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Local mean time

Local mean time (LMT) is a type of solar time that measures the position of the mean Sun—a fictitious sun moving at a constant speed along the celestial equator—at a specific longitude on Earth, providing a uniform 24-hour day based on the average length of a solar day.^[1] Unlike apparent solar time, which varies due to the Earth's elliptical orbit and axial tilt, LMT ensures a consistent time flow by using the mean Sun's hour angle plus 12 hours as the local time at that meridian.^[2] Historically, LMT served as the basis for civil timekeeping in the 19th century, with time differing by approximately 4 minutes for every degree of longitude (or about 1 hour per 15 degrees), making it practical for local communities but challenging for expanding railroads and telegraphs that required synchronized schedules across wider areas.^[1] This led to the establishment of standard time zones in the late 1800s, largely replacing LMT with zone-based systems like those referenced to Greenwich Mean Time (GMT), which is simply LMT at the prime meridian (0° longitude).^[1] GMT was a global standard until 1972, when it was succeeded by Coordinated Universal Time (UTC).^[3] LMT remains relevant in astronomy for precise observations and calculations involving the equation of time—the difference between apparent and mean solar times, which can vary by up to about 16 minutes throughout the year.^[2] In modern contexts, LMT is integral to systems like UT1, which tracks Earth's irregular rotation and is closely maintained by UTC through leap seconds, and is used by astronomers to determine local sidereal time or solar noon positions without the irregularities of true solar motion.^[2] To compute LMT, one starts with Universal Time (UT) and applies a longitude correction: subtract 4 minutes per degree east of Greenwich or add for west, though software and almanacs now handle these adjustments routinely for specific locations.^[2]

Fundamentals

Definition

Local mean time is the time indicated by a clock running at a uniform rate that corresponds to the average length of the solar day, determined by the meridian transit of a fictitious "mean sun."^[4] This system provides a standardized measure of solar-based time tied to a specific geographic location, ensuring consistent intervals between successive noons throughout the year. The mean sun is an imaginary celestial body that travels along the equator at a constant angular speed, completing one full circuit relative to the vernal equinox in exactly one tropical year.^[4] It serves to average out irregularities in the apparent sun's motion caused by Earth's elliptical orbit around the Sun and the 23.44° axial tilt, which together produce variations in the true solar day's length by up to about 20 seconds.^[5] By simulating this uniform motion, the mean sun enables clocks to maintain a steady rate, with local mean noon defined as the moment the mean sun crosses the observer's local meridian. As a location-specific time scale, local mean time varies continuously with longitude, differing by 4 minutes for every degree of separation from a reference meridian, since Earth rotates 360° in 24 hours or 15° per hour.^[6] This reflects the planet's rotational period, where time zones effectively discretize this continuous gradient for practical use.^[7] In contrast to apparent solar time, which tracks the actual sun's irregular position and fluctuates due to the equation of time—a correction reaching ±16 minutes—local mean time remains regular and predictable.^[8]

Relation to Apparent Solar Time

Local apparent solar time refers to the time determined by the actual position of the Sun in the sky, specifically when it crosses the local meridian, which occurs at local solar noon.^[9] This measurement is traditionally obtained using a sundial, as the shadow cast by the gnomon aligns with the meridian at that moment.^[10] In contrast to uniform clock time, apparent solar time varies slightly from day to day due to irregularities in the Sun's apparent motion. These variations arise primarily from two astronomical factors: the Earth's elliptical orbit around the Sun, which causes the planet to move at uneven speeds—faster near perihelion and slower near aphelion—and the 23.4° axial tilt relative to the orbital plane, known as obliquity, which affects the Sun's declination and path across the sky.^[9] The elliptical orbit leads to differences in the length of the apparent solar day, while the tilt introduces seasonal shifts that further disrupt uniformity.^[11] The cumulative effect of these irregularities is quantified by the equation of time, defined as the difference between apparent solar time and mean solar time, which can reach discrepancies of up to ±16 minutes over the course of a year.^[9] This equation peaks in magnitude around early November (when apparent time is about 16 minutes slow) and early February (when it is about 14 minutes fast), reflecting the combined influences of orbital eccentricity and obliquity.^[11] Local mean time was developed as a practical alternative to apparent solar time precisely to address these inconsistencies, providing a standardized daily cycle based on the average solar day over a year—equivalent to the motion of a hypothetical "mean Sun" that travels uniformly along the celestial equator.^[9] Without such averaging, mechanical clocks set to apparent solar time would require daily adjustments of several minutes to remain synchronized with societal needs, rendering them unreliable for scheduling trains, work shifts, or other coordinated activities in pre-standardized eras.^[12]

