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Earth's rotation

Earth's rotation refers to the spinning of the planet on its internal axis, which passes through the North and South Poles, completing one full rotation relative to the fixed stars (a sidereal day) every 23 hours, 56 minutes, and 4.55 seconds.^[1] This rotation, combined with Earth's orbit around the Sun, results in an apparent solar day of exactly 24 hours on average, defining the standard length of a day for timekeeping purposes.^[1] The axis of rotation is tilted at approximately 23.45 degrees relative to the plane of Earth's orbit, causing seasonal variations.^[1] The direction of Earth's rotation is from west to east, as viewed from above the North Pole, which causes the Sun, Moon, stars, and planets to appear to rise in the east and set in the west.^[2] This daily cycle produces alternating periods of daylight and darkness, with the illuminated half of Earth facing the Sun during the day and the darkened half experiencing night.^[1] The rotation establishes the basis for global time zones, dividing the planet into 24 standard meridians spaced 15 degrees apart, each corresponding to one hour of time difference.^[1] Earth's rotation also generates several notable geophysical effects, including the Coriolis effect, which deflects moving objects (such as air masses and ocean currents) to the right in the Northern Hemisphere and to the left in the Southern Hemisphere due to the planet's angular velocity.^[3] This phenomenon influences weather patterns, contributing to the counterclockwise rotation of hurricanes in the Northern Hemisphere and clockwise rotation in the Southern Hemisphere.^[3] Additionally, the rotation can be demonstrated by devices like the Foucault pendulum, whose plane of oscillation appears to rotate over time due to Earth's underlying spin, with the effect most pronounced at the poles where the period matches the sidereal day of about 23 hours and 56 minutes.^[4] Over long timescales, Earth's rotation rate has slowed due to tidal interactions with the Moon, lengthening the day by approximately 2.3 milliseconds per century.^[5]

Fundamentals

Definition and direction

Earth's rotation refers to the planet's spin around an internal axis passing through the North and South Poles, occurring in an eastward direction, or counterclockwise when viewed from above the North Pole. This prograde motion completes one full rotation relative to the distant stars—known as a sidereal day—in approximately 23 hours, 56 minutes, and 4 seconds.^[6]^[7] The sidereal day serves as the fundamental unit for measuring Earth's rotational period, distinct from the solar day influenced by the planet's orbital motion around the Sun.^[8] This rotation produces the diurnal cycle, alternating day and night as different parts of Earth's surface face toward or away from the Sun over roughly 24 hours. From an observer's perspective on the surface, the rotation causes the apparent daily motion of the Sun, Moon, and stars across the sky from east to west, creating the illusion that celestial bodies revolve around Earth.^[9]^[7] The centrifugal force generated by this rotation acts outward perpendicular to the axis, strongest at the equator, which causes the planet to bulge slightly at the equator while flattening at the poles. This deformation shapes Earth into an oblate spheroid, with the equatorial diameter about 42 kilometers longer than the polar diameter, influencing gravity and other geophysical properties.^[10]^[11]^[12]

Axis and obliquity

The rotational axis of Earth is an imaginary line that passes through the geographic North and South Poles and the center of the planet. This axis is tilted relative to the plane of Earth's orbit around the Sun (the ecliptic plane) by an angle known as the obliquity of the ecliptic, currently approximately 23.44°. The obliquity \epsilon can be approximated by the formula

\epsilon \approx 23^\circ 26' 21''.45 - 46''.815\, T - 0''.00059\, T^2 + 0.001813\, T^3,

where T represents Julian centuries elapsed since J2000.0.^[13] This tilt causes seasonal variations in sunlight distribution on Earth's surface, as different hemispheres receive more direct sunlight at different times of the year. It directly leads to solstices, when one pole is maximally tilted toward the Sun (resulting in the longest or shortest day), and equinoxes, when the axis is perpendicular to the Sun's rays (yielding equal day and night lengths globally).^[14] Over long timescales, the obliquity undergoes cyclic variations between 22.1° and 24.5° with a period of approximately 41,000 years, driven by gravitational perturbations from other planets.^[14]

