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. A MEAN value of 365.2596324 days (~31,558,432.12 seconds). Directly related to the ~20,938-year Perihelion precession cycle. The J2000 value is 31,558,432.46 seconds.

The point in an orbit where a celestial body is furthest from the Sun. For Earth, this currently occurs around July 4th. 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 orbiting object crosses the reference plane (typically the ecliptic) moving from south to north. It is one of two places where the orbit intersects the reference plane; the other is the descending node. Together they 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 ~25,771 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 circle of equal size, it completes one more rotation than expected. This geometric principle explains why Earth rotates one more time than the number of days in a year, and why there is one fewer sidereal year than solar years in a Great Year.

When two or more celestial bodies appear close together in the sky. Inferior conjunction: inner planet passes between Earth and Sun. Superior conjunction: planet is on the far side of the Sun. The "Great Conjunction" of Jupiter and Saturn occurs every ~19.86 years.

Recognized patterns of stars in the night sky. The 88 official constellations divide the celestial sphere into distinct regions. Twelve along the ecliptic form the zodiac. Due to axial precession, the constellation behind the Sun on any given date shifts over the ~~25,771-year precession cycle.

The moment the Sun reaches its southernmost point, around 21–22 December. In 1246 AD it last coincided with Earth's perihelion — the alignment the correction bases are anchored on.

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 ~25,771 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 (in heliocentric view) or the apparent path of the Sun across the sky as seen from Earth (in geocentric view). The ecliptic is tilted relative to Earth's equator by the obliquity angle.

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 specific moment in time used as a reference point for astronomical measurements. Orbital elements and positions are specified relative to a particular epoch (like J2000) and then calculated forward or backward in time.

The difference between apparent solar time (sundial) and mean solar time (clock), ranging from about −14 to +16 minutes throughout the year. Caused by orbital eccentricity and obliquity. Directly related to the analemma.

The imaginary great circle around Earth equidistant from both poles. The celestial equator is its projection onto the celestial sphere, used as the fundamental plane for the equatorial coordinate system (Right Ascension along it, Declination perpendicular to it).

The two times per year (around March 21 and September 22) when Earth's equatorial plane passes through the center of the Sun, resulting in approximately equal day and night lengths. The equinoxes move westward along the ecliptic due to 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.

A cycle related to the Moon's phases and orbital mechanics. In the framework, the Full Moon cycle ICRF is ~411.7665135216 days and the Full Moon cycle Earth is 411.78 days. This represents the time between alignments of the lunar phases with specific orbital configurations.

A theory of gravitation developed by Albert Einstein between 1907 and 1915, describing gravity not as a force but as a curvature of spacetime caused by mass and energy. One of its key proofs was explaining the anomalous precession of Mercury's perihelion (~43 arc-seconds per century).

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 increase in Earth's average surface temperature observed since the late 19th century. The framework emphasizes that climate has always changed naturally due to orbital mechanics over precession cycles of tens of thousands of years.

The fundamental force of attraction between objects with mass

~~25,771 years = the full time period for the Earth to complete one APO. This old term of the Axial precession (precession of the equinoxes) is related to Plato and can be seen as a popular term for Axial Precession.

Introduced by Pope Gregory XIII in 1582. Refines the Julian calendar by omitting 3 leap days every 400 years, giving an average year of 365.2425 days. Since the actual solar year (~365.2422036 days) differs slightly, the calendar gradually drifts relative to the seasons.

A model or frame of reference where the Sun is at the center and planets orbit around it. The standard modern astronomical model. From Greek: helios (sun) + centric (center).

International Celestial Reference Frame - A system of distant quasars used as fixed reference points for measuring positions and motions of celestial objects. Provides an inertial (non-rotating) reference frame for astronomical measurements.

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 - A standard reference epoch used in astronomy, corresponding to January 1, 2000, 12:00 TT (Terrestrial Time). Used as a baseline for measuring positions and motions of celestial objects.

Continuous count of days since January 1, 4713 BC at noon UT. Provides an unambiguous date reference across calendar systems. Example: June 21, 2000 AD 00:00 UTC = JD 2,451,716.5. Fractional part = time of day (.0 = noon, .5 = midnight).

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.

Three laws of planetary motion by Johannes Kepler (early 17th century): (1) Planets orbit in ellipses with the Sun at one focus, (2) A line from Sun to planet sweeps equal areas in equal times, (3) The square of the orbital period is proportional to the cube of the semi-major axis (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.

