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81-450: Since Earth rotates eastward, all celestial objects outside the circumpolar circle (including the Sun , Moon, and stars ) rise in the east and set in the west for observers outside the polar circles . Seasonal variation means that they sometimes rise in the east-northeast or east-southeast, and sometimes set in the west-southwest or west-northwest. This north-south variation of the point along

162-402: A graticule is drawn on the surface, but varying curvature in any other direction. For an oblate ellipsoid, the polar radius of curvature r p {\displaystyle r_{p}} is larger than the equatorial because the pole is flattened: the flatter the surface, the larger the sphere must be to approximate it. Conversely, the ellipsoid's north–south radius of curvature at

243-488: A spherical Earth offers a simple surface that is easy to deal with mathematically. Many astronomical and navigational computations use a sphere to model the Earth as a close approximation. However, a more accurate figure is needed for measuring distances and areas on the scale beyond the purely local. Better approximations can be made by modeling the entire surface as an oblate spheroid , using spherical harmonics to approximate

324-428: A circle and therefore that the ellipsoid is triaxial has been a matter of scientific inquiry for many years. Modern technological developments have furnished new and rapid methods for data collection and, since the launch of Sputnik 1 , orbital data have been used to investigate the theory of ellipticity. More recent results indicate a 70 m difference between the two equatorial major and minor axes of inertia, with

405-570: A flattening at the South Pole and a bulge of the same degree at the North Pole , with the sea level increased about 9 m (30 ft) at the latter. This theory implies the northern middle latitudes to be slightly flattened and the southern middle latitudes correspondingly bulged. Potential factors involved in this aberration include tides and subcrustal motion (e.g. plate tectonics ). John A. O'Keefe and co-authors are credited with

486-466: A mass distributed more closely around its centre of gravity spins faster. Among the ancient Greeks , several of the Pythagorean school believed in the rotation of Earth rather than the apparent diurnal rotation of the heavens. Perhaps the first was Philolaus (470–385 BCE), though his system was complicated, including a counter-earth rotating daily about a central fire. A more conventional picture

567-537: A point on Earth can be approximated by multiplying the speed at the equator by the cosine of the latitude. For example, the Kennedy Space Center is located at latitude 28.59° N, which yields a speed of: cos(28.59°) × 1,674.4 km/h = 1,470.2 km/h. Latitude is a placement consideration for spaceports . The peak of the Cayambe volcano is the point of Earth 's surface farthest from its axis; thus, it rotates

648-524: A rate depending on latitude. At the latitude of Paris, the predicted and observed shift was about 11 degrees clockwise per hour. Foucault pendulums now swing in museums worldwide . Earth's rotation period relative to the Sun ( solar noon to solar noon) is its true solar day or apparent solar day . It depends on Earth's orbital motion and is thus affected by changes in the eccentricity and inclination of Earth's orbit. Both vary over thousands of years, so

729-409: A shorter day, meaning Earth was turning faster throughout the past. Around every 25–30 years Earth's rotation slows temporarily by a few milliseconds per day, usually lasting around five years. 2017 was the fourth consecutive year that Earth's rotation has slowed. The cause of this variability has not yet been determined. Earth's original rotation was a vestige of the original angular momentum of

810-417: Is 86 164.090 530 832 88  seconds of mean solar time (UT1) (23 56 4.090 530 832 88 , 0.997 269 566 329 08  mean solar days ). Thus, the sidereal day is shorter than the stellar day by about 8.4 ms . Both the stellar day and the sidereal day are shorter than the mean solar day by about 3 minutes 56 seconds . This is a result of the Earth turning 1 additional rotation, relative to

891-407: Is a characteristic of perfect spheres, the Earth deviates from spherical by only a third of a percent, sufficiently close to treat it as a sphere in many contexts and justifying the term "the radius of the Earth". The concept of a spherical Earth dates back to around the 6th century BC , but remained a matter of philosophical speculation until the 3rd century BC . The first scientific estimation of

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972-435: Is about 20 seconds longer near a solstice when the projection of the Sun's apparent motion along the ecliptic onto the celestial equator causes the Sun to move through a greater angle than usual. Conversely, near an equinox the projection onto the equator is shorter by about 20 seconds . Currently, the perihelion and solstice effects combine to lengthen the true solar day near 22 December by 30 mean solar seconds, but