Rotational Periods

Sidereal day

The sidereal day represents the duration for Earth to complete one full 360° rotation relative to the distant stars or inertial space, serving as the true measure of the planet's rotational period. This time interval is precisely 23 hours, 56 minutes, and 4.091 seconds, equivalent to 86,164.091 seconds.^[15] Earth's orbital motion around the Sun introduces a key distinction from the solar day: during one sidereal day, the planet advances approximately 1° along its orbit, necessitating an additional ~1° of rotation to realign the Sun's apparent position and complete a solar day.^[16] In astronomy, the sidereal day forms the basis for sidereal timekeeping, enabling precise tracking of stellar positions as they rise and set due to Earth's rotation.^[1] Over geological timescales, the sidereal day lengthens slightly owing to tidal friction, primarily from the Moon's gravitational influence, which transfers angular momentum from Earth's rotation to the Moon's orbit and slows the planet's spin.^[17] The length of the sidereal day relates to Earth's mean angular velocity \omega via T = \frac{2\pi}{\omega}, where \omega = 7.292115 \times 10^{-5} rad/s.^[18]

Solar day

The solar day is defined as the interval between two successive passages of the Sun across the local meridian, known as solar noon.^[19] This true solar day varies in length throughout the year primarily due to Earth's elliptical orbit around the Sun (eccentricity), which causes the Sun's apparent motion to speed up and slow down, and due to the tilt of Earth's rotational axis (obliquity), which affects the Sun's path relative to the equator.^[19] As a result, the true solar day ranges from approximately 23 hours 59 minutes 39 seconds to 24 hours 0 minutes 30 seconds over the course of a year, differing from the mean by up to about 30 seconds.^[20] To provide a uniform basis for timekeeping, the mean solar day is used instead, defined as the average length of the true solar days in a year and standardized at exactly 24 hours, or 86,400 seconds.^[19] This mean solar day corresponds to the motion of a hypothetical "mean Sun" that travels along the celestial equator at a constant speed, serving as the foundation for civil clocks and calendars.^[20] The difference between apparent solar time (based on the true Sun) and mean solar time is quantified by the equation of time, which arises from the combined effects of orbital eccentricity and axial obliquity.^[20] An approximation for the equation of time e (in minutes) is given by:

e = 9.87 \sin(2B) - 7.53 \cos(B) - 1.5 \sin(B)

where B is the solar longitude in degrees.^[21] This discrepancy causes sundial time to deviate from clock time by up to ±16 minutes annually, with the true Sun appearing to run fast in November and slow in February.^[20]

Angular velocity

The angular velocity of Earth's rotation, denoted as \omega, quantifies the rate of spin around its axis and is defined as the angle swept per unit time in inertial space. It is derived from the fundamental relation \omega = \frac{2\pi}{T}, where T is the duration of the sidereal day in seconds, excluding orbital motion effects. With T \approx 86164 seconds, this yields \omega \approx 7.292115 \times 10^{-5} rad/s, a value adopted as the nominal constant for Earth's rotation in reference systems.^[22]^[23] This angular velocity remains highly uniform on average, providing a stable basis for timekeeping and geophysical models, though minor variations occur over time. The corresponding tangential linear velocity at the equator, v = \omega R where R = 6378 km is the equatorial radius, reaches approximately 465 m/s eastward.^[23] This speed diminishes to zero at the poles, illustrating the rotational gradient across latitudes. The kinetic energy from this rotation, \frac{1}{2} I \omega^2 where I is Earth's moment of inertia, manifests in observable effects such as the centrifugal force, which reduces apparent weight at the equator by about 0.3% relative to gravitational acceleration alone—equivalent to a minor mass adjustment in effective terms.^[24]

Axis Orientation Changes

Precession

Axial precession refers to the gradual wobble of Earth's rotational axis in space, driven by the gravitational torque from the Sun and Moon acting on the planet's equatorial bulge, which arises from its rotation. This torque is perpendicular to the axis and causes it to sweep out a circular path on the celestial sphere at a rate of approximately 1° every 72 years.^[25]^[26]^[27] The full cycle of this precession, known as the Great Year or platonic year, spans about 25,772 years, during which the axis completes one full rotation relative to the fixed stars. As a result, the orientation of the axis relative to the stars changes slowly; for instance, the north celestial pole, currently near Polaris, will shift toward Vega, making it the approximate pole star in roughly 12,000 years. This long-term motion was first discovered around 130 BCE by the Greek astronomer Hipparchus, who detected it through comparisons of ancient Babylonian star records with his own observations of shifts in stellar positions.^[28]^[29] The precession rate is quantified as \dot{\psi} \approx 50.29'' per year, where \dot{\psi} represents the angular speed of the axial wobble. This general precession is decomposed into two main components: the precession in longitude, which describes the primary westward shift along the ecliptic, and the precession in obliquity, which accounts for the slight variation in the tilt angle over time. These components together define the smooth, secular change in the equator's orientation, distinct from shorter-term perturbations.^[30]^[31]

