query: how long is earth 's rotation on its axis

pos: Earth's rotation Earth's rotation Earth's rotation is the rotation of Planet Earth around its own axis. Earth rotates eastward, in prograde motion. As viewed from the north pole star Polaris, Earth turns counter clockwise. 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 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

neg: Earth's rotation asymmetry during gravitational accretion resulted in the angular momentum of the eventual planet. However, if the giant-impact hypothesis for 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 the 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's rotation Earth's rotation is the rotation of Planet Earth around its own axis. Earth rotates eastward, in prograde motion.

neg: Sidereal time 23 h 56 min 4.1 s (86,164.1 s). Earth's rotation is not a simple rotation around an axis that would always remain parallel to itself. Earth's rotational axis itself rotates about a second axis, orthogonal to Earth's orbit, taking about 25,800 years to perform a complete rotation. This phenomenon is called the precession of the equinoxes. Because of this precession, the stars appear to move around Earth in a manner more complicated than a simple constant rotation. For this reason, to simplify the description of Earth's orientation in astronomy and geodesy, it was conventional to chart the positions of the

neg: Rotation around a fixed axis torque tends to cause rotation. To maintain rotation around a fixed axis, the total torque vector has to be along the axis, so that it only changes the magnitude and not the direction of the angular velocity vector. In the case of a hinge, only the component of the torque vector along the axis has an effect on the rotation, other forces and torques are compensated by the structure. The simplest case of rotation around a fixed axis is that of constant angular speed. Then the total torque is zero. For the example of the Earth rotating around its axis,

neg: Spheroid rotation, the figure of the Earth (and of all planets) is not quite a sphere, but instead is slightly flattened in the direction of its axis of rotation. For that reason, in cartography the Earth is often approximated by an oblate spheroid instead of a sphere. The current World Geodetic System model uses a spheroid whose radius is at the Equator and at the poles. The word "spheroid" originally meant "an approximately spherical body", admitting irregularities even beyond the bi- or tri-axial ellipsoidal shape, and that is how the term is used in some older papers on geodesy (for example,

neg: 4179 Toutatis result; to someone on the surface of Toutatis, the Sun would seem to rise and set in apparently random locations and at random times at the asteroid's horizon. It has a rotation period around its long axis (P) of 5.38 days. This long axis is precessing with a period (P) of 7.38 days. The asteroid may have lost most of its original angular momentum and entered into this tumbling motion as a result of the YORP effect. With a semimajor axis of 2.5294 AU, or roughly 2.5 times the distance between Earth and the Sun, Toutatis has a 3:1 orbital

neg: Fictitious force long enough time, the velocity v drops to zero as the matter comes to an equilibrium distribution. For more details, see the articles on sedimentation and the Lamm equation. A related problem is that of centrifugal forces for the Earth-Moon-Sun system, where three rotations appear: the daily rotation of the Earth about its axis, the lunar-month rotation of the Earth-Moon system about their center of mass, and the annual revolution of the Earth-Moon system about the Sun. These three motions influence the tides. Figure 5 shows another example comparing the observations of an inertial observer with those of an observer

neg: Polar motion however, are quite small in magnitude relative to the long-term core/mantle and isostatic rebound components of polar motion. In the absence of external torques, the vector of the angular momentum M of a rotating system remains constant and is directed toward a fixed point in space. In the case of the Earth, it is almost identical with its axis of rotation. The vector of the figure axis F of the system wobbles around M. This motion is called Euler's free nutation. For a rigid Earth which is an oblate spheroid to a good approximation, the figure axis F is its

neg: Foucault pendulum vector diagrams Earth in relation to the pendulum swing increases in time (decreases in effect) with decreasing latitude is related to the Coriolis Effect. As summarized in the Coriolis effect article, the effect is greatest in polar regions where the surface of the Earth is at right angles to the axis of rotation (the central axis of the pendulum aligns with the Earth's axis of rotation). The Coriolis effect decreases nearer the equator because the surface of the Earth is parallel to the axis of rotation (the central axis of the pendulum is perpendicular with the Earth's axis of rotation). Refer to

neg: Flywheel energy storage Left to its own, a spinning flywheel in a vehicle would slowly precess following the Earth's rotation, and precess further yet in vehicles that travel long distances over the Earth's curved spherical surface. A full-motion gimbal has additional problems of how to communicate power into and out of the flywheel, since the flywheel could potentially flip completely over once a day, precessing as the Earth rotates. Full free rotation would require slip rings around each gimbal axis for power conductors, further adding to the design complexity. To reduce space usage, the gimbal system may be of a limited-movement design, using

