Glossary

The puzzle that ice ages have followed a ~100,000-year rhythm for the past million years, although the eccentricity cycle at that period is far too weak to drive them directly.

1,296,000 arcseconds = 1,440 minutes (our celestial sphere) = 24 hours = 100% of 1 circle or revolution. The sky can be divided into a number of degrees, arcseconds, minutes or hours of RA.

The figure-eight the Sun traces if photographed at the same clock time through a year, shaped by Earth's axial tilt and by the eccentricity of its orbit.

The time between the Moon's passages through perigee, about 27.55 days. Longer than the sidereal month because the line of apsides turns forward, the way the Moon travels.

The time for Earth to return to perihelion, 365.2596350 days. It is set by the ~20,938-year perihelion precession cycle.

The point in an orbit furthest from the Sun, which Earth reaches around 4 July. From Greek ap (away from) + helios (Sun).

The slow turn of Earth's orbital ellipse in its own plane, carrying the perihelion around the sky. Measured against the fixed stars it takes about ~111,635 years.

An orbit's nearest and farthest points — for Earth, perihelion and aphelion. The line joining them is the line of apsides.

The angle, within the orbital plane, from the ascending node round to the point of closest approach, measured along the direction of motion. For a Sun orbit it is the argument of perihelion.

The point where an orbit crosses the reference plane — usually the ecliptic — going south to north. With the descending node opposite it, the two define the line of nodes.

The standard unit of distance for the solar system, fixed by definition at 149,597,870.7 km. It began as Earth's mean distance from the Sun, which is still about what it equals.

The slow westward drift of Earth's spin axis, carrying the equinoxes once around the sky in about ~25,772 years. It is the clock the model's other Earth periods are read against.

The everyday name for obliquity: the angle between Earth's spin axis and the perpendicular to its orbit, 23.439279° today and slowly decreasing.

The shared centre of mass that orbiting bodies circle. For Earth and the Moon it sits about 4,671 km from Earth's centre — inside the Earth, which is why the pair wobbles rather than swings.

A Bayesian synthesis of multi-proxy CO₂ estimates spanning the last 66 million years (CenCO2PIP Consortium, 2023). One of the four proxy records the climate formula is fitted against.

A composite deep-sea benthic isotope record covering the last 66 million years, assembled from many ocean drill cores. It is one of the proxy records the climate formula is fitted against.

An orbit path that forms a perfect circle, with eccentricity = 0. In the framework, the Sun's orbit around the Earth is modelled circular.

The model's reconstruction of Earth's climate record from orbital motion: a set of beat lines whose periods come from the engine, with only their amplitudes fitted to the proxy data.

Three layers: L1, the engine's orbital beat lines; L2, the ~405-kyr carbon thermostat; L3, six steps at Cenozoic boundaries. In the shipped fit L2 rides inside L1, leaving that layer empty.

When a circle rolls around another of equal size it turns once more than expected. This is why Earth rotates one more time than there are days in a year.

When two celestial bodies appear close together in the sky. For an inner planet, inferior conjunction is between Earth and Sun, superior conjunction beyond the Sun.

The 88 official star patterns dividing the celestial sphere, the twelve along the ecliptic forming the zodiac. Axial precession shifts which one sits behind the Sun on a given date.

The moment the Sun reaches its southernmost point, around 21–22 December. In 1246 AD it last coincided with Earth's perihelion, by the IAU mean elements.

Used in astronomy as the celestial equivalent of terrestrial latitude.

ΔT = TT − UT: the gap between Terrestrial Time, on a fixed 86,400-second day, and Universal Time, which tracks Earth's real rotation. It grows as Earth spins slower — ~0 in 1900, ~70 s by 2026.

The point where an orbiting body crosses the reference plane moving from north to south. Together with the ascending node, these two points define the line of nodes.

The time between the Moon's passages through the same orbital node, about 27.21 days. Shorter than the sidereal month because the nodes drift westward to meet it.

