Outer Natural Satellites Orbits Ephemerides. Outer satellites of Saturn Choose type of the ephemeride: Trigonometric series for the orbital elements ( a, e, i, ω, Ω) Values of the orbital elements    [ output   e⋅sin(ω),  e⋅cos(ω),  sin(i)⋅sin(Ω),  sin(i)⋅cos(Ω) ] Distances between the osculating orbits Choose Satellite S6 - Phoebe S19 S20 S21 S22 S23 S24 S25 S26 S27 S28 S29 S30 S31 S36 S37 S38 S39 S40 S41 S42 S43 S44 S45 S46 S47 S48 S50 S51 S52 S/2004 S7 S/2004 S12 S/2004 S13 S/2004 S17 S/2006 S1 S/2006 S3 S/2007 S2 S/2007 S3    of Saturn Choose Second Satellite (for the distances) S19 S20 S21 S22 S23 S24 S25 S26 S27 S28 S29 S30 S31 S36 S37 S38 S39 S40 S41 S42 S43 S44 S45 S46 S47 S48 S50 S51 S52 S/2004 S7 S/2004 S12 S/2004 S13 S/2004 S17 S/2006 S1 S/2006 S3 S/2007 S2 S/2007 S3   For the Values and Distances     Enter initial date (years)       Enter final date (years) Enter step of dates (years)   Enter lower limits for amplutudes of semi-major axis Gm        eccentricity          inclination deg.          pericenter deg.                  node deg. Enter upper limit of frequency deg/year At least do not include short-period terms (f > n)