Nutation

Nutation refers to the small, periodic wobbles in the orientation of Earth's rotation axis, superimposed on the longer-term precession, resulting from gravitational torques exerted by the Moon and Sun on Earth's equatorial bulge. These perturbations cause oscillations with typical amplitudes of around 9 arcseconds, primarily driven by the 18.6-year cycle of the Moon's orbital nodes, during which the Moon's orbital plane regresses relative to the ecliptic.^[32]^[1] The motion comprises two principal components: nutation in longitude, which shifts the position of the vernal equinox along the ecliptic and reaches amplitudes up to 17 arcseconds, and nutation in obliquity, which varies the tilt of Earth's axis relative to the ecliptic plane with amplitudes up to 9 arcseconds. These effects were first identified by English astronomer James Bradley in 1748, through careful analysis of stellar positions that initially appeared inconsistent with his discovery of stellar aberration.^[33] Theoretical modeling of nutation culminated in the International Astronomical Union (IAU) 1980 nutation series, a standard formulation comprising 106 Fourier terms that account for lunisolar and planetary influences on Earth's orientation. This series was later refined in the IAU 2000A model, which includes additional effects from Earth's non-rigidity and remains the current standard as of 2025, providing high-precision predictions for astronomical applications, with the dominant term arising from the lunar nodal precession. The principal nutation in longitude is expressed as

\Delta \psi = 17.2'' \sin \Omega

where \Omega denotes the mean longitude of the Moon's ascending node.^[34]^[35]

Rotation Rate Variations

Long-term deceleration

Earth's rotation has been gradually decelerating over geological timescales, primarily due to tidal interactions with the Moon, resulting in a lengthening of the day by approximately 2.3 milliseconds per century.^[36] This secular change in the length of day (LOD) is expressed as:

\Delta \text{LOD} / \text{century} \approx 2.3 \, \text{ms}

Integrating this rate over billions of years reveals significantly shorter days in Earth's distant past; for instance, models indicate that around 4.5 billion years ago, when the planet formed, a day lasted about 6 hours.^[37] This long-term slowing transfers angular momentum from Earth's spin to the Moon's orbit, causing the Moon to recede at a rate of about 3.8 cm per year, as measured by lunar laser ranging. Over extended periods, the cumulative effect is profound: integrating the deceleration rate suggests that during the Precambrian era, around 600 million years ago, days were approximately 22 hours long based on tidal rhythmite records.^[38] Fossil evidence supports these estimates; for example, growth rings in mollusk shells from the late Cretaceous period, about 70 million years ago, indicate days of roughly 23 hours, consistent with the ongoing tidal lengthening.

Short-term fluctuations

Short-term fluctuations in Earth's rotation occur on timescales from days to decades, manifesting as variations in the length of day (LOD) primarily driven by interactions between the solid Earth, atmosphere, oceans, and occasionally seismic events. These changes arise from the conservation of angular momentum, where redistributions of mass and momentum in the fluid layers alter the planet's spin rate. Typically, LOD fluctuates by ±1 millisecond around the mean value, with atmospheric winds and pressure systems contributing the largest seasonal signals, oceanic currents and tides adding sub-millisecond effects, and large earthquakes occasionally causing abrupt shifts of up to several milliseconds.^[39]^[40] A prominent example of these fluctuations is the Chandler wobble, a free nutation mode of Earth's rotation axis that superimposes a nearly circular motion on the geographic poles. This oscillation has a period of approximately 433 days (about 1.2 years) and an amplitude of roughly 10 meters at the pole, resulting from the Earth's elastic response to imbalances in its moments of inertia. The wobble is excited by stochastic atmospheric and oceanic torques but is gradually damped by internal dissipation in the mantle and core-mantle boundary, with a quality factor indicating decay over several decades without forcing. Polar motion due to the Chandler wobble can be described by the equation for the x-component (in the terrestrial frame):

