The Grand Orrery · CalculationTime.com Observatory

Sources & method

How positions are computed

Every body in this instrument is placed from a numerical ephemeris, not from an animation curve. Heliocentric state vectors come from Astronomy Engine, which implements the VSOP87 planetary theory with corrections fitted against the JPL DE405 ephemeris, and the Chapront ELP2000-82B lunar theory. Vectors are returned in the equatorial J2000 frame and rotated here into ecliptic coordinates using the IAU obliquity of 23.4392911°, so the solar system is drawn on the plane it actually occupies.

Nothing in this instrument is loaded from a third party at run time. The ephemeris, the renderer, the star catalogue and every surface map are contained in this single file, so it behaves identically offline, behind a strict content-security policy, and in ten years' time.

Rotation phase is taken from the engine's RotationAxis function, which returns the orientation of each body's prime meridian at the requested instant, following the IAU Working Group on Cartographic Coordinates and Rotational Elements. Jupiter's Galilean moons use the engine's own JupiterMoons model; the Moon uses a geocentric vector.

Verification

The ephemeris in this build was checked against three independently known results. The Jupiter–Saturn great conjunction of 21 December 2020 computes to a separation of 5.9 arcminutes against a published value of about 6.1. Earth's 2026 perihelion computes to 4 January at 0.983302 AU and aphelion to 7 July at 1.016646 AU. All eight semi-major axes fall within 0.54% of their IAU values.

Components

Ephemeris Astronomy Engine v2.1.19 — Don Cross. MIT licence. Current release as of this build.
github.com/cosinekitty/astronomy

Rendering three.js r160 — MIT licence.
threejs.org

Surface maps Photographic equirectangular basemaps, embedded in this file. The imagery is NASA and USGS derived — Blue Marble for Earth, Viking and MGS mosaics for Mars, Cassini and Voyager for the outer planets, MESSENGER for Mercury, LRO for the Moon — routed here through the three.js example assets (MIT) and the solar-system-threejs project (Apache 2.0). They are stored as base64 data URIs rather than fetched, so the instrument needs no network, is unaffected by content-security policy, and keeps the export canvas same-origin.

Generated maps Pluto and the four Galilean moons have no photographic map here and are drawn procedurally: albedo fields with a crater population weighted toward small diameters. These are representations, not photographs, and should not be used to identify surface features. The same generator is the fallback for any map that fails to decode.

Ring systems Built from measurement, not from a picture. Saturn's rings span 66,900–136,775 km from the planet's centre, which against an equatorial radius of 60,268 km is 1.110–2.269 Saturn radii — the geometry used here. The D, C, B and A rings, the Cassini Division and the Maxwell, Huygens, Encke and Keeler gaps are each placed at their published radius, with opacities following measured optical depth. Uranus carries its ten narrow rings with the epsilon ring dominant. The planet's shadow is cast across the rings in the shader.

Coastlines Earth's landmasses are real: Natural Earth 1:110m land polygons, public domain, decoded from TopoJSON and simplified to roughly 0.5° tolerance for texture use.
naturalearthdata.com

Star catalogue Bright-star positions in equatorial J2000, with B–V colour indices, drawn from the Yale Bright Star Catalogue lineage.

What is and is not to scale

Body radii and orbital distances cannot both be true on one screen: at true scale Earth is a fifth of a pixel when Neptune is in frame. Both are therefore adjustable, and the badge at the lower left always states which mode is active. Moon orbits are exaggerated in every mode, because the Moon's true separation from Earth is smaller than Earth's drawn radius. The instrument never presents an adjusted view as a true one.

Angles reported in the geometry panel are measured separations in heliocentric ecliptic longitude. They are geometric quantities. This instrument attaches no meaning to them.

Cite this instrument

Limits

Positions are reliable across roughly 1700–2200 CE, the interval over which the underlying theory is fitted. Outside it, accuracy degrades gracefully rather than failing. This is an educational and illustrative instrument; it is not intended for navigation, mission planning, or occultation timing.