1053-507: Is best seen from late night to early morning . The Moon rises 30 to 70 minutes (should be a fixed number, about 50 minutes, if it's the same 13 degrees) later each day /night than the day/night before, due to the fact that the Moon moves 13 degrees every day. Hence, the Earth must move 13 degrees after completing one rotation for the Moon to be visible. The Moon appears to be larger at moonrise or moonset due to an illusion. This illusion, known as

1134-426: Is intended to model the entire Earth or only some portion of it. A sphere has a single radius of curvature , which is simply the radius of the sphere. More complex surfaces have radii of curvature that vary over the surface. The radius of curvature describes the radius of the sphere that best approximates the surface at that point. Oblate ellipsoids have a constant radius of curvature east to west along parallels , if

1215-612: Is known as the equation of time . Earth's rotation period relative to the International Celestial Reference Frame , called its stellar day by the International Earth Rotation and Reference Systems Service (IERS), is 86 164.098 903 691 seconds of mean solar time (UT1) (23 56 4.098 903 691 , 0.997 269 663 237 16  mean solar days ). Earth's rotation period relative to the precessing mean vernal equinox , named sidereal day ,

1296-472: Is primarily due to free core nutation and the Chandler wobble . Over millions of years, Earth's rotation has been slowed significantly by tidal acceleration through gravitational interactions with the Moon. Thus angular momentum is slowly transferred to the Moon at a rate proportional to r − 6 {\displaystyle r^{-6}} , where r {\displaystyle r}

1377-492: Is rotating once around its axis requires that Earth rotate slightly more than once relative to the fixed stars before the mean Sun can pass overhead again, even though it rotates only once (360°) relative to the mean Sun. Multiplying the value in rad/s by Earth's equatorial radius of 6,378,137 m ( WGS84 ellipsoid) (factors of 2π radians needed by both cancel) yields an equatorial speed of 465.10 metres per second (1,674.4 km/h). Some sources state that Earth's equatorial speed

1458-501: Is slightly less, or 1,669.8 km/h . This is obtained by dividing Earth's equatorial circumference by 24 hours . However, the use of the solar day is incorrect; it must be the sidereal day , so the corresponding time unit must be a sidereal hour. This is confirmed by multiplying by the number of sidereal days in one mean solar day, 1.002 737 909 350 795 , which yields the equatorial speed in mean solar hours given above of 1,674.4 km/h. The tangential speed of Earth's rotation at

1539-430: Is slightly longer than an SI second because Earth's mean solar day is now slightly longer than it was during the 19th century due to tidal friction . The average length of the mean solar day since the introduction of the leap second in 1972 has been about 0 to 2 ms longer than 86,400 SI seconds. Random fluctuations due to core-mantle coupling have an amplitude of about 5 ms. The mean solar second between 1750 and 1892

1620-408: Is small, only about one part in 300. Historically, flattening was computed from grade measurements . Nowadays, geodetic networks and satellite geodesy are used. In practice, many reference ellipsoids have been developed over the centuries from different surveys. The flattening value varies slightly from one reference ellipsoid to another, reflecting local conditions and whether the reference ellipsoid

1701-524: Is the net effect of gravitation (due to mass attraction) and centrifugal force (due to rotation). It can be measured very accurately at the surface and remotely by satellites. True vertical generally does not correspond to theoretical vertical ( deflection ranges up to 50") because topography and all geological masses disturb the gravitational field. Therefore, the gross structure of the Earth's crust and mantle can be determined by geodetic-geophysical models of

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1782-406: Is the orbital radius of the Moon. This process has gradually increased the length of the day to its current value, and resulted in the Moon being tidally locked with Earth. This gradual rotational deceleration is empirically documented by estimates of day lengths obtained from observations of tidal rhythmites and stromatolites ; a compilation of these measurements found that the length of

1863-537: Is the other point where Earth's axis of rotation intersects its surface, in Antarctica . Earth rotates once in about 24 hours with respect to the Sun , but once every 23 hours, 56 minutes and 4 seconds with respect to other distant stars ( see below ). Earth's rotation is slowing slightly with time; thus, a day was shorter in the past. This is due to the tidal effects the Moon has on Earth's rotation. Atomic clocks show that