The Sun's return to the same lunar node as seen from Earth, about 346.6 days. Eclipses can only happen near a node, so this period sets the eclipse seasons.

A reference point in the simulation, not a physical object: Earth is drawn circling it to produce axial precession. One turn takes about ~25,772 years.

How far an orbit departs from a circle: 0 is a circle, and larger values are more elongated. Earth's is 0.01671 now, and drifts slowly as the other planets pull on its orbit.

The plane of Earth's orbit around the Sun — equivalently, the Sun's apparent yearly path across the sky. It is tilted from Earth's equator by the obliquity.

The turn of Earth's orbital plane on the invariable plane — its nodal mode s₃ — once in about ~68,751 years. Beating against the spin clock, it sets the obliquity cycle.

An Antarctic ice core holding a continuous climate record about 800,000 years long, including trapped CO₂. It is one of the proxy records the climate formula is fitted against.

A moment in time used as the reference for astronomical measurements. Orbital elements are given at an epoch such as J2000, then propagated forward or back.

The difference between sundial time and clock time, from about −14 to +16 minutes across the year. Earth's eccentricity and obliquity cause it, and the analemma plots it.

The great circle around Earth equidistant from both poles. Its projection on the sky, the celestial equator, is the reference plane for Right Ascension and Declination.

The two moments each year (about 21 March and 22 September) when Earth's equatorial plane passes through the Sun's centre. They drift westward along the ecliptic with axial precession.

This model: a Newtonian N-body engine carries the planets' orbits, while Earth's long periods are read as beats against its lunisolar precession clock, which lengthens through geological time.

The time between alignments of the lunar phases with the same orbital configuration: ~411.7664607945 days in ICRF, 411.78 days in the Earth frame.

Einstein's theory of gravity as curvature of spacetime caused by mass and energy, not as a force. Its early proof was Mercury's ~43″/century perihelion anomaly.

A frame of reference of the solar system that puts Earth at the center, and has Sun and Moon orbiting the Earth with other planets revolving around the Sun

The long-term rise in Earth's average surface temperature since the late 19th century. The framework notes that climate also changes naturally on orbital timescales.

The fundamental force of attraction between objects with mass

~~25,772 years — one full axial precession, the old popular name for the precession of the equinoxes. The term traces back to Plato.

Pope Gregory XIII's 1582 reform of the Julian calendar, dropping 3 leap days per 400 years for a mean year of 365.2425 days. The real solar year differs, so the seasons still drift.

A frame with the Sun at the centre and the planets orbiting it — the standard modern model. From Greek helios (sun) + centric (centre).

International Celestial Reference Frame — distant quasars used as fixed reference points for celestial positions and motions. It is inertial: it does not rotate.

The tilt of Earth's orbital plane against the invariable plane, about 1.58° at J2000. It changes as the plane turns on the planets' nodal modes, once in roughly ~68,751 years.

The plane through the solar system's centre of mass, square to its total angular momentum. Unlike the ecliptic it stays essentially fixed, so it is the steady reference for the planets' tilts.

Julian epoch 2000.0 — the standard astronomical reference epoch, 1 January 2000 at 12:00 TT. Positions and motions are quoted against it.

A continuous day count from 1 January 4713 BC at noon UT, giving one unambiguous reference across calendars. The fractional part is the time of day (.0 = noon).

The moment the Sun reaches its northernmost point, around 20–21 June: the longest day in the northern hemisphere and the shortest in the southern.

Kepler's three laws of planetary motion (early 17th century): orbits are ellipses with the Sun at one focus; the Sun-planet line sweeps equal areas in equal times; and T² ∝ a³.

The peak of the last ice age, roughly 26,500 to 19,000 years ago, with sea level about 125 m below today's. Its end coincides with rising obliquity.

Where an orbit's perihelion points, measured along the ecliptic from the March equinox: ϖ = Ω + ω. For Earth it completes a circuit in about ~20,938 years.

