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Thread: Why doesn't the earth leave its orbit?

  1. #1 Why doesn't the earth leave its orbit? 
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    I know that the reason that the earth can orbit the sun is that because the earth orbits the sun with the exact speed needed so that its centrifugal force is equal to
    the sun gravitational force.

    But actually, the earth's orbital speed does change, doesn't it? For example, when a meteorite fell to the earth, the meteorite pushed the earth a tiny little bit and the meteorite added the earth's mass a little, because of these "little changes", shouldn't the earth's orbital speed decreases(or maybe increased in some case) and it would not be orbiting the sun with the exact speed it needs to stay in the orbit?


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    Genius Duck Moderator Dywyddyr's Avatar
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    Its orbit ALSO changes a little 1.
    The fact is that to "leave orbit" requires quite substantial speed differences.
    Any lesser change in speed simply alters the radius of that orbit.


    1 Not necessarily from meteor impact, since the added mass/ velocity is almost entirely negligible in terms of orbital speed.


    Last edited by Dywyddyr; August 13th, 2014 at 03:05 PM.
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    Quote Originally Posted by Leonardus View Post
    I know that the reason that the earth can orbit the sun is that because the earth orbits the sun with the exact speed needed so that its centrifugal force is equal to
    the sun gravitational force.
    This isn't actually true, orbits do not rely on an exact balance between gravity and centrifugal force. The only time such a perfect balance could even exist would be for perfectly circular orbits, and such orbits don't exist in nature. All real orbits are elliptical and the planet's speed varies from point to point. You can think of it as a kind of a balance, but not like a pin balanced on its point so that the slightest nudge causes it to fall over, but more like that of a rocking chair. Give it a push and it doesn't fall over but just rocks back and forth. It takes a considerable push to get it to fall backward or forward.

    In the same way, if you give a planet a "push", it will speed and climb away from the Sun. As it climbs, it loses speed, and eventually stops climbing. By this time it is moving slow enough that gravity wins the battle again. This will happen 180 degrees around its orbit from where you gave it the push. It starts falling inward, picking up speed as it does so. By the time it has traveled another 180 degree, its increased speed has stopped its inward fall and it has returned to where you gave it the push, moving at the same speed and direction it was right after you pushed it, and is ready to repeat the same path again
    Basically what happens is that the planet enters a new orbit. One whose average distance from the Sun is greater than it was before the push, and is a bit more elliptical than it was before.

    IF you slow the planet, the new orbit will have a closer average distance.

    To break the planet completely free of the Sun you have to give it enough speed so that the Sun's gravity cannot ever stop its climb away. This is known as escape velocity. For a circular or nearly circular orbit, this works out to be ~42% more than the orbital speed for the planet. ( For elliptical orbits it depends on where you are in the orbit and how elliptical the orbit is).

    To cause a planet to crash into the Sun, you have to change its orbit so that its nearest approach to the Sun (Called the perihelion) is actually below the surface of the Sun. This actually take a larger change in the velocity of the planet than getting it to escape the Sun does. ( Meaning that it is actually easier to make a planet leave the solar system than to make it fall into the Sun.)


    So any nudges we might get from meteorites and such might slightly alter the Earth's orbit a tiny bit, but they are far too small to cause the Earth to leave orbit around the Sun.
    "Men are apt to mistake the strength of their feelings for the strength of their argument.
    The heated mind resents the chill touch & relentless scrutiny of logic"-W.E. Gladstone


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  5. #4  
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    Quote Originally Posted by Janus View Post
    Quote Originally Posted by Leonardus View Post
    I know that the reason that the earth can orbit the sun is that because the earth orbits the sun with the exact speed needed so that its centrifugal force is equal to
    the sun gravitational force.
    This isn't actually true, orbits do not rely on an exact balance between gravity and centrifugal force. The only time such a perfect balance could even exist would be for perfectly circular orbits, and such orbits don't exist in nature. All real orbits are elliptical and the planet's speed varies from point to point. You can think of it as a kind of a balance, but not like a pin balanced on its point so that the slightest nudge causes it to fall over, but more like that of a rocking chair. Give it a push and it doesn't fall over but just rocks back and forth. It takes a considerable push to get it to fall backward or forward.