1944-485: The 2004 Indian Ocean earthquake , have caused the length of a day to shorten by 3 microseconds by reducing Earth's moment of inertia . Post-glacial rebound , ongoing since the last ice age , is also changing the distribution of Earth's mass, thus affecting the moment of inertia of Earth and, by the conservation of angular momentum , Earth's rotation period. The length of the day can also be influenced by man-made structures. For example, NASA scientists calculated that

2025-491: The Equator bulges and the geographical poles are flattened. In his Principia , Newton predicted this flattening would amount to one part in 230, and pointed to the pendulum measurements taken by Richer in 1673 as corroboration of the change in gravity , but initial measurements of meridian lengths by Picard and Cassini at the end of the 17th century suggested the opposite. However, measurements by Maupertuis and

2106-583: The French Geodesic Mission in the 1730s established the oblateness of Earth , thus confirming the positions of both Newton and Copernicus . In Earth's rotating frame of reference, a freely moving body follows an apparent path that deviates from the one it would follow in a fixed frame of reference. Because of the Coriolis effect , falling bodies veer slightly eastward from the vertical plumb line below their point of release, and projectiles veer right in

2187-450: The Moon illusion , is caused by an effect of the brain . There is no definitive explanation for the Moon illusion. However, it is most likely because of how the brain perceives objects at different distances, and/or the distance we expect objects to be from us when they are near the horizon. The Moon appears to be more yellowish near the horizon. This is for the same reason the Sun and/or sky appears to be orangey-red at sunrise/sunset. When

2268-573: The Northern Hemisphere (and left in the Southern ) from the direction in which they are shot. The Coriolis effect is mainly observable at a meteorological scale, where it is responsible for the opposite directions of cyclone rotation in the Northern and Southern hemispheres (anticlockwise and clockwise , respectively). Hooke, following a suggestion from Newton in 1679, tried unsuccessfully to verify

2349-423: The geoid , or modeling a region with a best-fit reference ellipsoid . For surveys of small areas, a planar (flat) model of Earth's surface suffices because the local topography overwhelms the curvature. Plane-table surveys are made for relatively small areas without considering the size and shape of the entire Earth. A survey of a city, for example, might be conducted this way. By the late 1600s, serious effort

2430-465: The idea of a sphere of fixed stars that rotated about Earth. This was accepted by most of those who came after, in particular Claudius Ptolemy (2nd century CE), who thought Earth would be devastated by gales if it rotated. In 499 CE, the Indian astronomer Aryabhata suggested that the spherical Earth rotates about its axis daily and that the apparent movement of the stars is a relative motion caused by

2511-498: The orientation of the rotation axis in space. Earth rotates eastward , in prograde motion . As viewed from the northern polar star Polaris , Earth turns counterclockwise . The North Pole , also known as the Geographic North Pole or Terrestrial North Pole, is the point in the Northern Hemisphere where Earth's axis of rotation meets its surface. This point is distinct from Earth's North Magnetic Pole . The South Pole

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2592-458: The 8th century BCE, as well as from the medieval Islamic world and elsewhere. These observations can be used to determine changes in Earth's rotation over the last 27 centuries, since the length of the day is a critical parameter in the calculation of the place and time of eclipses. A change in day length of milliseconds per century shows up as a change of hours and thousands of kilometers in eclipse observations. The ancient data are consistent with

2673-409: The Earth is the size and shape used to model planet Earth . The kind of figure depends on application, including the precision needed for the model. A spherical Earth is a well-known historical approximation that is satisfactory for geography , astronomy and many other purposes. Several models with greater accuracy (including ellipsoid ) have been developed so that coordinate systems can serve

2754-444: The Earth as a sphere each yield a mean radius of 6,371 km (3,959 mi). Regardless of the model, any radius falls between the polar minimum of about 6,357 km (3,950 mi) and the equatorial maximum of about 6,378 km (3,963 mi). The difference 21 km (13 mi) correspond to the polar radius being approximately 0.3% shorter than the equatorial radius. As theorized by Isaac Newton and Christiaan Huygens ,

2835-402: The Earth is flattened at the poles and bulged at the equator . Thus, geodesy represents the figure of the Earth as an oblate spheroid . The oblate spheroid, or oblate ellipsoid , is an ellipsoid of revolution obtained by rotating an ellipse about its shorter axis. It is the regular geometric shape that most nearly approximates the shape of the Earth. A spheroid describing the figure of