Computation Methods

Longitude Correction

Local mean time (LMT) at a specific location is determined by applying a longitude correction to the mean time at a reference meridian, typically Greenwich Mean Time (GMT), to account for the Earth's rotation. This adjustment ensures that the local clock reflects the position of the mean sun relative to the observer's meridian.^[1]^[12] The correction is based on the fact that the Earth rotates 360 degrees in 24 hours, resulting in a time difference of 4 minutes per degree of longitude. The formula for the time difference \Delta t is:

\Delta t = \Delta \lambda \times 4 \text{ minutes},

where \Delta \lambda is the longitude difference in degrees from the reference meridian (positive for east, negative for west). Locations east of the reference are ahead in time, while those west are behind.^[11]^[1] For example, a location at 15° east longitude from Greenwich experiences a correction of $15 \times 4 = 60 minutes, or 1 hour ahead of GMT, so its LMT is 1 hour later than GMT at any given moment.^[1] This longitude correction aligns the local clock such that at 12:00 local mean noon, the mean sun is at its highest point on the local meridian.^[13]

Adjustment for Equation of Time

The equation of time (EOT) is defined as the difference between apparent solar time, which is determined by the actual position of the Sun, and mean solar time, which assumes a uniform daily motion of the Sun.^[9] This discrepancy arises primarily from the Earth's elliptical orbit and axial tilt, causing variations of up to ±16 minutes throughout the year.^[9] The conversion between local apparent time (LAT) and local mean time (LMT) uses the relation LMT = LAT - EOT, where EOT is expressed in time units such as minutes.^[9] Values of EOT are commonly obtained from astronomical tables or graphical representations provided by observatories, allowing precise adjustments for specific dates. For computational purposes, approximations like the simplified Spencer formula offer a practical method:

\text{EOT} \approx 9.87 \sin(2B) - 7.53 \cos(B) - 1.5 \sin(B)

where EOT is in minutes, trigonometric functions use degrees, and B = \frac{360^\circ (N - 81)}{365} with N as the day of the year (January 1 = 1).^[14] This formula, derived from a Fourier series analysis, provides accuracy within about 0.5 minutes.^[14] The EOT crosses zero four times annually, approximately on April 15, June 14, September 1, and December 25, when apparent and mean solar times coincide.^[15] It achieves a maximum positive value of roughly +14 minutes around early February, indicating apparent time ahead of mean time, and a minimum negative value of about -16 minutes around early November, where mean time leads apparent time.^[9] For example, on February 14, the EOT is approximately +14 minutes, meaning local mean time lags local apparent time by 14 minutes—a sundial would read about 12:14 p.m. when the mean clock shows noon.^[16]