A phenomenon every ~18.6 years when the Moon's declination range reaches its maximum (major standstill) or minimum (minor standstill) due to the nodal precession cycle. Ancient monuments like Stonehenge were aligned to observe these events.

In the Northern Hemisphere, the March equinox is called the vernal or spring equinox. In the Southern Hemisphere, the reverse is true. That's why the term March equinox is preferred over vernal equinox.

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 variations in Earth's climate caused by changes in orbital parameters: eccentricity, obliquity, and precession. Named after Serbian scientist Milutin Milanković who first calculated their effects on Earth's 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 ~41,098 years.

A problem-solving principle attributed to the 14th-century philosopher William of Ockham, stating that "of two competing theories, the simpler explanation of an entity is to be preferred." When multiple hypotheses explain the same observations, the one with the fewest assumptions should be selected.

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.

Six parameters that uniquely define an orbit: (1) semi-major axis, (2) eccentricity, (3) inclination, (4) longitude of ascending node, (5) argument of periapsis, and (6) true anomaly. Together they allow calculation of position and velocity at any point in time.

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 where a celestial body is closest to the Sun. For Earth, this currently occurs around January 3rd. 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 reference point near the Sun in the simulation, not a physical object: Earth's yearly orbit is centred on it, which is what gives perihelion and aphelion. It drifts round in about ~111,635 years.

A geological period (~299 to 252 million years ago) ending with the largest mass extinction ("Great Dying"), when ~96% of marine species went extinct. CO2 levels were 1,000-2,000+ PPM, far higher than today's ~430 PPM.

Where the model's correction bases start counting, set a number of perihelion-of-date beats back from the 1246 AD perihelion–solstice alignment. It is a calibration convention, not a date.

The North Star - currently Earth's celestial pole is pointing to the star Polaris. Due to Axial precession, different stars occupy this position over the approximately ~25,771-year precession cycle (currently experienced ~25,771 years).

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 or set of axes used to measure positions, velocities, and other properties of objects. Different reference frames can give different perspectives on the same motions. Examples include heliocentric, geocentric, and ICRF.

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

In the Northern Hemisphere, the September equinox is called the autumnal or fall equinox. In the Southern Hemisphere, the reverse is true. That's why the term September equinox is preferred over autumnal equinox.

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 ancient Babylonian mathematics. In astronomy, used to express angles and time: RA as hours:minutes:seconds (e.g., 12h34m56s) and Declination as degrees:arcminutes:arcseconds (e.g., +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, 86,164.092407 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 complete one orbit relative to the fixed stars. A FIXED period of ~31,558,149.76 seconds (MEAN 365.2563644 days). This is 1,224.5 seconds longer than the Solar year due to 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, 365.2421904 days — the year the seasons keep. It is shorter than the sidereal year because the equinox drifts to meet the Sun.

The two times per year (around June 21 and December 21) when the Sun reaches its highest or lowest point in the sky at noon, marking the longest and shortest days of the year. These dates are determined by Earth's tilt relative to the ecliptic.

Earth's true rotation against the fixed stars, 86,164.100782 s — one full turn of the Earth Rotation Angle. It is 8.37 ms longer than the sidereal day, which uses the drifting equinox.

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 exactly 86,400 SI seconds per day. Coincidentally aligned with the mean solar day around 1820 AD. Provides a stable reference for predicting astronomical events. The difference TT − UT 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 gravitational forces caused by the variation in gravitational pull across an extended object. In standard astronomy, tidal forces from the Sun and Moon on Earth's equatorial bulge are said to cause Axial precession.

The passage of a celestial body directly between a larger body and the observer. Mercury transits occur ~13-14 times per century; Venus transits occur in pairs separated by 8 years, with over a century between pairs.

The time for the Moon to return to the same ecliptic longitude relative to the vernal equinox, approximately 27.3215824151 days. This is very close to the sidereal month but slightly shorter due to the precession of the equinoxes.

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 based on Earth's actual rotation. Unlike Terrestrial Time (TT), UT varies because Earth's rotation speed is not constant. Corresponds to the actual day-night cycle as experienced on Earth. The difference TT − UT 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 — an analytical solution for computing planetary positions and orbital elements, developed by Bretagnon and Francou (1987). Valid for several thousand years around J2000 and widely used in astronomical software.

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.