x(t) = A \cos(\omega t + \phi)

where A is the amplitude (≈10 m), \omega \approx 2\pi / 433 days^{-1} is the angular frequency, and \phi is the phase.^[41] El Niño events exemplify interannual atmospheric influences on LOD, where anomalous equatorial winds redistribute angular momentum, typically lengthening the day by up to 1 millisecond during peak phases. For instance, the 1982–1983 El Niño caused an LOD increase of about 0.9 ms, primarily through enhanced easterly trade wind weakening that transfers momentum from the atmosphere to the solid Earth. These effects reverse during La Niña phases, shortening the day through stronger westerly momentum transfer.^[42]

Recent trends

In the 21st century, particularly since 2020, Earth's rotation has exhibited an unexpected acceleration, resulting in multiple record-shortest days compared to the nominal 86,400 seconds. According to data from the International Earth Rotation and Reference Systems Service (IERS), the 28 shortest days on record since 1960 all occurred in 2020 alone, with deviations up to 1.46 milliseconds shorter than average, and this trend has continued into the 2020s with further anomalies. For instance, on July 22, 2025, Earth completed its rotation approximately 0.87 milliseconds faster than standard, based on post-event IERS measurements, while August 5, 2025, saw a shortening of approximately 1.0 millisecond.^[43] These speed-ups contrast with the planet's long-term rotational deceleration, prompting considerations for a negative leap second—the first ever—to align atomic clocks with Earth's rotation, potentially as early as 2029, as outlined in a 2024 study published in Nature.^[44]^[45]^[46]^[47] Recent geophysical research has linked these variations to dynamics within Earth's interior, including the solid inner core. Studies indicate that the inner core's super-rotation—where it previously spun faster than the mantle—paused around 2009 to 2010 and has since begun reversing direction, moving slower relative to the surface at rates of up to 0.1 degrees per year. This reversal was first evidenced in 2023 seismic analyses showing waveform changes consistent with a temporary halt followed by backtracking, and confirmed in a 2024 University of Southern California study using multiplet seismic data from repeating earthquakes between 1991 and 2023. A 2025 follow-up in Nature further documented these shifts through inner core backtracking, suggesting a cyclical pattern that influences overall planetary rotation on decadal scales.^[48]^[49]^[50] Concurrent with these internal changes, anthropogenic climate effects are exerting a counteracting influence by slowing rotation through mass redistribution. A 2024 study led by researchers at the Scripps Institution of Oceanography, University of California San Diego, incorporating NASA satellite data, found that accelerated ice melt from Greenland and Antarctica—totaling over 400 billion tons annually—has shifted mass toward the equator, extending the length of day by approximately 1.33 milliseconds per century since 2000, with projections indicating further deceleration if emissions continue unchecked. This climate-driven effect partially offsets the observed speed-ups, highlighting the complex interplay of natural and human-induced factors in recent rotational trends. As of November 2025, IERS observations indicate persistent short days with average deviations of -0.5 to -1.0 ms, amid recovering atmospheric patterns.^[51]^[52]

Causes of Variations

Tidal friction

Tidal friction arises from the gravitational interactions between Earth, the Moon, and the Sun, which deform Earth's oceans into tidal bulges. Earth's faster rotation drags these bulges ahead of the Moon's position in the sky, creating a misalignment. The gravitational pull of the Moon on the leading bulge generates a torque that opposes Earth's spin, gradually slowing its rotation while transferring angular momentum to the Moon, causing it to recede in its orbit. This process primarily dissipates energy through friction in the oceans, with minor contributions from the atmosphere and solid Earth.^[5] The magnitude of this tidal torque can be expressed as

\tau = \frac{3 G M_m^2 R_e^5 k_2 \sin(2\delta)}{2 d^6},

where G is the gravitational constant, M_m is the Moon's mass, R_e is Earth's radius, k_2 is the second-degree Love number, \delta is the phase lag due to dissipation, and d is the Earth-Moon distance. This torque derives the secular deceleration of Earth's rotation rate, linking the energy loss directly to the observed lengthening of the day. Currently, tidal friction dissipates approximately 3.7 terawatts of rotational energy, accounting for an increase in the length of day (LOD) by about 2.3 milliseconds per century.^[53]^[54]^[36] Over geological timescales, this mechanism has significantly altered Earth's rotation. Analysis of tidal rhythmites—layered sedimentary deposits recording ancient tidal cycles—in South Australia indicates that the LOD was 21.9 hours approximately 620 million years ago, reflecting the cumulative effect of tidal friction since the Precambrian era.

