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Why don't the moon crash down to earth?

  1. May 16, 2010 #1
    I was reading about how Newton noticed the apple from the apple tree fall down to earth due to the influence of the earth's gravitational force.

    So why don't the moon fall down to earth? Why don't any of the man-made satellites just fall down to earth? Why are they able to stay in orbit around the earth?

    --Sorry if this question has been asked on here earlier, its just that I was not able to find anything like that or maybe I didn't look hard enough--
     
  2. jcsd
  3. May 16, 2010 #2

    diazona

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    The moon is moving sideways, fast enough that by the time it would have fallen down to the Earth's surface, the surface has "curved out" from under it. (At least, that's one way people often explain the connection between falling and orbiting, I don't like it so much myself)

    Same with satellites.

    You could do the same with an apple, in fact, but it'd have to be moving really fast.
     
  4. May 16, 2010 #3


    Thank you for your response diazona.

    You say the moon is moving sideways because we only see one side of the moon, right?

    And I am not sure as to what exactly you mean by "curved out from under it"

    If you could please put it in a much more simpler statement, that would be really helpful because I think my understanding/grasping level is very poor :(
     
  5. May 16, 2010 #4
    Well it doesn't have anything to do with the same side of the moon always facing earth. This is a different phenomenon related to the moon's rotation.

    Think of it this way. You know that the earth is round. You also know that any object you throw will follow a curved path and fall to the ground. If you throw an apple (or any object) fast enough, it will curve so slowly that it's curve will equal the curve of the earth, and it will never get any closer. That's what Diazona means when he says that the earth curves out from under a very fast moving object.
     
  6. May 16, 2010 #5

    russ_watters

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    The earth is round. So if you throw a baseball hard enough, the earth will curve down away from it before it can fall to the ground. So too with a satellite: the satellite is falling toward the earth, but just keeps missing.
     
  7. May 16, 2010 #6


    Thank you for your response arunma.
    So you mean that the moon is revolving around the earth at a speed which dont allow it to fall towards the earth and that speed is what keeps it in orbit around the earth? Why dont that same speed sling it out of orbit away from the earth?
     
    Last edited: May 16, 2010
  8. May 16, 2010 #7

    Thank you for your response russ_waters.

    So what your saying is that if I throw the baseball hard enough it will keep going and will stay in orbit around the earth but will not fall to earth unless acted upon by an external force?

    If so then why does it stay in orbit around the earth? Why don't it just keep going off into space?
     
  9. May 16, 2010 #8

    Fredrik

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    The moon is falling towards Earth all the time, but it has such a high velocity in the direction perpendicular to a line from the moon to Earth that it keeps "missing" Earth.

    If we neglect air resistance, the prediction is that if you throw the ball parallel to ground, with a high enough velocity, but not faster than the escape velocity (about 11 km/s), it will never hit the ground. Its path through space will be an ellipse, so the ball will eventually return to the same point. That's why you have to throw the ball almost exactly parallel to the ground. If you give it a speed that exceeds the escape velocity, it will never come back.

    Of course in the real world, there's air that would slow the ball down, so the ball would eventually hit the ground unless you give it speed that's much higher than the escape velocity. Of course at the speeds we're talking about, the ball would also burn up.
     
  10. May 16, 2010 #9

    russ_watters

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    I'd clarify to say that the moon is falling toward the earth, it's just that it keeps missing because of the sideways velocity.
    It happens to be moving at exactly the right speed to keep it in a nearly circular orbit.
    It does keep falling. It's just that the curvature of the earth means that as the ball "falls", it never gets any closer to the earth!
     
  11. May 17, 2010 #10
    Ok. Thanks a lot all of you.
     
  12. May 17, 2010 #11
    Yup, that's quite right.

    Well it's moving at just the right speed so that its orbit is circular. If it were moving any faster, you might think that it'll slowly drift away. But actually, the orbit of the moon would then become elliptical (sort of egg shaped). In order to drift away, it would have to exceed the earth's escape velocity (which is twice the circular orbital velocity).
     
  13. May 17, 2010 #12

    sophiecentaur

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    I'd like to know why the planets ended up with pretty near circular orbits. After all, there are so many alternatives. Where is the stabilising influence to keep them circular?
    The same effect seems to keep the rings of Saturn stable, too - and that involves huge numbers of tiny objects each affecting the orbits of the others.
     