2916-419: The Earth or other celestial body is called a reference ellipsoid . The reference ellipsoid for Earth is called an Earth ellipsoid . An ellipsoid of revolution is uniquely defined by two quantities. Several conventions for expressing the two quantities are used in geodesy, but they are all equivalent to and convertible with each other: Eccentricity and flattening are different ways of expressing how squashed

2997-406: The Earth's mass attraction ( gravitation ) and the centrifugal force of the Earth's rotation . As a result of the uneven distribution of the Earth's mass, the geoidal surface is irregular and, since the ellipsoid is a regular surface, the separations between the two, referred to as geoid undulations , geoid heights, or geoid separations, will be irregular as well. The geoid is a surface along which

3078-416: The Moon appears near the horizon, the light coming from it has to pass through more layers of atmosphere. This scatters the blue away, and leaves yellow, orange, and red. This is also the reason the Moon appears red during a deep partial or total lunar eclipse . Earth%27s rotation Earth's rotation or Earth's spin is the rotation of planet Earth around its own axis , as well as changes in

3159-431: The Moon, and possibly climate change, which is causing the ice at Earth's poles to melt. The masses of ice account for the Earth's shape being that of an oblate spheroid , bulging around the equator. When these masses are reduced, the poles rebound from the loss of weight, and Earth becomes more spherical, which has the effect of bringing mass closer to its centre of gravity. Conservation of angular momentum dictates that

3240-665: The South Pole. The polar asymmetry is about a thousand times smaller than the Earth's flattening and even smaller than its geoidal undulation in some regions. Modern geodesy tends to retain the ellipsoid of revolution as a reference ellipsoid and treat triaxiality and pear shape as a part of the geoid figure: they are represented by the spherical harmonic coefficients C 22 , S 22 {\displaystyle C_{22},S_{22}} and C 30 {\displaystyle C_{30}} , respectively, corresponding to degree and order numbers 2.2 for

3321-580: The angle of the North Star , which he incorrectly interpreted as having varying diurnal motion . The theory of a slightly pear-shaped Earth arose when data was received from the U.S.'s artificial satellite Vanguard 1 in 1958. It was found to vary in its long periodic orbit, with the Southern Hemisphere exhibiting higher gravitational attraction than the Northern Hemisphere. This indicated

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3402-418: The annual variation of the true solar day also varies. Generally, it is longer than the mean solar day during two periods of the year and shorter during another two. The true solar day tends to be longer near perihelion when the Sun apparently moves along the ecliptic through a greater angle than usual, taking about 10 seconds longer to do so. Conversely, it is about 10 seconds shorter near aphelion . It

3483-400: The astrolabe called al-zūraqī based on the idea believed by some of his contemporaries "that the motion we see is due to the Earth's movement and not to that of the sky." The prevalence of this view is further confirmed by a reference from the 13th century which states: "According to the geometers [or engineers] ( muhandisīn ), the Earth is in constant circular motion, and what appears to be

3564-503: The atmospheric tide, resulting in no net torque and a constant rotational period. This stabilizing effect could have been broken by a sudden change in global temperature. Recent computational simulations support this hypothesis and suggest the Marinoan or Sturtian glaciations broke this stable configuration about 600 Myr ago; the simulated results agree quite closely with existing paleorotational data. Some recent large-scale events, such as

3645-567: The celestial reference frame, as it orbits the Sun (so 366.24 rotations/y). The mean solar day in SI seconds is available from the IERS for the periods 1623–2005 and 1962–2005 . Recently (1999–2010) the average annual length of the mean solar day in excess of 86,400 SI seconds has varied between 0.25 ms and 1 ms , which must be added to both the stellar and sidereal days given in mean solar time above to obtain their lengths in SI seconds (see Fluctuations in

3726-531: The cloud of dust , rocks and gas that coalesced to form the Solar System . This primordial cloud was composed of hydrogen and helium produced in the Big Bang , as well as heavier elements ejected by supernovas . As this interstellar dust is heterogeneous, any asymmetry during gravitational accretion resulted in the angular momentum of the eventual planet. However, if the giant-impact hypothesis for

3807-452: The day has increased steadily from about 21 hours at 600 Myr ago to the current 24-hour value. By counting the microscopic lamina that form at higher tides, tidal frequencies (and thus day lengths) can be estimated, much like counting tree rings, though these estimates can be increasingly unreliable at older ages. The current rate of tidal deceleration is anomalously high, implying Earth's rotational velocity must have decreased more slowly in

