About

Neptune possesses 16 confirmed natural satellites. Their orbits range from a = 48,227 km (Naiad) to 49,285,000 km (Neso). This simulator solves Kepler's equation at each frame to compute true orbital positions, accounting for eccentricity e and inclination i. A simple two-body approximation is used. Perturbations from other moons, solar radiation pressure, and Neptune's oblateness (J₂) are not modeled. For irregular satellites with high eccentricities (e > 0.4), the rendered ellipse shape is accurate, but long-term orbital evolution (precession, Kozai-Lidov oscillations) is omitted.

Triton is the only large moon and orbits retrograde (inclination ≈ 157°), indicating capture origin. Its tidal interaction is causing slow inspiral. The remaining moons divide into regular prograde inner moons and irregular outer satellites on highly eccentric, inclined orbits. Orbital radii are displayed on a logarithmic scale to keep all 16 moons visible simultaneously. Moon disc sizes use log-scaling relative to Triton's diameter of 2,707 km.

Formulas

Each moon's position is computed by solving Kepler's equation at every animation frame. Given mean anomaly M advancing linearly with time, eccentric anomaly E is found iteratively.

M = E − e ⋅ sin(E)

This 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 from E:

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

Radial distance r from Neptune:

r = a ⋅ 1 − e²1 + e ⋅ cos(ν)

The 2D projection applies inclination as vertical offset: y_offset = r ⋅ sin(i) ⋅ sin(ν). Orbital radii are log-scaled: r_display = log₁₀(a) mapped linearly to canvas radius range.

Where: M = mean anomaly rad, E = eccentric anomaly rad, e = eccentricity (dimensionless), ν = true anomaly rad, a = semi-major axis km, i = orbital inclination rad, r = radial distance km.

Reference Data

Moon	Semi-Major Axis km	Period days	Eccentricity	Inclination °	Diameter km	Year	Group
Naiad	48,227	0.294	0.0004	4.75	58	1989	Inner
Thalassa	50,075	0.311	0.0002	0.21	82	1989	Inner
Despina	52,526	0.335	0.0002	0.07	150	1989	Inner
Galatea	61,953	0.429	0.0001	0.05	176	1989	Inner
Larissa	73,548	0.555	0.0014	0.20	194	1981	Inner
Hippocamp	105,283	0.950	0.0005	0.06	18	2013	Inner
Proteus	117,647	1.122	0.0005	0.08	420	1989	Inner
Triton	354,759	5.877	0.0000	156.87	2,707	1846	Major (retrograde)
Nereid	5,513,818	360.14	0.7507	7.23	340	1949	Irregular
Halimede	16,611,000	1879.1	0.2646	112.90	62	2002	Irregular
Sao	22,228,000	2912.7	0.1365	53.48	44	2002	Irregular
Laomedeia	23,567,000	3171.3	0.3969	37.87	42	2002	Irregular
Psamathe	48,096,000	9074.3	0.3809	126.31	40	2003	Irregular
Neso	49,285,000	9541.0	0.5714	136.44	60	2002	Irregular

Frequently Asked Questions

Neptune's moon system spans from Naiad at 48,227 km to Neso at 49,285,000 km - a ratio exceeding 1,000∶1. A linear scale would render all seven inner moons as a single indistinguishable dot near Neptune's center while Neso would sit at the canvas edge. Logarithmic scaling compresses this range, preserving the relative ordering while making every orbit visually distinct.

Nereid has an eccentricity of e = 0.7507, the highest of any known planetary moon. This means its distance from Neptune varies from periapsis a(1 − e) ≈ 1,372,000 km to apoapsis a(1 + e) ≈ 9,655,000 km. The rendered ellipse is visibly elongated, and the moon speeds up dramatically near periapsis per Kepler's second law.

Triton's orbital inclination is 156.87°, meaning it orbits retrograde. This is strong evidence that Triton was captured from the Kuiper Belt rather than forming in situ. No prograde capture mechanism produces inclinations above 90°. In the animation, Triton visibly moves clockwise while prograde inner moons move counterclockwise. Tidal dissipation is slowly decaying Triton's orbit; in approximately 3.6 billion years it will cross Neptune's Roche limit and disintegrate.

This simulator treats each moon as orbiting Neptune in a pure Keplerian two-body problem. It ignores gravitational perturbations between moons (particularly Triton's influence on inner moons), Neptune's oblateness coefficient J₂ = 0.003411 which causes nodal precession, solar tidal forces on irregular satellites, and radiation pressure effects on small bodies. For the inner moons these omissions are minor over short timescales. For irregular satellites like Neso (period ≈ 26 years), precession and Kozai-Lidov oscillations would significantly alter the orbit over centuries.

The code uses Newton-Raphson iteration starting from the initial guess E₀ = M. Each iteration applies the update E_n+1 = E_n − (E_n − e sin E_n − M) ÷ (1 − e cos E_n). Ten iterations are performed, which converges to machine precision for all eccentricities below 0.8. For Nereid (e ≈ 0.75) this remains adequate.

At 1× speed, 1 second of animation corresponds to approximately 0.5 Earth days. Inner moons (periods under 1 day) orbit visibly fast. Outer irregulars (periods of years to decades) require the 100× speed setting to observe meaningful orbital progress. The speed slider ranges from 0.1× to 500×.