What is the distance between Saturn's moons Polydeuces and Dione, Looking for Kilometers if one was to travel Nearest and farthest based on orbit.

Best I can find:

"Polydeuces can get as close as 39 degrees to Dione and then drift as far as 92 degrees from it, taking over two years to complete its journey around the Lagrange point."

I can't figure this out. What is it in Km?

  • 1
    $\begingroup$ Diona (and Polydeuces) orbit 377000km from Saturn. So you can easily work out how far round the orbit 39 and 92 degrees are, and then get the straight line distance from that if needed. $\endgroup$
    – Rory Alsop
    Commented Feb 11, 2023 at 18:58

1 Answer 1


Polydeuces and Dione are co-orbital, that is they are on the same "track" at 377000km from Saturn

When closest, they are 33.9° (or 33.9×π/180 = 0.188π radians) and so the "distance based on orbit" (the arc length) is $377000\times0.188π=222000km$ and the straight line distance is $2\sin(0.188π/2)\times377000=219000km$.

  • $\begingroup$ I need the drift. That's the near distance. in a regular orbit, This moon 92 degrees from Dione in an elliptical orbit. $\endgroup$
    – PatTracy
    Commented Feb 17, 2023 at 16:17
  • 1
    $\begingroup$ Sorry @PatTracy, I don't understand you. Dione and Polydeuce are both on (near) elliptical orbits, but their eccentricity is so low that the difference would only change the fourth or fifth significant figure. That is I've neglected eccentricity as a circular model gives sufficiently accurate results. I don't know what you mean by "drift". The answer above gives the "nearest distance" For the furthest distance, replace 33.9 by 92 in the calculation above. Please use your own calculator. $\endgroup$
    – James K
    Commented Feb 17, 2023 at 23:33

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