A cancelling layer in the Moon's scene: it mirrors the apsidal precession layer in rate and phase with the opposite sign, so the layers beneath it do not inherit that rotation.

The time between successive same lunar phases (new moon to new moon), averaging ~29.53 days. Longer than the sidereal month (~27.32 days) because Earth is also moving along its orbit.

The point in the ~18.6-year nodal cycle when the Moon's declination range is widest (major) or narrowest (minor). Stonehenge and other monuments align to it.

The equinox around 21 March — the vernal or spring equinox in the Northern Hemisphere, the autumn one in the Southern. The neutral name is preferred for that reason.

The shift, about a million years ago, when the dominant glacial rhythm changed from roughly 41,000 years to roughly 100,000. Why it happened is unsettled, and it is a standard test for climate models.

Long-term climate variations driven by changes in Earth's eccentricity, obliquity and precession. Named after Milutin Milanković, who first calculated their effect on climate.

The westward turn of the Moon's orbital plane, one circuit in about 18.6 years. It drives the lunar standstill rhythm and sets when eclipses are possible.

The tilt of Earth's equator against its own orbit, 23.439279° today. It swings between about 22.2° and 24.7° over roughly ~41,099 years.

The principle that where competing hypotheses explain the same observations equally well, the one resting on the fewest assumptions is preferred. Attributed to William of Ockham, 14th century.

When an outer planet is positioned directly opposite the Sun as seen from Earth (angular distance 180°). At opposition the planet is closest to Earth and appears brightest.

The six parameters that define an orbit: semi-major axis, eccentricity, inclination, longitude of ascending node, argument of periapsis and true anomaly.

The branch of physics that studies the motions of celestial bodies under the influence of gravitational forces. Includes calculations of orbits, trajectories, and interactions between multiple bodies.

Reconstructions of past climate from ice cores, sediments, tree rings and isotope ratios. The climate formula is fitted against four such records: LR04, CENOGRID, EPICA Dome C and CenCO2PIP.

The distance at which one astronomical unit subtends an angle of one arcsecond — about 3.26 light-years. The name contracts "parallax" and "arcsecond".

The partially shadowed outer region of a shadow where only part of the light source is blocked. During eclipses, observers in the penumbra see a partial eclipse.

Closest transit point of the Moon with respect to Earth.

The point in an orbit closest to the Sun, which Earth reaches around 3 January. From Greek peri (near) + helios (Sun).

The turn of Earth's perihelion against the moving equinox, one circuit in about ~20,938 years. It is the beat between the orbit's own apsidal turn and the precession of the equinoxes.

The turn of Mercury's orbital ellipse, about 575″ per century seen from the Sun. Newtonian gravity accounts for all but roughly 43″ of that, and the remainder is General Relativity's.

A simulation reference point near the Sun, not a physical object. Earth's orbit is centred on it, giving perihelion and aphelion; it drifts round in ~~111,635 years.

The geological period ~299 to 252 million years ago, ending in the largest known mass extinction, the "Great Dying". CO2 then ran 1,000-2,000+ PPM against today's ~430 PPM.

The model has no phase origin other than J2000: its movements are N-body series on a clock anchored to the J2000 general precession. The 1246 AD alignment is a dated event, not an origin.

The North Star, the star Earth's celestial pole currently points to. Axial precession moves the pole, so different stars hold the position over the ~~25,772-year cycle.

Parts per million, a measure of concentration — used here for atmospheric CO₂. It is about 430 ppm today and fell to roughly 170 ppm at the Last Glacial Maximum.

A slow change in the direction a spin axis or an orbital plane points. Earth has several, on different periods, and the model reads them all against one clock.

A celestial body is said to be "in prograde mode" when it moves in the same direction as the Sun.

Used in astronomy as the celestial equivalent of terrestrial longitude.

