph?
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  12. #11  
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    Are you agreeing that obits do tend to go circular?
    It is impossible to answer this question in general. Some orbits, under certain circumstances, may tend to become more circular over time. Other orbits do not. This depends on many factors, mainly orbital radius and the masses of the bodies involved.
    If you carefully read through the paper I referenced you will see that the tidal effects which cause this are relevant only for very close orbits ( which is also what Janus said ); in the general case of the planets in our solar system this effect is so small as to be irrelevant, and will have no influence on the eccentricity of their orbits even over long time scales. Remember for example that Pluto still has an orbital eccentricity of 0.244 even after something like 4 billion years.
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    Forum Senior bill alsept's Avatar
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    Quote Originally Posted by Markus Hanke View Post
    Are you agreeing that obits do tend to go circular?
    It is impossible to answer this question in general. Some orbits, under certain circumstances, may tend to become more circular over time. Other orbits do not. This depends on many factors, mainly orbital radius and the masses of the bodies involved.If you carefully read through the paper I referenced you will see that the tidal effects which cause this are relevant only for very close orbits ( which is also what Janus said ); in the general case of the planets in our solar system this effect is so small as to be irrelevant, and will have no influence on the eccentricity of their orbits even over long time scales. Remember for example that Pluto still has an orbital eccentricity of 0.244 even after something like 4 billion years.
    I guess now that we have established that orbits do tend to go circular on their own the next question is does the math show that this phenomena only happens up to a certain distance and after that it cannot happen? As you suggested I most likely cannot comprehend this math but it is a simple question for someone who can. Is there a cut off point for sure or will it eventually go circular even if it takes 10 billion years.
    Last edited by bill alsept; February 18th, 2013 at 04:21 PM.
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    Quote Originally Posted by bill alsept View Post
    Are you agreeing that obits do tend to go circular?
    Quote Originally Posted by Markus Hanke View Post
    It is impossible to answer this question in general.
    Quote Originally Posted by bill alsept View Post
    I guess now that we have established that orbits do tend to go circular on their own...
    This exchange cracked me up.
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  15. #14  
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    I guess now that we have established that orbits do tend to go circular on their own
    I really can't understand how you could manage to come to this conclusion based on the answers you've been given.
    Its the way nature is!
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    Quote Originally Posted by AlexG View Post
    I guess now that we have established that orbits do tend to go circular on their own
    I really can't understand how you could manage to come to this conclusion based on the answers you've been given.
    Well obviously it was a typo that should have read "orbits CAN tend to go circular" or I wouldn't have asked the follow up question "Is there a cut off point for sure or will it eventually go circular even if it takes 10 billion years?" My emphases was on the fact that we had established that orbits CAN (as opposed to cannot) tend to go circular. Now I am trying to find out if there is a cut off point for this phenomena. This article Tidal circularization of orbits (Henry Spencer) says that "the strength of tidal forces is an inverse-cube function of distance" If that is true and the tidal forces do have an effect no matter how small then eventually all orbits if left unaffected would tend to go circular. I would think true or false that there should be an answer to this. I don't care if they can or not I just need to know in order to move on to something else I'm working on.
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    This article Tidal circularization of orbits (Henry Spencer) says that "the strength of tidal forces is an inverse-cube function of distance" If that is true and the tidal forces do have an effect no matter how small then eventually all orbits if left unaffected would tend to go circular.
    All other things being strictly equal - yes, there would be a tendency for orbits to become more circular over time. Please bear in mind though that the orbital radius is not the only factor involved ( as was mentioned in both articles ) - this depends also on the masses of the bodies, and their own rotation periods. In practice therefore, this effect is not observed for the orbits of the planets in the solar system because the time frames needed for this effect to become significant are much longer than the lifetime of the central star.
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  18. #17  
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    Quote Originally Posted by bill alsept View Post
    Quote Originally Posted by AlexG View Post
    I guess now that we have established that orbits do tend to go circular on their own
    I really can't understand how you could manage to come to this conclusion based on the answers you've been given.
    Well obviously it was a typo that should have read "orbits CAN tend to go circular" or I wouldn't have asked the follow up question "Is there a cut off point for sure or will it eventually go circular even if it takes 10 billion years?" My emphases was on the fact that we had established that orbits CAN (as opposed to cannot) tend to go circular. Now I am trying to find out if there is a cut off point for this phenomena. This article Tidal circularization of orbits (Henry Spencer) says that "the strength of tidal forces is an inverse-cube function of distance" If that is true and the tidal forces do have an effect no matter how small then eventually all orbits if left unaffected would tend to go circular. I would think true or false that there should be an answer to this. I don't care if they can or not I just need to know in order to move on to something else I'm working on.
    The effects that tend to tend to reduce the eccentricity of the orbit are related to the effects that cause tidal locking. Tidal locking depends on a number of things: The masses of both satellite and primary, the radius of the body being tidally locked, the initial spin of same body, the dissipation factor and the Love number (which relies on the rigidity of the body in question. The time it take for tidal locking increases by the distance between the bodies to the power of 6 and decreases by the radius of the body to the power of 3.

