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Gravity and velocity of a body in an elliptical orbit

  1. Jan 21, 2015 #1

    Suraj M

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    consider a body revolving around a star and having a velocity v when closest to the star ( distance r) then the velocity of the body at a point farthest ( distance R) is?
    1)by angular momentum conservation ::
    r × mv = R× mV
    »V = (r/R).v

    2) By centrifugal and gravitatinal force
    v²/r = GM/r²
    v² α 1/r
    in this we can get V = (r/R)½ v

    the angular momentum method is the right method .... but what am i missing out on from method no. 2??
     
  2. jcsd
  3. Jan 21, 2015 #2

    A.T.

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    That's the centripetal acceleration for circular motion, not elliptical motion in general.
     
  4. Jan 21, 2015 #3

    Suraj M

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    considering a small sector of the particles motion ..can't we use this
    if not then how do we solve this through gravitational force??
     
  5. Jan 21, 2015 #4

    A.T.

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    No.

    Gravitational potential energy vs. kinetic energy?
     
  6. Jan 21, 2015 #5

    Suraj M

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    how'd you do that? Is the sum of the KE and GPE const.?? thats not necessary is it?
     
  7. Jan 21, 2015 #6

    A.T.

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    If M >> m then it's approximately true in the approximately inertial rest frame of M. Otherwise you have to consider the KE of M too.
     
  8. Jan 21, 2015 #7

    Suraj M

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    but in that way i would need the mass of the central body to find V ...and that's not a general case..
     
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