About

Pluto's system contains five known moons orbiting a barycenter dominated by the Pluto-Charon binary. Charon alone holds 12% of the system mass, making it the largest satellite relative to its primary in the solar system. The four smaller moons - Nix, Hydra, Kerberos, and Styx - occupy near-resonant orbits with period ratios close to 1:3:4:5:6 relative to Charon. Miscalculating orbital eccentricity e or ignoring inclination i produces trajectories that diverge from New Horizons flyby data within days. This tool solves Kepler's equation iteratively for each moon using real IAU orbital elements.

The simulation propagates mean anomaly M forward in time, solves for eccentric anomaly E via Newton-Raphson iteration, then computes true anomaly ν to place each body on its elliptical path. Orbital inclinations are projected onto the viewing plane. Note: this model assumes two-body Keplerian motion per moon and does not account for mutual perturbations between the small moons, which cause chaotic tumbling observed by Hubble. Scale is logarithmically compressed to fit all five orbits on screen simultaneously.

Formulas

Each moon's position is computed from Keplerian orbital elements at each timestep. The mean anomaly advances linearly with time:

M(t) = M₀ + 2πT ⋅ t

Kepler's equation relates eccentric anomaly E to mean anomaly M:

M = E − e ⋅ sin(E)

This transcendental equation is solved via Newton-Raphson iteration:

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

True anomaly ν is then derived:

ν = 2 ⋅ atan2(√1 + e ⋅ sin(E2), √1 − e ⋅ cos(E2))

The radial distance from Pluto is:

r = a ⋅ (1 − e ⋅ cos(E))

Where M = mean anomaly, E = eccentric anomaly, ν = true anomaly, e = orbital eccentricity, a = semi-major axis km, T = orbital period days, t = elapsed time days, r = radial distance km.

Reference Data

Moon	Semi-Major Axis km	Orbital Period days	Eccentricity e	Inclination i °	Diameter km	Discovered	Period Ratio (to Charon)
Charon	19,591	6.387	0.0002	0.080	1,212	1978	1.000
Styx	42,656	20.162	0.0058	0.809	16 × 9	2012	3.157
Nix	48,694	24.855	0.0020	0.133	49.8 × 33.2	2005	3.891
Kerberos	57,783	32.168	0.0033	0.389	19 × 10	2011	5.036
Hydra	64,738	38.202	0.0059	0.242	50.9 × 36.1	2005	5.981
Pluto	0 (center)	-	-	-	2,377	1930	-
Data: IAU / New Horizons mission (NASA/JHUAPL/SwRI). Diameters for irregular moons given as major × minor axes.
Near-resonance chain: Styx:Nix:Kerberos:Hydra ≈ 3:4:5:6 relative to Charon's period.

Frequently Asked Questions

Kepler's third law dictates that orbital period scales as the 3/2 power of semi-major axis. Hydra at 64,738 km has a period of 38.2 days versus Charon's 6.387 days at 19,591 km. The angular velocity decreases with distance. This is physically accurate, not an animation artifact.

Charon's eccentricity is 0.0002, effectively circular. The Newton-Raphson solver converges in 2-3 iterations for such low eccentricities. The visual difference between circular and elliptical paths at this eccentricity is sub-pixel at any practical zoom level, but the math is exact regardless.

The barycenter of the Pluto-Charon system lies outside Pluto's surface, approximately 2,035 km from Pluto's center. This simulation places Pluto at the visual center and orbits all moons around it for clarity. A physically rigorous model would show Pluto wobbling around the barycenter with a 6.387-day period.

The ratios Styx:Nix:Kerberos:Hydra relative to Charon are approximately 3:4:5:6. These near-resonances likely result from the giant impact that formed Charon. Debris in resonant orbits persists longer due to gravitational shepherding. However, these are near-resonances, not exact mean-motion resonances like Jupiter's Galilean moons.

Styx is roughly 16 km across while orbiting at 42,656 km. At true scale, it would be 0.04% of its orbital radius - invisible at any zoom. Moon radii are rendered with a minimum pixel size plus a logarithmic scaling factor to remain visible while preserving relative size differences.

Each moon's inclination (ranging from 0.080° for Charon to 0.809° for Styx) is applied as a foreshortening of the orbit's vertical component via cos(i) and a vertical offset via sin(i). At these small angles the effect is subtle but visible at high zoom, producing slightly tilted ellipses.