3888-427: The decades before. On June 29, 2022, Earth's spin was completed in 1.59 milliseconds under 24 hours, setting a new record. Because of that trend, engineers worldwide are discussing a 'negative leap second' and other possible timekeeping measures. This increase in speed is thought to be due to various factors, including the complex motion of its molten core, oceans, and atmosphere, the effect of celestial bodies such as

3969-472: The discovery that the Earth had a significant third degree zonal spherical harmonic in its gravitational field using Vanguard 1 satellite data. Based on further satellite geodesy data, Desmond King-Hele refined the estimate to a 45 m (148 ft) difference between north and south polar radii, owing to a 19 m (62 ft) "stem" rising in the North Pole and a 26 m (85 ft) depression in

4050-559: The ellipsoid in the vicinity of a given point is the Earth's osculating sphere . Its radius equals Earth's Gaussian radius of curvature , and its radial direction coincides with the geodetic normal direction. The center of the osculating sphere is offset from the center of the ellipsoid, but is at the center of curvature for the given point on the ellipsoid surface. This concept aids the interpretation of terrestrial and planetary radio occultation refraction measurements and in some navigation and surveillance applications. Determining

4131-451: The ellipsoid is. When flattening appears as one of the defining quantities in geodesy, generally it is expressed by its reciprocal. For example, in the WGS 84 spheroid used by today's GPS systems, the reciprocal of the flattening 1 / f {\displaystyle 1/f} is set to be exactly 298.257 223 563 . The difference between a sphere and a reference ellipsoid for Earth

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4212-443: The equator r e {\displaystyle r_{e}} is smaller than the polar where a {\displaystyle a} is the distance from the center of the ellipsoid to the equator (semi-major axis), and b {\displaystyle b} is the distance from the center to the pole. (semi-minor axis) The possibility that the Earth's equator is better characterized as an ellipse rather than

4293-405: The exact figure of the Earth is not only a geometric task of geodesy, but also has geophysical considerations. According to theoretical arguments by Newton, Leonhard Euler , and others, a body having a uniform density of 5,515 kg/m that rotates like the Earth should have a flattening of 1:229. This can be concluded without any information about the composition of Earth's interior . However,

4374-408: The fastest as Earth spins. Earth's rotation axis moves with respect to the fixed stars ( inertial space ); the components of this motion are precession and nutation . It also moves with respect to Earth's crust; this is called polar motion . Precession is a rotation of Earth's rotation axis, caused primarily by external torques from the gravity of the Sun, Moon and other bodies. The polar motion

4455-400: The figure of the Earth. The models for the figure of the Earth vary in the way they are used, in their complexity, and in the accuracy with which they represent the size and shape of the Earth. The simplest model for the shape of the entire Earth is a sphere. The Earth's radius is the distance from Earth's center to its surface, about 6,371 km (3,959 mi). While "radius" normally

4536-470: The fourteenth century. Not until Nicolaus Copernicus in 1543 adopted a heliocentric world system did the contemporary understanding of Earth's rotation begin to be established. Copernicus pointed out that if the movement of the Earth is violent, then the stars' movement must be much more so. He acknowledged the contribution of the Pythagoreans and pointed to examples of relative motion. For Copernicus, this

4617-481: The geoid. The angle between the plumb line which is perpendicular to the geoid (sometimes called "the vertical") and the perpendicular to the ellipsoid (sometimes called "the ellipsoidal normal") is defined as the deflection of the vertical . It has two components: an east–west and a north–south component. Simpler local approximations are possible. The local tangent plane is appropriate for analysis across small distances. The best local spherical approximation to

4698-402: The gravity potential is equal everywhere and to which the direction of gravity is always perpendicular. The latter is particularly important because optical instruments containing gravity-reference leveling devices are commonly used to make geodetic measurements. When properly adjusted, the vertical axis of the instrument coincides with the direction of gravity and is, therefore, perpendicular to

4779-433: The horizon is bookended by two lunar standstills or turnarounds, the directions of which are sometimes depicted in archaeoastronomical constructions. It takes 18.6 years for the Moon to traverse this variation viewed from a vantage point on Earth. The Moon's position relative to Earth and the Sun determines the moonrise and moonset time. For example, a last quarter rises at midnight and sets at noon . A waning gibbous