Historical Development

Origins in Astronomy

The origins of local mean time trace back to ancient astronomical observations that revealed irregularities in the length of solar days, particularly through systematic monitoring of equinoxes and solstices. Babylonian astronomers, from around the 2nd millennium BCE, conducted detailed records of celestial events, including the identification of solstices and equinoxes by associating them with the rising of specific constellations, which highlighted variations in daylight duration across seasons.^[17] These observations laid early groundwork for recognizing that apparent solar days were not uniform, as equinox timings showed deviations influenced by the Earth's tilt and orbital path. Greek astronomers built upon this foundation, with Hipparchus in the 2nd century BCE noting discrepancies between expected and observed solar positions at equinoxes, attributing them to non-uniform solar motion along the ecliptic.^[18] A pivotal advancement came in the 2nd century CE with Claudius Ptolemy's Almagest, which formalized the concept of the Sun's mean motion as a uniform circular progression to model planetary paths more accurately. In Book III, Ptolemy described mean motion as the average angular speed of the Sun around the ecliptic, distinct from its apparent irregular path, enabling the construction of ephemerides that accounted for daily variations. This distinction addressed the equation of time—the difference between apparent and mean solar time—through tabulated corrections derived from equinox and solstice data, though Ptolemy's mean time still incorporated minor offsets from modern definitions.^[19] In the 17th century, Isaac Newton's Philosophiæ Naturalis Principia Mathematica (1687) provided a theoretical explanation for these irregularities by demonstrating that the Earth's elliptical orbit around the Sun, governed by universal gravitation, causes the Sun's apparent speed to vary, directly contributing to the equation of time's eccentricity component.^[20] Concurrently, Christiaan Huygens' invention of the pendulum clock in 1656 revolutionized precise time measurement, achieving accuracy of less than one minute per day and allowing astronomers to track mean time independently of solar observations for the first time.^[21] By the 18th century, the term "mean solar time" was standardized in astronomical tables, such as those in John Flamsteed's Historia Coelestis Britannica (1725), for ephemeris calculations that required uniform temporal references over irregular apparent solar intervals.^[19]

Adoption in Civil Timekeeping

During the 18th and 19th centuries, the proliferation of precise mechanical clocks enabled the widespread adoption of local mean time for civil timekeeping in Europe and North America, replacing the irregular apparent solar time to ensure more uniform day lengths for societal routines.^[22] This shift was accelerated by the rapid growth of railroad networks, which demanded synchronized local times across regions to coordinate timetables and prevent accidents from mismatched schedules.^[23] In Britain, for instance, the expansion of railways from the 1830s onward highlighted the limitations of disparate local times, prompting efforts to align clocks based on mean solar positions.^[24] A pivotal development occurred in 1847 when the British Railway Clearing House, an industry regulatory body, mandated the use of Greenwich Mean Time—the local mean time at the 0° meridian—for all railway stations to facilitate seamless operations across the expanding network.^[25] This standardization on a specific local mean time variant not only resolved rail coordination issues but also influenced public clock settings in connected urban areas, promoting broader civil reliance on mean time principles.^[26] By the mid-19th century, the majority of cities in these regions calibrated their public clocks to local mean noon, achieved through daily observations of the sun or stars crossing the local meridian at observatories, or by telegraphic dissemination of precise signals from reference sites.^[27] Such methods ensured clocks approximated the Earth's average rotation rate, supporting reliable commerce, public services, and early industrial schedules without the daily fluctuations of apparent time.^[28] In the United States, major cities such as Philadelphia adhered to local mean time until 1883, resulting in substantial temporal disparities—often exceeding three hours—between coastal and continental interiors due to longitude spans, which exacerbated challenges for transcontinental rail travel.^[29]

Transition and Modern Context

Shift to Standard Time Zones

The shift from local mean time to standardized time zones gained momentum in the late 19th century, primarily to address the logistical challenges posed by rapid industrialization, expanding rail networks, and growing international trade. In the United States, the General Railroad Time Convention, convened in October 1883, represented a key catalyst, as representatives from major railroad companies approved a plan to divide North America into five time zones—Intercolonial, Eastern, Central, Mountain, and Pacific—each centered on meridians 15 degrees of longitude apart.^[29] These zones approximated local mean time for practicality but intentionally ignored precise local longitudes to prioritize uniformity across vast distances, thereby simplifying train schedules and reducing scheduling errors that had previously required adjustments for hundreds of disparate local times.^[29] Building on this domestic initiative, the International Meridian Conference, held in Washington, D.C., from October to November 1884, advanced the global standardization effort by adopting the Greenwich meridian as the international prime meridian and recommending a system of 24 standard time zones worldwide.^[30] Attended by delegates from 25 nations, the conference emphasized the need for a common temporal reference to harmonize navigation, communication, and commerce, effectively laying the groundwork for replacing fragmented local mean times with a coordinated framework based on Greenwich Mean Time.^[30] Each standard time zone ideally spans 15 degrees of longitude to align with the Earth's 24-hour rotation, creating a one-hour difference between adjacent zones and resulting in potential offsets of up to 30 minutes from true local mean time at zone boundaries.^[31] While the 1883 railroad initiative and 1884 conference provided the framework, the transition was gradual, with standard time zones becoming legally mandated in the United States via the Standard Time Act of 1918, and similar processes occurring internationally over subsequent decades.^[32] This transition markedly decreased confusion in cross-regional travel and economic activities, as synchronized clocks facilitated reliable railroad operations, telegraph coordination, and market transactions.^[29] Nonetheless, it encountered initial resistance from many communities, particularly those near zone edges, who favored the solar alignment of local mean time and perceived the new system as an artificial disruption to natural daily cycles and local autonomy.^[29]

