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Thread: Types of orbits

  1. #1
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    Types of orbits

    I know a few basic types of orbits, but I was curious as to how each one works (please don't bombard me with algebra-it murders more of my precious grey cells ).

    Elliptical Orbit: When a planet orbits the sun in an egg shape (it could be a artificial/natural satellite orbiting a planet), so that at perihelion its closer to the sun (or planet-SOP for short) than at aphelion. The planet moves faster closer to the SOP and slows down when farther away. As BA said in his Seasons page on the main site, this means the Southern Hemisphere recieves shorter and hotter summers but longer and cooler winters (Northern other way round...oh well, fair's fair! 8-[ ).

    Open Orbit: The object..er...swings in then away from the body never to return (e.g. when a spacecraft takes a gravity whip).

    Collision Course: Don't know if there's a name for this kind of orbit-A collision orbit? Think Galileo smashing into Jupiter (but not exploding it!) :roll:

    Circular Orbit: A perfect circle-I believe only Venus or Mercury has this kind of orbit.

    Figure Eight Orbit: When there's a binary star system, a planet might weave in between the stars. But this can get dodgy because the planet's orbit becomes too unstable.

    I'd love to know some other orbits that are possible!

    OT, but is there a certain number of topics a member is allowed to do?

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    Re: Types of orbits

    Quote Originally Posted by NZborngal
    I know a few basic types of orbits, but I was curious as to how each one works (please don't bombard me with algebra-it murders more of my precious grey cells ).

    Elliptical Orbit: When a planet orbits the sun in an egg shape (it could be a artificial/natural satellite orbiting a planet), so that at perihelion its closer to the sun (or planet-SOP for short) than at aphelion. The planet moves faster closer to the SOP and slows down when farther away. As BA said in his Seasons page on the main site, this means the Southern Hemisphere recieves shorter and hotter summers but longer and cooler winters (Northern other way round...oh well, fair's fair! 8-[ ).

    Open Orbit: The object..er...swings in then away from the body never to return (e.g. when a spacecraft takes a gravity whip).
    Specifically, such orbit is either a parabola or a hyperbola.

    Collision Course: Don't know if there's a name for this kind of orbit-A collision orbit? Think Galileo smashing into Jupiter (but not exploding it!) :roll:
    Strictly speaking, it is still an ellipse (in Galileo's case), parabola or hyperbola, which happens to intersect planet's surface

    Circular Orbit: A perfect circle-I believe only Venus or Mercury has this kind of orbit.
    Venus comes very close, but it still not a PERFECT circle. I think closest moons of giant planets really orbit in perfect circles.

    Figure Eight Orbit: When there's a binary star system, a planet might weave in between the stars. But this can get dodgy because the planet's orbit becomes too unstable.
    I don't think it is possible long enough to even qualify as an "orbit" as opposed to "temporary aberration".

    I'd love to know some other orbits that are possible!
    Trojan Orbit: Body A orbits much more massive body B. Body C, much less massive than A can orbit B either 60 degrees ahead or 60 degrees behind A. In solar system, A is Jupiter, B is Sun, C is a bunch of asteroids "trailing" or "following" Jupiter in its orbit. It is very stable.

    LaGrange Orbit: A orbits B. C remains between them where their gravity force balances out, such as between Earth and Sun 1,500,000 km toward the Sun. Also 1,500,000 km further from the Sun than Earth. Ultimately not stable.

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    Multiple objects can share the same orbital path so long as they have more or less the same mass and are equally spaced along their orbit. For example, three Earth-sized planets could all orbit the sun at the same distance so long as they were spaced out by 120 degrees. Likewise, four such objects could orbit if spaced 90 degrees, and so on.

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    Quote Originally Posted by RoboSpy
    Multiple objects can share the same orbital path so long as they have more or less the same mass and are equally spaced along their orbit. For example, three Earth-sized planets could all orbit the sun at the same distance so long as they were spaced out by 120 degrees. Likewise, four such objects could orbit if spaced 90 degrees, and so on.
    I don't think those would be stable for the long-term, though, or, if so, only in an ideal situation with no external influences and a perfectly circular orbit.. The only stable co-orbital points are the Lagrange points, at 60 degrees ahead or behind the main body.
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    As ToSeek just pointed out, the "Trojan Orbit" is a "LaGrange Orbit". So tick that one off the list.

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    The Lagrange points are only orbits for objects whose mass is negligible compared to the mass of the two primary objects, so that concept doesn't apply to the equally spaced, equal mass scenario RoboSpy mentioned. It's not immediately obvious to me whether his scenario is stable or not, though it's obviously very unlikely to arise normally.