    In addition, the tendency for orbits to decrease their eccentricity becomes less as the eccentricity decreases.
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  19. #18  
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    Quote Originally Posted by Markus Hanke View Post
    This article Tidal circularization of orbits (Henry Spencer) says that "the strength of tidal forces is an inverse-cube function of distance" If that is true and the tidal forces do have an effect no matter how small then eventually all orbits if left unaffected would tend to go circular.
    All other things being strictly equal - yes, there would be a tendency for orbits to become more circular over time.
    Thanks, thats all I was trying to confirm. I had read about tidal forces before but had never heard of this tendency for orbits to go circular. For some reason I find this fascinating.
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    Quote Originally Posted by bill alsept View Post
    Thanks, thats all I was trying to confirm. I had read about tidal forces before but had never heard of this tendency for orbits to go circular. For some reason I find this fascinating.
    To me it's one of the more obscure and difficult to calculate aspects of classical mechanics, since so many factors are involved - see the paper I referenced.
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    Speaking of tidal forces does anyone know what kind, how much and how fast of an effect the melting of the polar caps will have on either the Earths rotation or the moons orbit? More specifically is there a varying effect as the oceans rise and fall through all the ice ages?
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    Quote Originally Posted by bill alsept View Post
    Speaking of tidal forces does anyone know what kind, how much and how fast of an effect the melting of the polar caps will have on either the Earths rotation or the moons orbit? More specifically is there a varying effect as the oceans rise and fall through all the ice ages?
    If, let's say, the polar caps melt completely then this would lead to a small change in the earth's moment of inertia, which, due to conservation of angular momentum, should have a small effect on the earth's rotation. I don't have any numbers to present, but I would expect the effect to be so small as to be virtually undetectable.

    I don't think this would have any effect on the moon's orbit.
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  23. #22  
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by bill alsept View Post
    Speaking of tidal forces does anyone know what kind, how much and how fast of an effect the melting of the polar caps will have on either the Earths rotation or the moons orbit? More specifically is there a varying effect as the oceans rise and fall through all the ice ages?
    If, let's say, the polar caps melt completely then this would lead to a small change in the earth's moment of inertia, which, due to conservation of angular momentum, should have a small effect on the earth's rotation. I don't have any numbers to present, but I would expect the effect to be so small as to be virtually undetectable.

    I don't think this would have any effect on the moon's orbit.
    It could have a small effect on the Moon. Rising sea levels and the resultant change of the coastlines would conceivably change the tidal friction between Earth and ocean and, in turn, effect the tidal acceleration of the moon. Though probably it would not be a very noticeable effect.
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  24. #23  
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    Quote Originally Posted by Janus View Post
    It could have a small effect on the Moon. Rising sea levels and the resultant change of the coastlines would conceivably change the tidal friction between Earth and ocean and, in turn, effect the tidal acceleration of the moon. Though probably it would not be a very noticeable effect.
    Do you mean through the increase in the total mass of liquid water on the surface ? I didn't think of that; but again, I would say that this effect would be so small as to be very hard to detect.
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    Forum Senior bill alsept's Avatar
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    The effect may not be much between now and a complete melting but what about from peek of ice age to peek of melting? I would think those differences would be large.
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    Quote Originally Posted by bill alsept View Post
    The effect may not be much between now and a complete melting but what about from peek of ice age to peek of melting? I would think those differences would be large.
    The differences in sea levels were definitely large, no question, but I think the effect on the moon's orbit would have been exceedingly small.
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    Quote Originally Posted by Markus Hanke View Post
    Quote Originally Posted by Janus View Post
    It could have a small effect on the Moon. Rising sea levels and the resultant change of the coastlines would conceivably change the tidal friction between Earth and ocean and, in turn, effect the tidal acceleration of the moon. Though probably it would not be a very noticeable effect.
    Do you mean through the increase in the total mass of liquid water on the surface ? I didn't think of that; but again, I would say that this effect would be so small as to be very hard to detect.
    That and the additional effect of how the altered coastlines could effect the tidal patterns. The tidal acceleration of The Moon is caused by the rotating Earth dragging the tidal bulge with it. If you change this, you will change the acceleration. For instance, something that had quite a sizable effect over long periods of time is continental drift. During our past, when the super-continents existed, the drag between Earth and tidal bulge was less and the Moon receded at a slower pace.

    I'm not saying that it would necessarily be easily measured, just that it would be a contributing factor.
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