neg: Axial precession off-center on the opposite side. The gravitational pull on the closer half is stronger, since gravity decreases with the square of distance, so this creates a small torque on the Earth as the Sun pulls harder on one side of the Earth than the other. The axis of this torque is roughly perpendicular to the axis of the Earth's rotation so the axis of rotation precesses. If the Earth was a perfect sphere, there would be no precession. This average torque is perpendicular to the direction in which the rotation axis is tilted away from the ecliptic pole, so that

neg: Symmetry element represented by an axis about which the object rotates in its corresponding symmetry operation. For proper axes of rotation, cyclic symmetry is denoted as C, where n is the order of rotation. Improper rotation, also known as screw axis symmetry, is denoted by S. Improper rotation is the composition of a rotation axis and a mirror plane. In its symmetry operation, the object is rotated about the axis, then reflected across a mirror plane that is normal to the axis of rotation. For inversion, denoted i, there must be a point in the center of an object that is the

neg: Quaternions and spatial rotation the quaternion associated with a spatial rotation R is constructed from its rotation axis S and the rotation angle φ this axis. The associated quaternion is given by, Then the composition of the rotation R with R is the rotation R=RR with rotation axis and angle defined by the product of the quaternions that is Expand this product to obtain Divide both sides of this equation by the identity, which is the law of cosines on a sphere, and compute This is Rodrigues formula for the axis of a composite rotation defined in terms of the axes of the two

neg: 3D rotation group the quaternion associated with a spatial rotation R is constructed from its rotation axis S and the rotation angle "φ" this axis. The associated quaternion is given by, Then the composition of the rotation R with R is the rotation R=RR with rotation axis and angle defined by the product of the quaternions that is Expand this product to obtain Divide both sides of this equation by the identity, which is the law of cosines on a sphere, and compute This is Rodrigues' formula for the axis of a composite rotation defined in terms of the axes of the two

neg: Rotation around a fixed axis linear momentum in rotational motion is angular momentum. The greater the angular momentum of the spinning object such as a top, the greater its tendency to continue to spin. The Angular Momentum of a rotating body is proportional to its mass and to how rapidly it is turning. In addition, the angular momentum depends on how the mass is distributed relative to the axis of rotation: the further away the mass is located from the axis of rotation, the greater the angular momentum. A flat disk such as a record turntable has less angular momentum than a hollow cylinder of

neg: Axial precession stars, centered on the ecliptic north pole (the blue "E") and with an angular radius of about 23.4°, an angle known as the obliquity of the ecliptic. The direction of precession is opposite to the daily rotation of the Earth on its axis. The orange axis was the Earth's rotation axis 5,000 years ago, when it pointed to the star Thuban. The yellow axis, pointing to Polaris, marks the axis now. The equinoxes occur where the celestial equator intersects the ecliptic (red line), that is, where the Earth's axis is perpendicular to the line connecting the centers of the Sun

neg: Tellurion "tellus", meaning "earth". Tellurion A tellurion (also spelled "tellurian", "tellurium", and yet another name is "loxocosm"), is a clock, typically of French or Swiss origin, surmounted by a mechanism that depicts how day, night, and the seasons are caused by the rotation and orientation of Earth on its axis and its orbit around the Sun. The clock normally also displays the age of the Moon and the four-year (perpetual) calendar. It is related to the orrery, which illustrates the relative positions and motions of the planets and moons in the solar system in a heliocentric model. The word tellurion derives

neg: Ulysses (spacecraft) corrections inbound to Jupiter, and later used exclusively to repoint the spin axis (and thus, the antenna) at Earth. The spacecraft was controlled by eight thrusters in two blocks. Thrusters were pulsed in the time domain to perform rotation or translation. Four Sun sensors detected orientation. For fine attitude control, the S-band antenna feed was mounted slightly off-axis. This offset feed combined with the spacecraft spin introduced an oscillation to an S-band radio signal transmitted from Earth when received on board the spacecraft. The amplitude and phase of this oscillation was proportional to the orientation of the spin axis relative

neg: Slerp The effect is a rotation with uniform angular velocity around a fixed rotation axis. When the initial end point is the identity quaternion, Slerp gives a segment of a one-parameter subgroup of both the Lie group of 3D rotations, SO(3), and its universal covering group of unit quaternions, S. Slerp gives a straightest and shortest path between its quaternion end points, and maps to a rotation through an angle of 2Ω. However, because the covering is double ("q" and −"q" map to the same rotation), the rotation path may turn either the "short way" (less than 180°) or the "long