    I've seen the term 'orbit' used to describe any path an object takes through a system of gravitating objects, though I don't think that's what NZborngal is talking about. There are lots of closed orbits that exist for any system of objects you can imagine, though we can't write them down analytically in general. But as has already been made clear, the stability of the orbits is the key issue, and I suspect most of them would be unstable. (That's generally the case for any nonlinear dynamical system with many degrees of freedom.)

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    There's also the 'horseshoe' type of orbit, as for the asteroid Cruithne. From the website:
    "The near-Earth asteroid 3753 Cruithne is in an unusual orbit about that of the Earth, one which is known in the lingo of celestial mechanics as being co-orbital with the Earth (meaning it shares the Earth's orbit with it) and, more particularly, as being of the "horseshoe" type."

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    Just thought of something. A circle is an ellipse of eccentricity 0. Drop another category!

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    What about quasi satelites ?

    They seem to be theoretical at the moment so I don't know if PXers have spotted one yet!

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    Re: Types of orbits

    Quote Originally Posted by NZborngal
    Circular Orbit: A perfect circle-I believe only Venus or Mercury has this kind of orbit.
    Mercury's orbit is quite elliptical, actually.

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    Re: Types of orbits

    The two body problem involves a large mass attractor and a small mass orbiter. Depending on its velocity and radius at any given point, the orbit of the orbiter will fall into one of four categories defined by their eccentricity:

    Circular orbit e=0 In this orbit, the radius scalar and speed remain constant throughout and the velocity is always perpendicular to the radius vector.

    Elliptical orbit 0<e<1 This orbit is elongated giving a point nearest to the attractor (periapsis) and a point furthest from the attractor (apoapsis). The further away from the attractor the orbiter is, the slower it moves.

    Parabolic orbit e=1 This orbit is the minimum escape orbit. It is an ellipse of such elongation that the apoapsis is at infinite and the outbound speed only drops to zero when the orbiter reaches infinite.

    Hyperbolic orbit 1<e This orbit is an escape orbit that leaves the orbiter with leftover speed once it reaches infinite. Mathematically, there are two branches to the hyperbola, but the other one has little physical significance.

    In the three body problem, things get screwy.

    NB the seasons aren't caused by the eccentricity of Earth's orbit. The eccentricity is minimal.

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    Quote Originally Posted by Ut
    Just thought of something. A circle is an ellipse of eccentricity 0. Drop another category!
    A parabola is an ellipse of eccentricity = 1.
    A hyperbola is an ellipse of eccentricity > 1.

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    Quote Originally Posted by NZborngal
    Circular Orbit: A perfect circle-I believe only Venus or Mercury has this kind of orbit.
    Most of the planets have orbits with reasonably low eccentricities. Here is a quick table just to get an idea

    Mercury - .2056
    Venus - .0068
    Earth - .0167
    Mars - .0934
    Jupiter - .0483
    Saturn - .0560
    Uranus - .0461
    Neptune - .0097
    Pluto - .2482

    From that you can see that Mercury and Pluto have rather eccentric orbits, while the others are mostly circular with some variation.

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    Quote Originally Posted by Kaptain K
    Quote Originally Posted by Ut
    Just thought of something. A circle is an ellipse of eccentricity 0. Drop another category!
    A parabola is an ellipse of eccentricity = 1.
    A hyperbola is an ellipse of eccentricity > 1.
    No, a parabola is not an ellipse. A parabola is a conic section, of eccentricity = 1. Similarly, for hyperbola.

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    Quote Originally Posted by hendy
    There's also the 'horseshoe' type of orbit, as for the asteroid Cruithne. From the website:
    "The near-Earth asteroid 3753 Cruithne is in an unusual orbit about that of the Earth, one which is known in the lingo of celestial mechanics as being co-orbital with the Earth (meaning it shares the Earth's orbit with it) and, more particularly, as being of the "horseshoe" type."
    I was hoping someone would mention this one. Your site's animation is quite good at showing it's orbital path. It's 'horshoe' appearance is only as seen from Earth. It is an ellipitcal orbit that varies from Mercury's orbit to beyond Earth's. It's inclination and synchronization, apparently, keeps it (and others reportedly) stable. Quite impressive.
    We know time flies, we just can't see its wings.

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    What about a Kempler rosette(sp?). Is it stable?

