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Orbital velocity

  1. Oct 10, 2015 #1
    why orbital velocity of a satellite is independent of mass?
     
  2. jcsd
  3. Oct 10, 2015 #2

    CWatters

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    Have you looked at the maths? Write down the equation for the required centripetal force and for the gravitational attraction that provides it. Equate the two.
     
  4. Oct 11, 2015 #3

    HallsofIvy

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    An "orbit" is just like falling with enough side-ways velocity that you keep "missing" the earth. That does not depend upon mass for the same reason the speed, at any time, of a falling object does not depend upon mass- the gravitational force is a multiple of mass so it cancels out of "F= ma".
     
  5. Oct 12, 2015 #4
    Well, if the satellite's mass is large enough, it's not (independent of mass). For instance, the Moon.
    However, if the satellite's mass is something like 1 ten-billionth of the mass of the body it's orbiting, and another satellite's mass is 5 ten-billionths, then you will see negligible difference in their motion about the body.
     
  6. Oct 12, 2015 #5

    DaveC426913

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    Are you asserting that a small object in the same orbit as the Moon's would orbit at a different speed than the Moon?
     
  7. Oct 12, 2015 #6
    Well, yes. Newton says the force between them (the Earth and whatever) is proportional to the product of their masses. Therefore, the Moon orbits a little faster, in the same orbit than say, a baseball. A basketball's orbit would not be noticeably different from the baseball's.
    What are you saying?
     
  8. Oct 12, 2015 #7

    russ_watters

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    Note that two objects orbit their combined center of mass, which for the Earth-Moon system is 4,671 km from the center of the Earth. So a small object will have an orbit around Earth more centered around Earth's center, have a different distance or radius (pick one) and a different speed.
     
  9. Oct 12, 2015 #8

    Janus

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    Yes. Such an object could orbit as much as ~ 6 m/s slower than the Moon. ( and have a period ~4 hrs longer)
     
  10. Oct 13, 2015 #9

    CWatters

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    Just in case the OP is lost...

    If one of the masses (m2) is very small compared to the other (M1) then the maths simplifies to ..

    Centripetal force = gravitational attraction

    m2v2/r = GM1m2/r2

    M2 cancels which is why V is independent of mass.

    If m2 isn't small then see the last few posts above.
     
  11. Oct 13, 2015 #10

    DaveC426913

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    Yeah, I thought maybe that was the confounding factor.

    I was imagining small objects in simultaneous orbit, ahead of the Moon, being overtaken and swept up by Moon.
     
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