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When will gravity lose its grip?

  1. Jul 21, 2009 #1
    How much mass attraction is necessary for a stone (mass 1 kg) to rotate together with same velocity than the earth?

    I mean in which altitude will the stone will no longer be able to follow the earth’s rotation.

    Do it exist any equation to calculate this?
     
  2. jcsd
  3. Jul 21, 2009 #2
    The second the rock leaves the ground it is no longer following the earth's rotation.
     
  4. Jul 21, 2009 #3
    So when jumping I am not following the Earths rotation ? Really?
    I mean we ignore the atmosphere.

    How can we calculate ?
     
  5. Jul 21, 2009 #4

    Janus

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    Really. The minute you leave the ground, you are following a path independent of the Earth's rotation. You actually follow an orbital path which intersects the surface of the Earth. Even if you jump straight up, you will not come back down exactly where you jumped. For low height jumps, you will not notice any difference, but as you increase the height of the jump the difference will increase.

    It takes some orbital mechanics. First you have to determine the properties of the orbital path you take from the initial speed of your jump and your linear velocity at your latitude due the Earth's rotation. Then you need to calculate the time it takes for you to travel the segment of your orbit from when you left the surface to when it intersects the Earth again. You will also need to calculate how many degrees of on orbit you traveled. Compare this to the number of degrees the Earth turned while you were "in the Air". Use the difference between the two and the radius of the Earth to find the distance between the point you jumped and the point where you landed.
     
  6. Jul 21, 2009 #5

    DaveC426913

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    But do not confuse this with following a path independent of Earth's gravitational pull.
     
  7. Jul 21, 2009 #6

    DavidSnider

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    The earth is rotating at 1000 MPH Right? Obviously, when I jump the ground doesn't move 1000 MPH. I'm guessing that is because because my velocity when I jump is 1000 MPH too? If I were in a stationary position in space and looked at a jet travelling 1000MPH on earth would it appear to be fixed in place?
     
  8. Jul 21, 2009 #7

    DaveC426913

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    Assuming you qualify all those 1000mph's with 'at the equator', and
    assuming the plane was headed East, and
    assuming by 'fixed in place' you mean 'in your line of sight as the Earth turns under it', yes.
     
  9. Jul 21, 2009 #8
    when you feet leave the ground you are veering on a path that is tangentional to the rotating path you were taking when your feet were on the ground which, yes, would be the same as the earth's rotation speed the moment before you jumped. Think of it like you're twirling a weight on a string above your head and then you let go. The thing flies of tangentionally at the speed your were spinning.
     
  10. Jul 21, 2009 #9
    well no, generally when we say that a plane is going 1000mph we're implying that we mean RELATIVE to the surface of the earth.
     
  11. Jul 21, 2009 #10

    DaveC426913

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    Read snider's post #6.

    He is asking if the plane, travelling at 1000mph would remain 'fixed in place' to an observer stationary in space. I am simply pointing out that 'fixed in place' is ambiguous. 'Fixed in place' would normally mean relative to the Earth. In this case, I'm hoping the poster means 'fixed in your line of sight'.
     
  12. Jul 21, 2009 #11

    russ_watters

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    Not unless you jump straight sideways you aren't!

    When you are standing still on the ground, your direction of motion is tangential to the rotating path of the surface of the earth. When you jump, your direction of motion is some angle above the tangent. Not a big angle, but an angle, nonetheless.
     
  13. Jul 21, 2009 #12
    Sorry, my bad. The TANGENTIONAL component, or the component with a projection on the rotation axis of the earth, will be the velocity of the earth's rotation. Your full velocity will include the small vertical jumping velocity as well.
     
  14. Jul 21, 2009 #13

    rcgldr

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    Without the atmoshpere, the stone traveling east at the equator would orbit the earth faster than the earth rotates until it's at an altitude of 35,786 km == 22,236 miles above ground, where the orbital rate would match up with the surface of the earth:

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

    At higher altitudes, it would orbit slower.
     
  15. Aug 22, 2009 #14
    Which law of nature is responsible for that the atmosphere follows the Earth's surface?
    Density off course, - but which equation?
     
  16. Aug 22, 2009 #15

    DaveC426913

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    What?

    The atmosphere is held to the Earth by gravity. It forms a sphere whose shape does not reflect the underlying altitude of the terrain. Just ask the people in Denver Colorado, who live at 5000ft.
     
  17. Aug 22, 2009 #16

    russ_watters

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    I think he's asking why the atmosphere rotates with the earth. There are two ways to look at it, both using Newton's First law:
    1. There is no force that would make the atmosphere stop rotating.
    2. If the atmosphere were not rotating with earth, there'd be aerodynamic drag causing it to speed up and rotate with the earth.
     
  18. Aug 22, 2009 #17
    Right...

    What do you mean: "aerodynamic drag".

    Lets image we could stop the atmosphere rotating, - and push the STOP.
    How fast would it begin to rotate again after pushing START ?

    Does any equation exist to calculate this?
    I mean what happens in higher altitude..
     
  19. Aug 22, 2009 #18

    russ_watters

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    I mean aerodynamic drag! It's the thing that pushes your hand back when you stick it out the window of a moving car.
    If you could "stop" the atmosphere rotating, then the wind speed at ground level near the equator would be about 1000 mph. It would rip anything and everything off the ground, but in so doing, those things would slow the wind down a little. And even after the earth was swept mostly smooth in those first few seconds, there'd be friction between the wind and the ground. A lot of friction. It would take only minutes for the wind at ground level to lose most of that speed. Then viscous friction between molecules in the air would eventually slow the rest of the atmosphere. Would it take days or weeks? I don't know. But it wouldn't be a very long time. It certainly wouldn't be years.
     
  20. Aug 22, 2009 #19
    so what is the difference between earth's rotation and an orbital path?
     
  21. Aug 22, 2009 #20
    I didn't quite understand what you meant by the orbit intersecting with the Earth
     
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