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    Quote Originally Posted by A Thousand Pardons
    Quote Originally Posted by Kaptain K
    Quote Originally Posted by Ut
    Just thought of something. A circle is an ellipse of eccentricity 0. Drop another category!
    A parabola is an ellipse of eccentricity = 1.
    A hyperbola is an ellipse of eccentricity > 1.
    No, a parabola is not an ellipse. A parabola is a conic section, of eccentricity = 1. Similarly, for hyperbola.
    But in projective geometry, they're all the same.
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    I suppose if I really wanted to I could sit down and crunch the numbers for it, but I'm just too damn lazy - does anyone know if a "rose" orbit is possible under any circumstances? For an idea of what I mean, look at the graph for cos(3θ) in polar coordinates. (Of course, an actual orbit of this type wouldn't intersect the origin - it would just pass really close to it.) Even if such an orbit were to exist, I tend to think it would be extremely unstable, and probably decay into an ellipse fairly quickly, or become hyperbolic and separate.

    Hopefully people have graphing calculators nearby to see what I mean...

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    Does Mercury's orbit precess enough to be considered a "rose"?

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    Re: Types of orbits

    Quote Originally Posted by Glom
    The two body problem involves a large mass attractor and a small mass orbiter.
    The solutions to the two body problem are trivially generalized to any ratio of masses, including equal masses. They both will follow conic section orbits with a focus at their mutual center of mass. The same formulas apply, except with the reduced mass, mu = m_1*m_2/(m_1 + m_2), substituted for the objects' masses.

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    Quote Originally Posted by Ut
    Does Mercury's orbit precess enough to be considered a "rose"?
    I guess it depends on what you mean by a rose! The total precession of Mercury is about 1.5 degrees in a century (415 orbits), so I'd say not really.

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    Quote Originally Posted by ToSeek
    But in projective geometry, they're all the same.
    Depends upon what you mean by "same"
    Quote Originally Posted by Ut
    Does Mercury's orbit precess enough to be considered a
    "rose"?
    5600 arcseconds per century (about a degree and a half, as I see chiaroscuro25 says), with an orbital period of 88 days so it moves 13.5 arcseconds each orbit. That's a bit less than the width of the main body of Saturn, as seen from Earth.

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    Yeah, I'd count that. It's really more of a daisy, though.

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    Quote Originally Posted by Ut
    Yeah, I'd count that.
    Then they all do!

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    Of course they all do, but let's not get carried away here. A flower can only have so many pedals before it enters the realm of self-parody

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    Well, Mercury's orbit has 96056 petals then, which seems excessive to me!

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    Quote Originally Posted by Ut
    Of course they all do, but let's not get carried away here. A flower can only have so many pedals before it enters the realm of self-parody
    You're the one that said a flower with 96000 (360*60*60/13.5) petals was a daisy.

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    Quote Originally Posted by RoboSpy
    I suppose if I really wanted to I could sit down and crunch the numbers for it, but I'm just too damn lazy - does anyone know if a "rose" orbit is possible under any circumstances? For an idea of what I mean, look at the graph for cos(3θ) in polar coordinates. (Of course, an actual orbit of this type wouldn't intersect the origin - it would just pass really close to it.) Even if such an orbit were to exist, I tend to think it would be extremely unstable, and probably decay into an ellipse fairly quickly, or become hyperbolic and separate.

    Hopefully people have graphing calculators nearby to see what I mean...
    Rose orbits (and their relatives, boxes and tubes) are the general rule when dealing not with a small massive object and insignificant companion, but stellar orbits in a distributed mass distribution. Even for something like the Sun, you have an orbit whose periods of radial and "vertical" oscillation about the mean sort-of circle have different periods. And for barred galaxies, you can have odd repeating stellar orbits that have a little backwards loop at either end (at least in the rotating bar frame of reference in which te orbit repeats). That doesn't work more thasn once for clouds of interstellar gas, though.

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    Wouldn't a figure-8 orbit be considered a "Chaotic" orbit. Aren't there Chaotic orbits that are stable around a 2-mass attractor?

    I thought I remember hearing about that from some science show years ago.

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    Quote Originally Posted by A Thousand Pardons
    Quote Originally Posted by Ut
    Of course they all do, but let's not get carried away here. A flower can only have so many pedals before it enters the realm of self-parody
    You're the one that said a flower with 96000 (360*60*60/13.5) petals was a daisy.
    Mercury's aphelion distance is 69,800,000 km. So petal tips are 4570 km apart. Mercury's diameter is slightly more than that, so... draw your own picture.

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