4860-414: The larger semidiameter pointing to 15° W longitude (and also 180-degree away). Following work by Picard, Italian polymath Giovanni Domenico Cassini found that the length of a degree was apparently shorter north of Paris than to the south, implying the Earth to be egg -shaped. In 1498, Christopher Columbus dubiously suggested that the Earth was pear-shaped based on his disparate mobile readings of

4941-403: The length of day ). The angular speed of Earth's rotation in inertial space is (7.292 115 0 ± 0.000 000 1) × 10 ^   radians per SI second . Multiplying by (180°/π radians) × (86,400 seconds/day) yields 360.985 6  °/day , indicating that Earth rotates more than 360 degrees relative to the fixed stars in one solar day. Earth's movement along its nearly circular orbit while it

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5022-428: The measured flattening is 1:298.25, which is closer to a sphere and a strong argument that Earth's core is extremely compact. Therefore, the density must be a function of the depth, ranging from 2,600 kg/m at the surface (rock density of granite , etc.), up to 13,000 kg/m within the inner core. Also with implications for the physical exploration of the Earth's interior is the gravitational field , which

5103-665: The mid- to late 20th century, research across the geosciences contributed to drastic improvements in the accuracy of the figure of the Earth. The primary utility of this improved accuracy was to provide geographical and gravitational data for the inertial guidance systems of ballistic missiles . This funding also drove the expansion of geoscientific disciplines, fostering the creation and growth of various geoscience departments at many universities. These developments benefited many civilian pursuits as well, such as weather and communication satellite control and GPS location-finding, which would be impossible without highly accurate models for

5184-449: The modern day is longer by about 1.7 milliseconds than a century ago, slowly increasing the rate at which UTC is adjusted by leap seconds . Analysis of historical astronomical records shows a slowing trend; the length of a day increased by about 2.3 milliseconds per century since the 8th century BCE . Scientists reported that in 2020 Earth had started spinning faster, after consistently spinning slower than 86,400 seconds per day in

5265-438: The motion of Earth about the Sun are called "semi-Copernicans". A century after Copernicus, Riccioli disputed the model of a rotating Earth due to the lack of then-observable eastward deflections in falling bodies; such deflections would later be called the Coriolis effect . However, the contributions of Kepler, Galileo , and Newton gathered support for the theory of the rotation of the Earth. Earth's rotation implies that

5346-602: The motion of the heavens is actually due to the motion of the Earth and not the stars." Treatises were written to discuss its possibility, either as refutations or expressing doubts about Ptolemy's arguments against it. At the Maragha and Samarkand observatories , Earth's rotation was discussed by Tusi (born 1201) and Qushji (born 1403); the arguments and evidence they used resemble those used by Copernicus. In medieval Europe, Thomas Aquinas accepted Aristotle's view and so, reluctantly, did John Buridan and Nicole Oresme in

5427-454: The origin of the Moon is correct, this primordial rotation rate would have been reset by the Theia impact 4.5 billion years ago. Regardless of the speed and tilt of Earth's rotation before the impact, it would have experienced a day some five hours long after the impact. Tidal effects would then have slowed this rate to its modern value. Earth%27s shape In geodesy , the figure of

5508-489: The past. Empirical data tentatively shows a sharp increase in rotational deceleration about 600 Myr ago. Some models suggest that Earth maintained a constant day length of 21 hours throughout much of the Precambrian . This day length corresponds to the semidiurnal resonant period of the thermally driven atmospheric tide ; at this day length, the decelerative lunar torque could have been canceled by an accelerative torque from

5589-493: The precise needs of navigation , surveying , cadastre , land use , and various other concerns. Earth's topographic surface is apparent with its variety of land forms and water areas. This topographic surface is generally the concern of topographers, hydrographers , and geophysicists . While it is the surface on which Earth measurements are made, mathematically modeling it while taking the irregularities into account would be extremely complicated. The Pythagorean concept of

5670-573: The predicted eastward deviation of a body dropped from a height of 8.2 meters , but definitive results were obtained later, in the late 18th and early 19th centuries, by Giovanni Battista Guglielmini in Bologna , Johann Friedrich Benzenberg in Hamburg and Ferdinand Reich in Freiberg , using taller towers and carefully released weights. A ball dropped from a height of 158.5 m departed by 27.4 mm from

