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Homework Help: Orbits of Particle Around a Black Hole using Effective Potential

  1. Apr 27, 2010 #1
    1. The problem statement, all variables and given/known data
    The possible orbit of a particle moving around a black hole can be described using the effective potential UGR(r) (in effect, potential energy per unit mass):

    UGR(r) = -GM/r + l2/2m2r2 - Rsl2/2m2r3

    where the symbols have their usual meaning and in particular Rs = 2GM / c2 is the Schwarzschild radius for the black hole. We then use the energy balance equation

    K = 1/2 mr2 + mUGR = constant

    to illustrate the main features of the possible orbits.

    (a) Show that the function UGR has a minimum and maximum value at r = r- and r = r+ respectively and determine expressions for these qualities.
    (b) Briefly describe the possible orbits.

    2. Relevant equations

    Listed above

    3. The attempt at a solution

    Please help.
  2. jcsd
  3. Apr 27, 2010 #2
    Begin by plotting the effective potential with respect to r and look for turning points.
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