Climate effects

The melting of polar ice sheets due to global warming redistributes mass from the poles toward the equator, primarily through sea-level rise, which increases Earth's moment of inertia and thereby slows its rotation. For instance, the Greenland Ice Sheet has been losing an average of 280 gigatons of ice per year between 2002 and 2021, contributing to this equatorial mass shift.^[55] This process is analogous to a figure skater extending their arms to slow their spin, conserving overall angular momentum while reducing rotational speed. The change in angular velocity \omega can be approximated by the relation

\Delta \omega \approx -\frac{\Delta I}{I} \omega,

where \Delta I represents the change in moment of inertia due to mass redistribution, I is Earth's total moment of inertia, and \omega is the initial angular velocity; this equation quantifies the rotational slowing from increased oblateness. A 2024 study funded by NASA attributes recent accelerations in this effect to anthropogenic climate change, estimating a length-of-day (LOD) increase of 1.33 milliseconds per century since 2000, compared to 0.3–1.0 milliseconds per century in the 20th century overall.^[56]^[57] Additionally, these mass shifts have contributed to a poleward drift of the rotation axis by approximately 80 centimeters between 1993 and 2010, driven by related anthropogenic water redistribution including groundwater depletion exacerbated by warming.^[58] Oceanic processes, such as thermal expansion from warming waters and variations in current strengths, further influence Earth's angular momentum by altering mass distribution and flow patterns, leading to short-term LOD variability on the order of 0.1 milliseconds.^[59] These effects are superimposed on the longer-term trends from ice melt and are projected to intensify under high-emission scenarios, potentially reaching 2.62 milliseconds per century by 2100.^[57]

Internal dynamics

The interactions between Earth's fluid outer core and solid mantle primarily drive variations in the planet's surface rotation rate through core-mantle coupling, which facilitates the transfer of angular momentum via electromagnetic and topographic torques. Electromagnetic coupling arises from the dynamo-generated magnetic field in the core interacting with the weakly conducting lower mantle, inducing currents that produce Lorentz forces and thus torques at the core-mantle boundary (CMB). Topographic coupling occurs as turbulent flows in the outer core exert pressure on the irregular undulations of the CMB, generating pressure differences that translate into net torques on the mantle. These mechanisms collectively account for exchanges of angular momentum that manifest as observable changes in Earth's rotation.^[60]^[61] The solid inner core's rotation relative to the mantle exhibits a multidecadal oscillation with a period of approximately 70 years, driven by gravitational and electromagnetic interactions at the inner core boundary and CMB. Seismological analyses of repeating earthquakes and nuclear explosions from 1991 to 2020 revealed this oscillatory behavior, with the inner core super-rotating relative to the mantle from the 1970s to around 2009 before slowing. Studies between 2023 and 2025, building on this model, confirmed a reversal in the inner core's differential rotation after 2010, where it began rotating more slowly than the mantle, contributing to a length-of-day (LOD) variation of approximately 0.5 milliseconds through associated angular momentum adjustments in the outer core. This reversal aligns with broader core dynamics, including a noted slowdown in outer core flows observed in recent trends.^[62]^[49] On decadal timescales, fluctuations in Earth's rotation arise from mantle convection and geomagnetic field variations, which modulate electromagnetic torques and induce LOD changes of about 1 millisecond. Mantle convection, operating over long timescales, creates heterogeneous density distributions that interact with core flows to produce topographic torques, while secular variations in the magnetic field—linked to dynamo processes in the core—alter the electromagnetic coupling strength at the CMB. These processes drive torsional oscillations in the fluid core, propagating angular momentum exchanges that correlate with observed decadal LOD variability.^[63]^[64] The torque mediating angular momentum exchange in these interactions can be approximated in viscous models as \Gamma = \eta \Omega, where \eta represents the effective viscosity at the boundary and \Omega is the differential rotation rate between the core and mantle; this formulation captures the shear stress-induced drag that couples the layers.^[65]

