About

Earth completes one orbit around the Sun every 365.256 days along an elliptical path with eccentricity e = 0.0167. The semi-major axis measures 149.598 million km (1 AU). A miscalculation of orbital parameters historically led to navigation errors of hundreds of kilometers for interplanetary missions. This tool renders Earth's orbit (and the inner planets) using Kepler's equation solved via Newton-Raphson iteration, projecting 3D positions onto a 2D canvas through perspective transformation. Axial tilt of 23.44° is visualized. All orbital elements use IAU/JPL reference values.

Limitations apply: perturbations from Jupiter and other giant planets are not modeled. Precession of perihelion (11.45″/yr) is omitted. Orbits are treated as fixed Keplerian ellipses, accurate to within 0.1% over a single orbital period but divergent over geological timescales. Planet sizes are exaggerated for visibility; true scale would render them invisible at orbital distances.

Formulas

Planetary position at time t requires solving Kepler's equation for the eccentric anomaly E:

M = E − e ⋅ sin(E)

where M is the mean anomaly computed as M = 2πT ⋅ t, T is the orbital period, and e is eccentricity. Newton-Raphson iteration solves for E:

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

The true anomaly ν is then derived:

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

The radial distance r from the focus:

r = a ⋅ (1 − e ⋅ cos(E))

3D perspective projection maps world coordinates to screen:

x_screen = x ⋅ fz + f , y_screen = y ⋅ fz + f

where f is the focal length (field of view parameter), a = semi-major axis, e = orbital eccentricity, T = orbital period, M = mean anomaly, E = eccentric anomaly, ν = true anomaly, r = heliocentric distance.

Reference Data

Planet	Semi-Major Axis (AU)	Eccentricity	Orbital Period (days)	Inclination (°)	Axial Tilt (°)	Mean Radius (km)	Perihelion (AU)	Aphelion (AU)
Mercury	0.387	0.2056	87.97	7.00	0.03	2,439.7	0.307	0.467
Venus	0.723	0.0068	224.70	3.39	177.36	6,051.8	0.718	0.728
Earth	1.000	0.0167	365.26	0.00	23.44	6,371.0	0.983	1.017
Mars	1.524	0.0934	686.97	1.85	25.19	3,389.5	1.381	1.666
Jupiter	5.203	0.0489	4,332.59	1.30	3.13	69,911	4.950	5.457
Saturn	9.537	0.0565	10,759.22	2.49	26.73	58,232	9.021	10.054
Uranus	19.191	0.0457	30,688.50	0.77	97.77	25,362	18.324	20.078
Neptune	30.069	0.0113	60,182.00	1.77	28.32	24,622	29.710	30.441
Moon (Earth)	0.00257	0.0549	27.32	5.14	6.68	1,737.4	0.00243	0.00271
Ceres (dwarf)	2.768	0.0758	1,682.00	10.59	4.00	473	2.558	2.977
Pluto (dwarf)	39.482	0.2488	90,560.00	17.16	122.53	1,188.3	29.658	49.305
Halley's Comet	17.834	0.9671	27,510.00	162.26	-	5.5	0.586	35.082

Frequently Asked Questions

Mercury has an eccentricity of 0.2056, meaning its distance from the Sun varies by about 52% between perihelion and aphelion. Earth's eccentricity is only 0.0167, producing a variation of roughly 3.4%. At visual scale, Earth's orbit is indistinguishable from a circle. The animation preserves these real eccentricity values.

For a single orbital period, Kepler's equation yields positions accurate to within 0.1% of JPL ephemeris data. Over centuries, accumulated perturbations from Jupiter (which shifts Earth's eccentricity between 0.000055 and 0.0679 on Milankovitch cycles of ~100,000 years) cause divergence. For educational visualization, unperturbed Keplerian motion is standard practice.

At true scale, Earth (6,371 km radius) orbiting at 149.6 million km would be a dot smaller than 0.004 pixels on any screen. Planet radii are exaggerated by a factor of approximately 500-2000× to remain visible. The orbital distances and shapes remain proportionally accurate.

The 23.44° axial tilt is rendered as an angled rotation axis on the Earth sphere. In reality, this tilt relative to the orbital plane causes seasons. The obliquity oscillates between 22.1° and 24.5° over a 41,000-year cycle. This tool uses the current J2000 epoch value.

For elliptical orbits (e < 1), Newton-Raphson converges in 3-5 iterations when initialized with E₀ = M. The function f(E) = E − e⋅sin(E) − M is monotonically increasing for e < 1, ensuring a unique root. The implementation uses a tolerance of 1×10⁻⁸ radians.

The visualization focuses on the inner solar system (Mercury through Mars) to maintain useful visual resolution. Including Jupiter at 5.2 AU would compress the inner orbits to a tiny cluster at center. The reference table includes all planets for data completeness. Zoom controls allow exploring the displayed orbital region in detail.