Remaining Applications

In modern astronomy, local mean time continues to serve as a foundational reference for sidereal-to-solar time conversions at observatories, enabling precise scheduling of observations based on the mean Sun's position relative to the local meridian.^[33] This is particularly useful for calculating when celestial objects transit the meridian, as local sidereal time is derived by adjusting Greenwich mean sidereal time for longitude and then relating it back to local mean solar time, which accounts for the Earth's uniform rotation under an idealized mean Sun.^[34] For instance, observatory software often employs local mean time to determine exact solar noon for aligning telescopes or modeling planetary positions, ensuring accuracy in ephemeris computations independent of civil time zones.^[33] In celestial navigation, local mean time retains a legacy role in traditional methods, particularly for interpreting sight reduction tables and computing meridian passages in the Nautical Almanac.^[35] Mariners using sextants for latitude or longitude fixes convert zone time to local mean time by applying a longitude correction (up to about 30 minutes at sea), which serves as the reference for the mean Sun's transit at noon.^[35] Although GPS has largely supplanted these techniques for routine positioning, local mean time persists in training, backup systems, and scenarios where electronic aids are unavailable or unreliable, such as in remote oceanic voyages.^[35] Certain legal and regulatory contexts reference local mean time equivalents for defining solar-dependent boundaries, such as in statutes governing sunrise and sunset for activities like fishing or hunting to ensure consistency with natural light cycles.^[9] For example, some environmental regulations approximate these times using local mean solar time on the central meridian of a time zone, which aligns closely with civil time (to within 0.9 seconds) but provides a standardized solar baseline for compliance.^[9] This application underscores local mean time's role in niche fact-finding where apparent solar variations could otherwise complicate enforcement. Contemporary software and mobile applications facilitate instantaneous computation of local mean time from UTC by incorporating longitude and equation-of-time adjustments, making it accessible for specialized users without manual calculations.^[36] Tools from the U.S. Naval Observatory, for instance, output local mean sidereal and solar times for any date and location, supporting both astronomical and navigational needs.^[33] However, with the global dominance of UTC and standard time zones, local mean time holds no relevance for everyday clocks or synchronization, rendering it obsolete in civil timekeeping.^[1]