  14. May 17, 2010 #13
    The moon is escaping the earth, it is spiraling away.
     
  15. May 17, 2010 #14
    Because the solar system formed from a collapsing cloud of gas. This gas cloud was initially rotating in some direction. During collapse, the cloud's rotation "sped up" to conserve angular momentum, and it flattened out into a disk because partilcles arranged in a disk have lower potential energy, and a system usually seeks the lowest level of potential energy as it approaches equilibrium conditions. The circular orbits are a "remnant" of this rotating disk. The entire gas disk was already rotating in a particular direction, so when nodes of overdensities (the beginnings of planets) formed along the disk, they kept revolving around and accumulating mass until they reached planet sizes
     
  16. May 18, 2010 #15

    sophiecentaur

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    OK, as far as it goes but is there a reason why the orbits remain as near-circles? They all definitely interact with each other. Why doesn't this interaction cause wild fluctuations - whilst keeping the angular momentum the same?
    The elements within the original rings were all pulling each other into an assortment of orbits.
    For the planets to have formed, there must have been inelastic collisions, removing some Kinetic Energy (from the mutual GPE between the elements, I think) but maintaining the overall angular momentum (causing the planetoids to spin) and maintaining the orbits of the planetoids around the Sun.
    Something must be different, once the planets get big enough and with enough separation to keep them from interacting enough for the orbits to go wild.
    It's interesting that Pluto, a recent visitor (they say) has a more eccentric orbit than the rest.
     
  17. May 18, 2010 #16

    diazona

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    The planets do interact with each other, but on average, over a long time, the interactions cancel out. Think of it like this: Jupiter might be pulling the Earth away from the sun at one point, but then slightly more than 6 months later, it'll be pulling the Earth back toward the sun, thus undoing the effect of the previous pull away (well, roughly speaking). So over a long period, Jupiter's gravity has a net effect of nearly zero on the Earth's orbit. Same with all the other planets. And fortunately, orbits in 3D space are stable, which means that a slight perturbation (like the slight nonzero effect of Jupiter's gravity) doesn't cause the Earth to fly away into space or crash into the Sun; it just shifts the orbit a bit.

    Incidentally, it is possible to achieve resonance between the orbit of a planet and the gravitational influence of another planet. For instance, if some planet were located at a radius where its orbital period were exactly half, or a third, etc. of Jupiter's period, then the gravitational influence of Jupiter on this planet would not cancel out over the long term. It would build up over time and eventually either throw the planet out into a different orbit, or break it apart. And in fact, if you look at the layout of the solar system, you can see that there are blank areas with virtually no planets or asteroids at the radii corresponding to simple fractions of the orbital period of Jupiter.
     
  18. May 18, 2010 #17

    sophiecentaur

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    So what you're implying is that certain orbit groups will remain stable but others wouldn't and so we don't see them.
    Fairy nuff.
     
  19. May 18, 2010 #18

    rcgldr

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    Getting back to the original question, imagine that the earth was a tiny point in space. At any point in time, the moon is always accelerating towards the earth, with the rate of acceleration = G Mearth / R, where G is gravititational constant, Mearth is the mass of the earth, and R is distance from the center of the earth. (I'm ingoring the fact that the earth is accelerating by a small amount towards the moon). If the moon's speed isn't zero, and it's direction isn't directly towards that tiny point, then it misses that tiny point each time it goes by (assuming an elliptical orbit) by some minimal distance. If this smallest distance away from that point is greater than the actual radius of the earth and it's atmosphere, the moon (or a satellite) will not collide with the earth.

    In the case of some low orbit satellites, they are in the fringes of the atmosphere, enough to eventually slow them down and burn up as they reenter the atmosphere. This is a planned self-destructive orbit (except for skylab where the issue was that the shuttles weren't ready in time to give it a boost to maintain it's orbit).

    In the special case where G Mearth / R = V2 / R, and the direction is of the speed is perpendicular to the direction of gravity, then the orbit is a circle.
     
  20. May 18, 2010 #19

    diazona

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    I guess you could put it that way.
     
  21. May 18, 2010 #20
    Perhaps this will shed some light on what diazona is talking about: http://en.wikipedia.org/wiki/Newton's_cannonball
     
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