Historical and Modern Observations

Ancient measurements

Ancient civilizations, including the Babylonians around the 2nd millennium BCE, developed a geocentric model of the universe in which Earth was stationary at the center, with the apparent daily motion of the stars and Sun attributed to the rotation of a celestial sphere around it. This view emphasized the diurnal cycle as evidence of heavenly motion rather than Earth's spin, based on meticulous observations of planetary positions and eclipses recorded on clay tablets. Aristotle, in the 4th century BCE, reinforced this geocentric perspective by arguing that Earth's fixed position was necessary for the observed stability of falling objects and the circular shadow it cast during lunar eclipses, while proposing a spherical Earth to explain variations in stellar visibility across latitudes.^[66]^[67] In the 3rd century BCE, Eratosthenes of Cyrene advanced understanding by measuring Earth's circumference through the differing lengths of shadows cast by the Sun at noon in Syene and Alexandria on the summer solstice, yielding an estimate of approximately 252,000 stadia (about 40,000 km), remarkably close to modern values. This experiment not only confirmed Earth's sphericity but also allowed him to calculate the axial tilt at around 23° 51', using solstice observations to infer the orientation of the rotation axis relative to the ecliptic. Similarly, ancient structures like the Neolithic Taosi observatory in China (circa 2300–1900 BCE) featured solstice markers—aligned trenches and posts—that tracked the Sun's extreme positions, enabling early estimates of obliquity through seasonal shadow patterns and horizon alignments. Hipparchus, in the 2nd century BCE, refined these ideas by measuring Earth's obliquity to within 1/24 of a degree via solstice gnomon observations and discovered axial precession by comparing his star catalog with earlier Babylonian records, noting a westward shift of the equinoxes at about 1° per century due to the gradual wobble of Earth's rotational axis.^[68]^[69]^[70]^[71] The heliocentric shift began with Nicolaus Copernicus's 1543 publication De revolutionibus orbium coelestium, which posited that Earth's daily rotation on its axis explained the apparent motion of the stars more simply than the geocentric model's vast celestial sphere, while also accounting for its annual orbit around the Sun. This model revived earlier ideas, such as those from Aristarchus of Samos in the 3rd century BCE, but gained traction by resolving discrepancies in planetary retrograde motion. In 1728, James Bradley, seeking stellar parallax, observed unexpected shifts in the position of γ Draconis (Thuban), leading to the discovery of stellar aberration due to Earth's orbital velocity and, from residual variations, the nutation of its axis caused by lunar gravitational torque, with an 18.6-year period. Finally, in 1851, Léon Foucault demonstrated Earth's rotation directly through a laboratory pendulum experiment at the Panthéon in Paris, where the swing plane rotated clockwise by about 11° per hour due to the Coriolis effect from Earth's spin beneath it, providing the first simple, visual proof independent of astronomical observations.^[72]^[67]^[73]^[74]

