Orbital period vs. diameter

1. Feb 7, 2006

DaveC426913

Is this true?

(excerpted from http://www.astro.uni-bonn.de/~bertoldi/ub313/" [Broken] 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.

Last edited by a moderator: May 2, 2017
2. Feb 7, 2006

Creator

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

Last edited by a moderator: May 2, 2017