About

Neptune completes one orbit every 164.8 Earth years at a mean distance of 30.07 AU from the Sun. Its orbital eccentricity is only 0.0086, making it nearly circular, yet even this slight deviation produces a perihelion - aphelion difference of roughly 0.52 AU (77.8 million km). This tool solves Kepler's equation M = E − e ⋅ sin(E) via Newton-Raphson iteration for each planet at every frame, converting mean anomaly to true anomaly and computing heliocentric distance from the conic equation. Planetary data (semi-major axes, eccentricities, orbital periods, mean longitudes at J2000.0) are sourced from NASA planetary fact sheets. The simulation does not use circular approximations.

Orbital mechanics errors compound quickly. A circular approximation for Mercury (eccentricity 0.2056) misplaces it by up to 12 million km. This tool preserves elliptical geometry for all eight planets and renders relative motion at adjustable timescales. Planet sizes are exaggerated for visibility. Distances use logarithmic scaling by default because Neptune is 77 times farther from the Sun than Mercury. Linear scaling is available but compresses the inner system to a single pixel.

Formulas

Each planet's position is computed by solving Kepler's equation at every animation frame. The mean anomaly M advances linearly with time:

M(t) = M₀ + 2πT ⋅ t

where M₀ is the mean anomaly at epoch J2000.0 and T is the orbital period. The eccentric anomaly E is obtained from Kepler's equation:

M = E − e ⋅ sin(E)

This transcendental equation is solved iteratively using Newton-Raphson: E_n+1 = E_n − E_n − e ⋅ sin(E_n) − M1 − e ⋅ cos(E_n), converging to machine precision in 5-10 iterations. The true anomaly ν is then:

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

The heliocentric distance r follows from the conic equation:

r = a(1 − e²)1 + e ⋅ cos(ν)

where a = semi-major axis (AU), e = orbital eccentricity, T = sidereal period (yr), t = elapsed time (yr), ν = true anomaly (rad).

Reference Data

Planet	Semi-Major Axis (AU)	Eccentricity	Orbital Period (yr)	Mean Motion (°/yr)	Inclination (°)	Perihelion (AU)	Aphelion (AU)
Mercury	0.3871	0.2056	0.2408	1494.7	7.00	0.307	0.467
Venus	0.7233	0.0068	0.6152	585.2	3.39	0.718	0.728
Earth	1.0000	0.0167	1.0000	360.0	0.00	0.983	1.017
Mars	1.5237	0.0934	1.8809	191.4	1.85	1.381	1.666
Jupiter	5.2034	0.0485	11.862	30.35	1.31	4.950	5.457
Saturn	9.5371	0.0542	29.457	12.22	2.49	9.020	10.054
Uranus	19.1913	0.0472	84.021	4.28	0.77	18.286	20.097
Neptune	30.0690	0.0086	164.8	2.18	1.77	29.81	30.33
Pluto (dwarf)	39.4821	0.2488	247.9	1.45	17.16	29.66	49.31
Halley's Comet	17.834	0.9671	75.32	4.78	162.26	0.586	35.082
Ceres (dwarf)	2.7675	0.0758	4.600	78.26	10.59	2.558	2.977

Frequently Asked Questions

Mercury's eccentricity is 0.2056, meaning its aphelion distance is 52% greater than its perihelion. Neptune's eccentricity is only 0.0086, producing a perihelion-to-aphelion ratio of roughly 1.017. The elliptical shape is geometrically present but imperceptible at typical zoom levels. Switch to Neptune Focus preset and enable orbit lines to observe the slight offset of the Sun from Neptune's orbital center.

This tool uses a two-body Keplerian model with fixed orbital elements at J2000.0. It does not account for gravitational perturbations from other planets, general relativistic precession, or time-varying elements. For Neptune, positional error grows at roughly 0.01° per century due to Jupiter and Saturn perturbations. For educational and visualization purposes, the accuracy is sufficient. For mission planning, use JPL Horizons.

Neptune orbits at 30.07 AU while Mercury orbits at 0.387 AU, a ratio of 77.7. On a linear scale, if Neptune's orbit fills the screen, Mercury's entire orbit fits inside a 5-pixel circle. Logarithmic scaling compresses the outer distances while expanding the inner system, making all orbits simultaneously visible. Toggle to linear mode to see the true scale disparity.

At 1x speed, one second of animation equals one Earth year. At 10x, one second equals 10 years. Neptune completes a full orbit in 164.8 seconds at 1x, or 16.5 seconds at 10x. The elapsed time counter displays years since J2000.0 (January 1, 2000, 12:00 TT).

Pluto's orbital eccentricity is 0.2488, giving it a perihelion of 29.66 AU, which is less than Neptune's semi-major axis of 30.07 AU. Between 1979 and 1999, Pluto was actually closer to the Sun than Neptune. The two never collide because Pluto's orbit is inclined 17.16° to the ecliptic and they are in a 3:2 mean-motion resonance.

No. The Sun's radius is 0.00465 AU. Even Jupiter, the largest planet, has a radius of 0.000477 AU. At any zoom level that shows Neptune's orbit, all planets would be sub-pixel. Planet radii are exaggerated by a factor shown in the info panel. The relative planet sizes to each other are approximately preserved.