Modern techniques

Modern techniques for measuring Earth's rotation parameters have advanced significantly since the 20th century, enabling sub-millisecond precision in tracking variations in length of day (LOD), polar motion, precession, and nutation. Very Long Baseline Interferometry (VLBI) stands as a cornerstone method, utilizing a global network of radio telescopes to observe distant quasars and directly determine Earth's orientation in space. By correlating signals from antennas separated by thousands of kilometers, VLBI achieves accuracies of about 0.1 milliarcseconds (mas) for polar motion and 0.03 milliseconds (ms) for LOD variations, providing essential data on universal time and axis wobbles.^[75]^[76] Complementing VLBI, the Global Positioning System (GPS) and Satellite Laser Ranging (SLR) offer high-frequency observations of polar motion with centimeter-level accuracy. GPS receivers track satellite signals to monitor instantaneous changes in Earth's rotation axis position, routinely delivering daily polar motion estimates at 0.4 mas (approximately 1.2 cm at the equator).^[77] SLR, by firing laser pulses to retroreflectors on satellites and the Moon, refines these measurements to 150-200 microarcseconds (µas) for polar motion and 15-20 µs for universal time components, enhancing the detection of short-term fluctuations.^[78]^[79] The International Earth Rotation and Reference Systems Service (IERS) integrates these techniques to monitor LOD with a precision of 0.1 ms, disseminating Earth orientation parameters (EOPs) through global data centers.^[80] Atomic clocks, underpinning Coordinated Universal Time (UTC), facilitate leap second adjustments to align UTC with astronomical time (UT1), which tracks Earth's rotation. In 2025, amid Earth's accelerated spin—shortening some days by up to 1.6 ms—IERS considered the first negative leap second to prevent UTC from drifting beyond ±0.9 seconds of UT1, though none was implemented by November.^[81]^[82] Satellite missions further refine rotation measurements by quantifying mass redistributions that influence angular momentum. The Gravity Recovery and Climate Experiment (GRACE) and its follow-on (GRACE-FO), launched in 2002 and 2018 respectively, detect monthly gravity variations from hydrological and cryospheric changes, revealing how continental water storage shifts contribute up to 83% of observed polar motion amplitude.^[83] Similarly, the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE), operational from 2009 to 2013, mapped the static gravity field to isolate rotational effects from mass anomalies. Gyroscopic instruments provide direct, ground-based detection of precession and nutation. A 2025 study using a ring laser gyroscope at Germany's Geodetic Observatory Wettzell measured Earth's axial precession at 242 μrad/year (equivalent to 50 arcseconds/year), confirming the slow westward drift of the rotation axis due to gravitational torques from the Sun and Moon, with nutation signals showing prominent fortnightly periods at sensitivities of 10^{-8} relative to the rotation rate.^[84] The IERS Conventions standardize these observations through established models for precession and nutation, adopting the IAU 2006/2000A theory, which includes over 1,300 terms to predict celestial pole offsets with residuals below 0.2 mas. These conventions ensure consistency across techniques, supporting applications from satellite navigation to fundamental physics tests.^[85]

Evolutionary Origin

Protoplanetary accretion

The formation of Earth's rotation traces back to the protoplanetary disk phase approximately 4.6 billion years ago, when the gravitational collapse of a rotating molecular cloud fragment produced a central protostar—the young Sun—and a flattened, rotating disk of gas and dust surrounding it. Conservation of angular momentum during this collapse amplified the rotation, resulting in a Keplerian disk where orbital velocities increased toward the inner regions. This disk, spanning roughly 100-200 AU initially, served as the birthplace of the planets, with Earth's building blocks forming in its inner terrestrial zone at about 1 AU from the protostar.^[86] Within this disk, the accretion process began with microscopic dust grains colliding and adhering through van der Waals forces and aerodynamic drag, growing into centimeter-sized pebbles and eventually kilometer-scale planetesimals over timescales of 10^3 to 10^5 years. These planetesimals, orbiting in the prograde direction of the disk, gravitationally attracted and merged to form protoplanets, imparting a net prograde spin to the accreting bodies due to the tangential velocities inherited from their orbits. For Earth, this hierarchical accretion in the inner disk led to an initial rotation period estimated at 5-10 hours, reflecting the rapid spin acquired from the orderly, disk-aligned impacts rather than random collisions.^[87]^[88] Viscous processes in the disk played a crucial role in redistributing angular momentum, with turbulent stresses—primarily driven by magnetorotational instability—transporting it outward while enabling gas and solids to spiral inward toward the protostar. This outward spreading expanded the disk's outer edge while concentrating angular momentum in the denser inner regions, facilitating efficient planet formation by enhancing the density of material available for accretion. Simulations of disk turbulence reveal velocities of 10-20 m/s in the midplane, which stirred the gas and influenced the relative velocities of accreting particles, thereby contributing to the spin-up of protoplanets like proto-Earth.^[89] The specific angular momentum in the Keplerian disk follows the relation

h \propto \sqrt{G M r},

where [G](/page/Gravitational_constant) is the gravitational constant, [M](/page/Mass) is the mass of the central protostar, and r is the radial distance from the center. This scaling implies higher angular momentum per unit mass at larger radii, but the inner disk's faster orbital speeds resulted in more rapid spins for terrestrial planets, setting the stage for Earth's primordial rotation.

