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Orbital period vs. diameter

  1. Feb 7, 2006 #1

    DaveC426913

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    Is this true?

    (excerpted from an article about 2003 UB313)

    "...Its very elongated orbit takes it up to 97 times farther from the Sun than is the Earth - almost twice as far as the most distant point of Pluto's orbit – so that it takes twice as long as Pluto to go around the Sun..."

    Is there a direct correlation between orbital diameter and orbital period? I would have thought it would be logarthmic.
     
  2. jcsd
  3. Feb 7, 2006 #2
    Yes there is.....
    but they've made very rough verbal approximations.
    Actually to make orbital period determinations you must use the semi-major axis of the orbit.
    In this case the semi- major axis of UB313 is 67.7 AU compared to Pluto's 39.5 AU. So it is really only 1.7 times as distant as Pluto.

    The orbital period vs. orbital radius (s-m axis) scales as T^2/R^3, (Kepler's law).

    So the period T = sq.rt.(1.7)^3 = 2.25, meaning its orbital period is 2.25 times that of Pluto.
    Since Pluto's orbital period is 248 yrs, then the orbital period of UB313 is about 558 yrs. -- Approximately since all my figures are truncated.

    Creator:biggrin:
     
    Last edited: Feb 7, 2006
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