About

Saturn possesses 146 confirmed moons as of 2024. This tool animates the 8 major moons using Keplerian orbital mechanics derived from their real semi-major axes a, orbital periods T, and eccentricities e. Positions are computed by solving Kepler's equation M = E − e sin(E) via Newton-Raphson iteration at each frame. Orbital radii are logarithmically scaled to preserve spatial ordering while keeping all moons visible on screen. The simulation assumes co-planar orbits with minor inclination offsets for visual clarity. It does not model gravitational perturbations, mean-motion resonances between Mimas-Tethys or Enceladus-Dione, or Saturn's oblateness (J₂). For precise ephemeris data, consult JPL Horizons.

Formulas

Each moon's position at simulation time t is computed from Keplerian orbital elements. The mean anomaly advances linearly with time:

M(t) = 2πT ⋅ t

The eccentric anomaly E is found by solving Kepler's equation iteratively using Newton-Raphson:

M = E − e sin(E)

E_n+1 = E_n − E_n − e sin(E_n) − M1 − e cos(E_n)

The true anomaly ν and radial distance r are then:

ν = 2 atan2(√1 + e sin(E/2), √1 − e cos(E/2))

r = a(1 − e cos E)

where M = mean anomaly, E = eccentric anomaly, e = orbital eccentricity, a = semi-major axis km, T = orbital period days, ν = true anomaly, r = radial distance from Saturn's center. Orbital radii are mapped to screen coordinates via logarithmic scaling: r_screen = k ⋅ ln(r_real / r_min).

Reference Data

Moon	Semi-Major Axis km	Orbital Period days	Eccentricity	Inclination °	Diameter km	Discovered	Discoverer
Mimas	185,539	0.942	0.0196	1.574	396	1789	W. Herschel
Enceladus	238,042	1.370	0.0047	0.009	504	1789	W. Herschel
Tethys	294,672	1.888	0.0001	1.091	1,062	1684	G. Cassini
Dione	377,415	2.737	0.0022	0.028	1,123	1684	G. Cassini
Rhea	527,068	4.518	0.0012	0.345	1,528	1672	G. Cassini
Titan	1,221,870	15.945	0.0288	0.348	5,150	1655	C. Huygens
Hyperion	1,481,009	21.277	0.1230	0.615	270	1848	Bond & Lassell
Iapetus	3,560,854	79.322	0.0276	15.47	1,469	1671	G. Cassini
Saturn Ring System
D Ring	66,900 - 74,510	Innermost faint ring
C Ring	74,658 - 92,000	"Crepe Ring" - semi-transparent
B Ring	92,000 - 117,580	Brightest, most opaque ring
Cassini Division	117,580 - 122,170	Gap between B and A rings
A Ring	122,170 - 136,775	Contains Encke Gap
F Ring	140,180	Narrow, braided ring

Frequently Asked Questions

Iapetus orbits at 3.56 million km while Mimas orbits at 185,539 km - a ratio of roughly 19:1. Rendering this linearly would make inner moons invisible. The tool uses logarithmic scaling to preserve orbital ordering while keeping all 8 moons visible simultaneously. The relative positions (which moon is closer to Saturn) remain accurate.

The Newton-Raphson iteration converges to machine precision (below 1e-8 rad) within 6 iterations for all eccentricities encountered in Saturn's major moons. Hyperion has the highest eccentricity at 0.123, which converges in 4 iterations. The solver does not account for gravitational perturbations from other moons or Saturn's oblateness J₂ = 0.01629.

Iapetus has an orbital inclination of 15.47° relative to Saturn's equatorial plane, far higher than any other major moon. This is reflected in the simulation as a visible vertical offset. The other seven major moons orbit within 1.6° of the equatorial plane.

At 1× speed, one real second equals one simulated Earth day. Mimas completes an orbit in under 1 second, while Iapetus takes about 79 seconds. Use the speed slider to adjust from 0.1× to 100×.

The rings are rendered as concentric ellipses matching the real radial extents of the D, C, B, A, and F rings with the Cassini Division gap. Ring opacity approximates real optical depth. However, ring particle dynamics, spokes, and seasonal tilt variations are not modeled.

Titan's semi-major axis is 1,221,870 km, roughly 6.6× that of Mimas. Even with logarithmic scaling, the gap is visible. Titan contains 96% of the mass orbiting Saturn and is the only moon in the solar system with a dense atmosphere (1.5 atm surface pressure, mostly N₂).