Post-formation adjustments

Following the giant impact that formed the Moon approximately 4.5 billion years ago, Earth's rotation underwent significant adjustments as the planet differentiated into layers and interacted tidally with its new satellite. The collision with Theia, a Mars-sized protoplanet, not only ejected material to form the Moon but also accelerated Earth's spin to a period of about 5 hours per day and tilted its rotation axis to an obliquity that evolved to the current 23.4 degrees, establishing the foundation for seasonal variations.^[90]^[91] Subsequent core formation further shaped these dynamics. As Earth cooled from its post-impact magma ocean state, dense iron sank to form the core around 4.5 billion years ago, differentiating the planet and redistributing angular momentum between the core and mantle; this process contributed to stabilizing the overall rotational framework while the fast initial spin persisted. Later, the ongoing solidification of the inner core, which began roughly 1 billion years ago and grows at about 1 mm per year, influences long-term spin variations through electromagnetic and gravitational couplings at the core-mantle boundary, including contributions to observed 70-year oscillations in Earth's length of day.^[92]^[93] Tidal interactions with the newly formed Moon drove profound evolutionary changes to Earth's rotation. Initially, the Moon orbited at a distance of roughly 20,000–25,000 km from Earth's center, generating enormous tidal bulges that exerted strong frictional torques, gradually slowing the planet's spin from its ~5-hour day to the current 24 hours over billions of years. This process exemplifies the conservation of angular momentum in the Earth-Moon system: as tidal friction transfers rotational energy from Earth to the Moon's orbit, the Moon recedes at an average rate of 3.8 cm per year, synchronizing the system's total angular momentum while lengthening Earth's day.^[94]^[91]

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Oct 4, 2017 · Areas facing away from the sun experience nighttime. As the planet spins, most places on Earth cycle through day and night once every 24 hours.
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Sep 22, 2004 · The rest arises because the Earth is not a perfect sphere: the centrifugal force of its rotation causes its equator to bulge out, making the ...
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The Rotating Earth - PWG Home - NASA
Sep 22, 2004 · One important rotating frame is the surface of the Earth, rotating with a period of about 24 hours--more accurately, 23 hrs 56.07 min or 86164 seconds.
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[PDF] Geometric Reference Systems in Geodesy
εA = 23° 26′ 21.448″ – 46.8150 T + 0.00059 T. 2. + 0.001813 T. 3. +. (– 46.8150 ... where ε is the mean obliquity at epoch, t, and r = cosα cosδ sinα cosδ.
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Milankovitch (Orbital) Cycles and Their Role in Earth's Climate
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NASA GISS: Mars24 Sunclock — Technical Notes on Mars Solar Time
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The Earth does a full rotation each day, but because it is also traveling on its orbit around the Sun, it has to rotate about 1° more than a full 360° to ...
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Lecture 20: Tides
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It is defined as a prturbational ngle with respect to a uniform rotation with nominal angular velocity 7.292115146706979 · 10-5 rad/sec. Units: seconds.
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The Equation of Time - Astronomical Applications Department
Technically, the Equation of Time is the difference apparent solar time minus mean solar ... longitude, apparent solar time is different for every longitude. We ...
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Solar Time | PVEducation
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USEFUL CONSTANTS
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Why Don't Humans Get Thrown Off the Surface of the Earth Due to ...
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Do I weigh less on the equator than at the North Pole?
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The precession of the Earth's axis of rotation may be visualized as a slow, wobbling motion of the axis in space, pivoting at the Earth's center.
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[PDF] Observation Model and Parameter Partials for the JPL VLBI ...
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[PDF] The Day is Getting Longer - EarthDate
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(PDF) Atmospheric Torques and Earth's Rotation: What Drove the ...
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Inner core backtracking by seismic waveform change reversals
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Evaluation of earth rotation parameters from modernized GNSS ...
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[PDF] LONG TERM MONITORING OF GEOPHYSICAL PARAMETERS ...
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Planet formation: statistics of spin rates and obliquities of extrasolar ...
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[PDF] Heterogeneous Distribution of Angular Momentum between Core ...
Our canonical Moon-forming impact simulations show that, after the impact, the average angular velocity of the mantle near the equator is 1.05 rad/hour.
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