    In the same way, if you give a planet a "push", it will speed and climb away from the Sun. As it climbs, it loses speed, and eventually stops climbing. By this time it is moving slow enough that gravity wins the battle again. This will happen 180 degrees around its orbit from where you gave it the push. It starts falling inward, picking up speed as it does so. By the time it has traveled another 180 degree, its increased speed has stopped its inward fall and it has returned to where you gave it the push, moving at the same speed and direction it was right after you pushed it, and is ready to repeat the same path again
    Basically what happens is that the planet enters a new orbit. One whose average distance from the Sun is greater than it was before the push, and is a bit more elliptical than it was before.

    IF you slow the planet, the new orbit will have a closer average distance.

    To break the planet completely free of the Sun you have to give it enough speed so that the Sun's gravity cannot ever stop its climb away. This is known as escape velocity. For a circular or nearly circular orbit, this works out to be ~42% more than the orbital speed for the planet. ( For elliptical orbits it depends on where you are in the orbit and how elliptical the orbit is).

    To cause a planet to crash into the Sun, you have to change its orbit so that its nearest approach to the Sun (Called the perihelion) is actually below the surface of the Sun. This actually take a larger change in the velocity of the planet than getting it to escape the Sun does. ( Meaning that it is actually easier to make a planet leave the solar system than to make it fall into the Sun.)


    So any nudges we might get from meteorites and such might slightly alter the Earth's orbit a tiny bit, but they are far too small to cause the Earth to leave orbit around the Sun.
    The above is a beautiful post.
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    Quote Originally Posted by Leonardus View Post
    I know that the reason that the earth can orbit the sun is that because the earth orbits the sun with the exact speed needed so that its centrifugal force is equal to
    the sun gravitational force.

    But actually, the earth's orbital speed does change, doesn't it? For example, when a meteorite fell to the earth, the meteorite pushed the earth a tiny little bit and the meteorite added the earth's mass a little, because of these "little changes", shouldn't the earth's orbital speed decreases(or maybe increased in some case) and it would not be orbiting the sun with the exact speed it needs to stay in the orbit?

    A simpler way to describe what Janus just did is to say that so long as the total energy of a planet in orbit remains less than zero then the planet will orbit the sun. Adding energy or taking away energy in the way you described only changes the kinetic energy. If energy is removed then it's more tightly bound in orbit than it was before. If energy is put in then it's less tightly bound and has more energy to escape then it did before. The eccentricity of the orbit describes how elliptical the orbit is.

    If the energy is negative and the eccentricity of the orbit is zero then the orbit is a circle.
    If the energy is negative and the eccentricity of the orbit is between 0 and 1 then the orbit is an ellipse.
    If the energy is zero and the eccentricity is 1 then the orbit is a parabola.
    If the energy is greater than zero and the eccentricity greater than 1 then the orbit is a hyperbola.

    So adding or taking away energy merely changes which kind of orbit the plant is in. I hope that helped.
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    Janus, that was an exceptionally coherent explanation. I wish you would consider writing a few pop science books. Just to merely collate your contributions to-date would be a few exciting books in themselves.
    Quidquid latine dictum, altum videtur
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    I woulld only add that planetary systems are usually complex systems which the n-body problem describes.
    The math is complicated nonlinear and interdependant.
    The results are not easily predictable, if they are even predictable.
    Stable solutions are scarce.
    In truth even one odd perturbation in one iteration would be enough for any of the planetary orbits, maybe all of them, to escape to infinity.

    I suppose I could say that Earth stays in its orbit because the Sun is an attractor and the whole system is chaotic.
    (I will likely be ridiculed for these comments too)

    Three-body problem - Wikipedia, the free encyclopedia
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    Quote Originally Posted by dan hunter
    I woulld only add that planetary systems are usually complex systems which the n-body problem describes.
    The problem with that argument is that argument assumes that the gravitational force between the three bodies can't be ignored whereas in real life they can.
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  10. #9  
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    Quote Originally Posted by physicist View Post
    Quote Originally Posted by Leonardus View Post
    I know that the reason that the earth can orbit the sun is that because the earth orbits the sun with the exact speed needed so that its centrifugal force is equal to
    the sun gravitational force.