A coordinate system used to measure positions and velocities; the same motion reads differently in different frames. Heliocentric, geocentric and ICRF are examples.

A celestial body is said to be "in retrograde mode" when it moves in the opposite direction of the Sun.

The equinox around 22 September — the autumnal equinox in the Northern Hemisphere, the spring one in the Southern. The neutral name is preferred for that reason.

The fitting method used for the climate formula: lines are added one at a time, each fitted with ridge regularisation so a near-duplicate line cannot inflate its own amplitude.

A base-60 numeral system inherited from Babylonian mathematics. Astronomy uses it for angles and time — Right Ascension as 12h34m56s, Declination as +23°26'21".

The base unit of time, defined by a caesium-133 atomic transition. Astronomy reckons on a fixed day of exactly 86,400 of them, while the real solar day drifts slightly around that.

Earth's rotation measured against the moving vernal equinox, 86,164.091730 s. Slightly shorter than the stellar day, because the equinox drifts toward the oncoming rotation.

The Moon's orbit of Earth measured against the fixed stars, about 27.32 days. Shorter than the synodic month, because Earth's own motion delays the return to the same phase.

The time for Earth to orbit once relative to the fixed stars, 365.2563630 days. That is 1,224.5 seconds longer than the solar year, by the coin rotation paradox.

The slow negative feedback that stabilises Earth's climate: warmth speeds up rock weathering, weathering draws down CO₂, and the cooling slows it again. It acts over hundreds of thousands of years.

The time from one noon to the next — the Sun back on the same meridian, ~86,400 s. It runs about four minutes longer than a sidereal day because Earth moves along its orbit while it spins.

The angle Earth's equatorial radius subtends seen from the Sun's centre, about 8.794 arcseconds. Dividing Earth's radius by it is the classical route to the Earth–Sun distance.

The time from one March equinox to the next, 365.2421905 days — the year the seasons keep. It is shorter than the sidereal year because the equinox drifts to meet the Sun.

The two moments each year (about 21 June and 21 December) when the noon Sun is at its highest or lowest, giving the longest and shortest days. Earth's tilt sets them.

Earth's true rotation against the fixed stars, 86,164.100105 s — one turn of the Earth Rotation Angle. It runs 8.38 ms longer than the sidereal day.

A celestial body completes a "synodic" period each time it aligns again with the Sun.

A uniform time scale independent of Earth's rotation, fixed at 86,400 SI seconds per day. The difference from Universal Time is Delta-T (ΔT).

A JavaScript library for creating 3D graphics in a web browser using WebGL. The Interactive 3D Solar System Simulation is built in Three.js.

Differential gravity across an extended body, from the pull varying with distance. Standard astronomy attributes axial precession to the Sun's and Moon's tidal torque on Earth's bulge.

The passage of a body directly between a larger body and the observer. Mercury transits the Sun ~13 times a century; Venus transits come in pairs eight years apart.

The time for the Moon to return to the same ecliptic longitude relative to the equinox, 27.3215822584 days. Precession makes it slightly shorter than the sidereal month.

The darkest central part of a shadow where the light source is completely blocked. During eclipses, only observers within the umbra see a total eclipse.

A time standard tracking Earth's actual rotation, so it varies as the rotation does. The difference from Terrestrial Time is Delta-T (ΔT).

Coordinated Universal Time, the civil time standard: atomic time with leap seconds inserted so it stays within a second of mean solar time.

Variations Séculaires des Orbites Planétaires — Bretagnon and Francou's 1987 analytical solution for planetary positions. It is valid for a few thousand years around J2000.

An informal name for axial precession: the slow conical circling of Earth's spin axis, which carries the equinoxes westward around the sky.

A sharp return to near-glacial cold about 12,900 to 11,700 years ago, interrupting the warming that followed the Last Glacial Maximum. It coincides with the obliquity cycle's maximum.

The apparent path our Sun travels across the celestial sphere over the course of the year through the 12 constellations.