✶ Planetarium

Built by Claude Fable 5, an AI model by Anthropic — every orbital calculation, line of code, and pixel on this page was generated by the model.

Sun, Moon & five planets from Keplerian elements — no libraries, no network, no data files.

Step time:

Chart size Planet size Star names scroll / pinch to zoom · drag to pan · double-click resets

Horizon = outer circle, zenith = center. You are lying on your back looking up with your head toward North, so East appears on the left. Azimuth: N = 0°, E = 90°, measured clockwise from true North. Altitude is geometric — no atmospheric refraction. Background stars are real: the 57 brightest stars, plotted from catalog positions.

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Date, time & place

Date (1900–2100)

Local clock time at the location

Location

Latitude (−90 to 90)

Longitude (−180 to 180, east +)

UTC offset (hours, e.g. −5)

Tip: search “my coordinates” on Google to find your latitude and longitude. Custom mode uses the fixed UTC offset you enter — daylight saving is not applied automatically.

Calculation inputs in use

Location—

Coordinates—

Local time entered—

UTC offset applied—

UTC date & time—

Julian Date (UT)—

Positions — equinox of date

Body	RA	RA (°)	Dec	Azimuth	Altitude	Horizon

Methods & stated simplifications

Planets (Mercury–Saturn) & Earth: JPL/Standish J2000 mean Keplerian elements with secular rates (the 1800–2050 table, extrapolated through 2100 — accuracy degrades slightly after 2050). Kepler’s equation solved by Newton iteration; heliocentric vectors differenced for geocentric positions. Earth is approximated by the Earth–Moon barycenter (≤ 0.01° effect). Planetary light-time and aberration neglected (≤ ~0.06°).
Sun: Meeus low-accuracy solar theory (mean longitude, equation of center to sin 3M) with the −0.0057° aberration constant. Accuracy ≈ 0.01°.
Moon: truncated ELP-style series after Meeus ch. 47 — 30 longitude terms, 20 latitude terms, 26 distance terms, the E eccentricity damping factor, and the A1/A2/A3 planetary & flattening additive terms. This includes all principal perturbations: evection (1.27°), variation (0.66°), annual equation (0.19°), and parallactic terms. Truncation error ≲ 0.01°. Topocentric parallax is applied to the Moon’s altitude (up to ~1°); Sun/planet parallax (≤ 0.0024°) ignored.
Reference frame: RA/Dec are for the equinox of date (J2000 planetary positions precessed via general precession in ecliptic longitude, 1.39697°/century). Nutation (≤ 0.005°) ignored. Altitude is geometric — no refraction (adds ~0.5° at the horizon in real skies).
Time: local clock time is converted to UTC with the selected city’s IANA time zone rules including DST (via the browser’s built-in zone database); custom coordinates use your fixed offset. ΔT (TT−UT) from the Espenak–Meeus piecewise polynomials; UT≈UTC assumed (< 0.9 s).
Moon phase: illumination k = (1 − cos ψ)/2 from the geocentric Sun–Moon elongation ψ — the Sun is treated as infinitely distant (error < 0.3% of k).
Stars: the 57 brightest stars (to magnitude ≈ 2.2) plotted from J2000 catalog positions with low-precision precession applied; proper motion (≤ 0.07°/century for these stars) neglected. Every plotted star is named (toggleable in the chart toolbar).

Self-Test running…

Every test below calls the same calculation functions used for the chart and table above. Thresholds: 1° for the Sun and planets, 2° for the Moon, unless a stricter threshold is shown.

Test	Expected	Computed	Difference	Result