    But actually, the earth's orbital speed does change, doesn't it? For example, when a meteorite fell to the earth, the meteorite pushed the earth a tiny little bit and the meteorite added the earth's mass a little, because of these "little changes", shouldn't the earth's orbital speed decreases(or maybe increased in some case) and it would not be orbiting the sun with the exact speed it needs to stay in the orbit?

    A simpler way to describe what Janus just did is to say that so long as the total energy of a planet in orbit remains less than zero then the planet will orbit the sun. Adding energy or taking away energy in the way you described only changes the kinetic energy. If energy is removed then it's more tightly bound in orbit than it was before. If energy is put in then it's less tightly bound and has more energy to escape then it did before. The eccentricity of the orbit describes how elliptical the orbit is.

    If the energy is negative and the eccentricity of the orbit is zero then the orbit is a circle.
    If the energy is negative and the eccentricity of the orbit is between 0 and 1 then the orbit is an ellipse.
    If the energy is zero and the eccentricity is 1 then the orbit is a parabola.
    If the energy is greater than zero and the eccentricity greater than 1 then the orbit is a hyperbola.

    So adding or taking away energy merely changes which kind of orbit the plant is in. I hope that helped.
    Fair enough, except that I suspect it may be a bit confusing to the casual reader to invoke "negative" values of energy.

    What you mean, of course, is that, by convention, one often sets the gravitational potential energy at zero when two bodies are infinitely far apart. As they approach one another the gravitational potential energy becomes less and hence increasingly negative relative to that (arbitrarily chosen) zero value convention.
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    Quote Originally Posted by exchemist
    Fair enough, except that I suspect it may be a bit confusing to the casual reader to invoke "negative" values of energy.
    I agree. However, I think it’s better to put the truth out there for the casual reader to struggle with than have them learn it incorrectly because when someone learnssomething incorrectly it becomes very hard for them to give that up later on. Besides, I wasn't aware that our target audience was the casual reader an not the person looking for the answer to this question. Is there a difference?

    Quote Originally Posted by exchemist
    What you mean, of course, is that, by convention, one often sets the gravitational potential energyat zero when two bodies are infinitely far apart. As they approach one anotherthe gravitational potential energy becomes less and hence increasingly negative relative to that (arbitrarily chosen) zero value convention.
    That's quite true, yes.

    Consider also the following - If you have the potential energy as V(r) = -GM/r then no matter what you use as a reference point there will always be places where a particle at rest will have a total energy which is negative. The astute student will pick up on that.
    Last edited by physicist; August 14th, 2014 at 06:02 AM.
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    Quote Originally Posted by physicist View Post
    Quote Originally Posted by dan hunter
    I woulld only add that planetary systems are usually complex systems which the n-body problem describes.
    The problem with that argument is that argument assumes that the gravitational force between the three bodies can't be ignored whereas in real life they can.
    The gravitational effects of more than two bodies are not really being ignored if you still have to deal with calling the effects perturbations and correct for them.

    Fortunately the Sun operates as an attractor and the nonlinearity allows the system to correct for most minor disturbances, much like Dywyddyr and Janus said.
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    Quote Originally Posted by dan hunter
    The gravitational effects of more than two bodies are not really being ignored if you still have to deal with calling the effects perturbations and correct for them.
    That depends on when it needs to be done. If you want to get to the moon then you don't need to know the orbit of Mars. The geometry of the paths that planets move in are ellipses. It's only in rare instances that you need to use perturbations.
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    Quote Originally Posted by Implicate Order View Post
    Janus, that was an exceptionally coherent explanation. I wish you would consider writing a few pop science books. Just to merely collate your contributions to-date would be a few exciting books in themselves.
    Hi IO - without wishing to give Janus a big head, I gotta say I agree. It's the first time I understood it so easily and so clearly.
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    Quote Originally Posted by marcbo View Post

    Hi IO - without wishing to give Janus a big head, I gotta say I agree. It's the first time I understood it so easily and so clearly.
    Hi marcbo. He is a clever fella but better still he is a gifted educator. It's best to call a spade a spade.
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    Well, all I can speak from is from experience, and thus far, I have recieved a profitable reply from him on any issue I might have.

    I'm having some problem making progress on the other thread (relative motion) - as you said, Groundhog Day. But even Groundhog Day had a positive ending. I'll go back to that thread and ask Janus to see if he can sort it out.
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