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Electric orbit of positronium

  1. May 13, 2004 #1
    Hi there! I hope someone can help me with this problem. I've been working on this for over 5 hours and I've gotten nowhere!

    A positron is a particle with the same mass as an electron but with a positive charge. A positron and an electron can briefly form an unusual atom known as positronium. Imagine a situation where the two particles are in a circular orbit about their center of mass. Since the particles have equal mass, the center of mass is midway between them. Let r be the separation of the particles (so that the orbits are each of radius r/2).

    (a) Show that the orbital period T is related to the separation distance r by:

    T^2 = (16)(pi^3)(E0)(me)(mp) (r^3)
    (e^2)[(me) + (mp)]

    This is a consequence of Kepler's third law for electrical orbits.

    (b) Show that if an electron and a proton are in circular orbits about their center of mass (which is not at the midway point between them but much closer to the proton), then the same expression results.

    * * * * *

    OK, so so far, I'm guessing that I somehow use the formulae:

    q = ne

    F = 1 |Q||q|
    -------- x ---------
    4(pi)(E0) (r^2)

    But I'm not really sure where the rest of it comes from

    If someone could help me out, I would really appreciate it!


  2. jcsd
  3. May 14, 2004 #2
    The bad idea of Keplerian orbits being used aside, if the orbit is indeed a circle, then the force each particle feels must obey the centripetal force equation, F=mv2/r. In this case the centripetal force is the electrostatic force, so they two equations can be set equal to each other.
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