5751-411: The radius of the Earth was given by Eratosthenes about 240 BC, with estimates of the accuracy of Eratosthenes's measurement ranging from −1% to 15%. The Earth is only approximately spherical, so no single value serves as its natural radius. Distances from points on the surface to the center range from 6,353 km (3,948 mi) to 6,384 km (3,967 mi). Several different ways of modeling

5832-430: The rotation of the Earth. He provided the following analogy: "Just as a man in a boat going in one direction sees the stationary things on the bank as moving in the opposite direction, in the same way to a man at Lanka the fixed stars appear to be going westward." In the 10th century, some Muslim astronomers accepted that the Earth rotates around its axis. According to al-Biruni , al-Sijzi (d. c. 1020) invented an

5913-417: The size and shape of the Earth in the area of the survey. The actual measurements made on the surface of the Earth with certain instruments are however referred to the geoid. The ellipsoid is a mathematically defined regular surface with specific dimensions. The geoid, on the other hand, coincides with that surface to which the oceans would conform over the entire Earth if free to adjust to the combined effect of

5994-414: The solstice effect is partially cancelled by the aphelion effect near 19 June when it is only 13 seconds longer. The effects of the equinoxes shorten it near 26 March and 16 September by 18 seconds and 21 seconds , respectively. The average of the true solar day during the course of an entire year is the mean solar day , which contains 86,400 mean solar seconds. Currently, each of these seconds

6075-442: The triaxiality and 3.0 for the pear shape. It was stated earlier that measurements are made on the apparent or topographic surface of the Earth and it has just been explained that computations are performed on an ellipsoid. One other surface is involved in geodetic measurement: the geoid. In geodetic surveying, the computation of the geodetic coordinates of points is commonly performed on a reference ellipsoid closely approximating

6156-552: The vertical compared with a calculated value of 28.1 mm. The most celebrated test of Earth's rotation is the Foucault pendulum first built by physicist Léon Foucault in 1851, which consisted of a lead-filled brass sphere suspended 67 m from the top of the Panthéon in Paris. Because of Earth's rotation under the swinging pendulum, the pendulum's plane of oscillation appears to rotate at

6237-1103: The water stored in the Three Gorges Dam has increased the length of Earth's day by 0.06 microseconds due to the shift in mass. The primary monitoring of Earth's rotation is performed by very-long-baseline interferometry coordinated with the Global Positioning System , satellite laser ranging , and other satellite geodesy techniques. This provides an absolute reference for the determination of universal time , precession and nutation . The absolute value of Earth rotation including UT1 and nutation can be determined using space geodetic observations, such as very-long-baseline interferometry and lunar laser ranging , whereas their derivatives, denoted as length-of-day excess and nutation rates can be derived from satellite observations, such as GPS , GLONASS , Galileo and satellite laser ranging to geodetic satellites. There are recorded observations of solar and lunar eclipses by Babylonian and Chinese astronomers beginning in

6318-415: Was chosen in 1895 by Simon Newcomb as the independent unit of time in his Tables of the Sun . These tables were used to calculate the world's ephemerides between 1900 and 1983, so this second became known as the ephemeris second . In 1967 the SI second was made equal to the ephemeris second. The apparent solar time is a measure of Earth's rotation and the difference between it and the mean solar time

6399-457: Was devoted to modeling the Earth as an ellipsoid, beginning with French astronomer Jean Picard 's measurement of a degree of arc along the Paris meridian . Improved maps and better measurement of distances and areas of national territories motivated these early attempts. Surveying instrumentation and techniques improved over the ensuing centuries. Models for the figure of the Earth improved in step. In

6480-402: Was supported by Hicetas , Heraclides and Ecphantus in the fourth century BCE who assumed that Earth rotated but did not suggest that Earth revolved about the Sun. In the third century BCE, Aristarchus of Samos suggested the Sun's central place . However, Aristotle in the fourth century BCE criticized the ideas of Philolaus as being based on theory rather than observation. He established

6561-487: Was the first step in establishing the simpler pattern of planets circling a central Sun. Tycho Brahe , who produced accurate observations on which Kepler based his laws of planetary motion , used Copernicus's work as the basis of a system assuming a stationary Earth. In 1600, William Gilbert strongly supported Earth's rotation in his treatise on Earth's magnetism and thereby influenced many of his contemporaries. Those like Gilbert who did not openly support or reject

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