References

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What Is Local Mean Time (LMT)? - Time and Date
Local Mean Time (LMT) is a type of solar time, a timekeeping method using the Sun's movements across the sky. It is based on the average length of a solar day.
[2]
[PDF] Chapter 7 Time
The Local Mean Solar Time at a particular longitude is the hour angle of the Mean Sun plus 12 hours. Although, like local apparent solar time, it is local to a ...
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apparent solar day
To make our solar day of uniform length, astronomers have invented the mean sun, a fictitious body which is imagined to move at a uniform rate along the ...Missing: definition | Show results with:definition
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Apparent solar time is based on the position of the Sun in the sky, and mean solar time is based on the average value of a solar day during the year.
[5]
How to read the Alumni Association Sundial at Caltech
It takes the sun 1 day = 1440 minutes to go around the Earth (360 degrees of longitude), so it takes 1440/360 = 4 minutes to go each degree. Hence, whatever ...
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[PDF] STUDY of EARTH'S ATMOSPHERE
has a different value of local mean time tAm. At each longitude tim leads or lags tstd by 4 minutes (or 1/15 hours) for each degree displacement from the.
[7]
The Measurement of Time - NASA ADS
This difference between mean solar time indicated by the mean sun, and true or `apparent' solar time indicated by the true sun is termed the equation of time ...
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The Equation of Time - Astronomical Applications Department
We define apparent solar time at a specific location as 12h + the local hour angle (expressed in hours) of the apparent position of the Sun in the sky. Apparent ...
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4.3 Keeping Time – Astronomy - UCF Pressbooks
Apparent Solar Time. We can define apparent solar time as time reckoned by the actual position of the Sun in the sky (or, during the night, ...
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2.5 Solar Time and Watch Time | EME 810
The time that we use in solar energy is the apparent time and path of the sun relative to the aperture or collection device, called Solar Time. A solar day ...
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Everyday Time and Atomic Time: Part 4 | NIST
Apr 21, 2021 · Greenwich Mean Time (GMT) is then defined as mean solar time as observed at the Greenwich meridian.
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The equation of time specifies the difference between time calculated using ... minutes, and attains its maximum value between the autumnal equinox and ...
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Solar Time | PVEducation
The net Time Correction Factor (in minutes) accounts for the variation of the Local Solar Time (LST) within a given time zone due to the longitude variations ...<|control11|><|separator|>
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Jul 28, 2014 · The four zero value dates are April 15th, June 13th, September 1st and December 25th respectively. The exact timing of these also slip to the ...
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The equation of time is the difference between true and mean solar time, caused by the Earth's elliptical orbit and axis tilt, resulting in variations in true ...
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Aug 19, 2021 · They were the first to identify the solstices and equinoxes of each year with the rising of four constellations, which they identified with ...<|control11|><|separator|>
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Nov 10, 2019 · According to our definitions, the equation of time is therefore the difference between the hour angles of the true sun and the mean sun.Sidereal Time · Non-Uniformity Of True Solar... · The Equation Of Time
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[PDF] The Equation of Time in Ancient Astronomy
Finally, we examine thoroughly the circumstances of the invention of the modern equation of time and we show that Flamsteed was, without any doubt, the inventor.
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Aug 12, 2004 · Paragraph V appeals to the fact that astronomy distinguishes between absolute and relative time in its use of the so-called equation of time.
[20]
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Aug 12, 2009 · In 1656, Christiaan Huygens, a Dutch scientist, made the first pendulum clock, regulated by a mechanism with a "natural" period of oscillation.
[21]
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Oct 4, 2018 · Until the mid-19th century, towns relied on local time, set by the Sun, and the time in London was ahead of that of any town further west—hence ...<|separator|>
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As railroads began to shrink the travel time between cities from days or months to mere hours, however, these local times became a scheduling nightmare.
[23]
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Local mean time varied across Britain from east to west. This is because the Sun rises in the east, and it takes time for it to travel to the west.
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In 1847, the Railway Clearing House, an industry standards body, recommended that Greenwich Mean Time (GMT) be adopted at all stations as soon as the General ...
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Essentially, mean time is clock time rather than solar (astronomical) time. ... In 1767 Maskelyne introduced the Nautical Almanac as part of the great 18th ...
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Nov 1, 2024 · Time in the late 19th century was a regional affair. Cities would set their clocks by measuring the path of the sun across the meridian.
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On November 18, 1883, local times across the nation—determined by the position of the sun overhead—were consolidated into standardized time zones.Missing: mean | Show results with:mean
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[PDF] THE CENTENARY OF THE PRIME MERIDIAN AND OF ...
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[30]
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At 150 degrees west (or 150° W) longitude, the time should be 150 degrees divided by 15 degrees = 10 hours behind UTC, or UTC-10. At 75 degrees east (or 75° E) ...Missing: bands | Show results with:bands
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Sidereal Time - Astronomical Applications Department
This data service calculates Greenwich and local mean and apparent sidereal time.
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Astronomical Time Keeping Systems | Telescope Live
Local Mean Time (LMT): LMT is just the sun's position relative to the local meridian and depends on the observer's geographic position. An LMT of Noon is ...
[33]
None
### Summary of Local Mean Time in Celestial Navigation and Its Current Relevance
[34]
mysolartime.com: Real-Time Solar Time
The site displays true, mean, and legal solar time. You can select a date and hour, and set a timezone, or click on the map for location.