neg: Earth Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. According to radiometric dating and other sources of evidence, Earth formed over 4.5 billion years ago. Earth's gravity interacts with other objects in space, especially the Sun and the Moon, Earth's only natural satellite. Earth revolves around the Sun in 365.26 days, a period known as an Earth year. During this time, Earth rotates about its axis about 366.26 times. Earth's axis of rotation is tilted with respect to its orbital plane, producing seasons on Earth. The gravitational interaction between Earth and

neg: Equation of time one year. If the Earth orbited the Sun with a constant speed, in a circular orbit in a plane perpendicular to the Earth's axis, then the Sun would culminate every day at exactly the same time, and be a perfect time keeper (except for the very small effect of the slowing rotation of the Earth). But the orbit of the Earth is an ellipse not centered on the Sun, and its speed varies between 30.287 and 29.291 km/s, according to Kepler's laws of planetary motion, and its angular speed also varies, and thus the Sun appears to move faster (relative

neg: Universe the notion that the Earth rotates is very old, dating at least to Philolaus (c. 450 BC), Heraclides Ponticus (c. 350 BC) and Ecphantus the Pythagorean. Roughly a century before Copernicus, the Christian scholar Nicholas of Cusa also proposed that the Earth rotates on its axis in his book, "On Learned Ignorance" (1440). Al-Sijzi also proposed that the Earth rotates on its axis. Empirical evidence for the Earth's rotation on its axis, using the phenomenon of comets, was given by Tusi (1201–1274) and Ali Qushji (1403–1474). This cosmology was accepted by Isaac Newton, Christiaan Huygens and later scientists. Edmund Halley

neg: Daytime amounts to slightly more than half the surface. The hemisphere of the Earth experiencing daytime at any given instant changes continuously as the planet rotates on its own axis. The axis of the Earth's rotation is not perpendicular to the plane of its orbit around the Sun (which is parallel with the direction of sunlight), and so the length of the daytime period varies from one point on the planet to another. Additionally, since the axis of rotation is relatively fixed in comparison to the stars, it moves with respect to the Sun as the planet orbits the star. This

neg: Latitude constant latitude and constant longitude, which are constructed with reference to the rotation axis of the Earth. The primary reference points are the poles where the axis of rotation of the Earth intersects the reference surface. Planes which contain the rotation axis intersect the surface at the meridians; and the angle between any one meridian plane and that through Greenwich (the Prime Meridian) defines the longitude: meridians are lines of constant longitude. The plane through the centre of the Earth and perpendicular to the rotation axis intersects the surface at a great circle called the Equator. Planes parallel to the

neg: Improper rotation they differ in angle of rotation by 180°, and the point of inversion is in the plane of reflection. An improper rotation of an object thus produces a rotation of its mirror image. The axis is called the rotation-reflection axis. This is called an "n"-fold improper rotation if the angle of rotation is 360°/"n". There are several different systems for naming individual improper rotations: The direct subgroup, index 2, is C, ["n"], ("nn"), order "n", as the rotoreflection generator applied twice. "S" for odd "n" contain inversion, with is the group generated by inversion. "S" contain indirect isometries but not

neg: Liquid mirror telescope that, in a frame of reference that is stationary relative to the local surface of the Earth, the mirror experiences a torque about an axis that is perpendicular to both rotation axes, i.e. a horizontal axis aligned east-west. Since the mirror is liquid, it responds to this torque by changing its aim direction. The point in the sky at which the mirror is aimed is not exactly overhead; it is displaced slightly to the north or south. The amount of the displacement depends on the latitude, the rotation speeds, and the parameters of the telescope's design. On the Earth, the

neg: Geopotential model z") is the mass density at the volume element and of the direction from the volume element to the point mass. In the special case of a sphere with a spherically symmetric mass density then ρ = ρ("s"), i.e. density depends only on the radial distance These integrals can be evaluated analytically. This is the shell theorem saying that in this case: with corresponding potential where "M" = ∫ρ("s")"dxdydz" is the total mass of the sphere. In reality, Earth is not exactly spherical, mainly because of its rotation around the polar axis that makes its shape slightly oblate. If this

neg: Orrery the "rotation rate", as shown in the table above. A tellurion will show the earth with the moon revolving around the sun. It will use the angle of "inclination of the equator" from the table above to show how it rotates around its own axis. It will show the earth's moon, rotating around the earth. A lunarium is designed to show the complex motions of the moon as it revolves around the earth. Orreries are usually not built to scale. Human orreries, where humans move about as the planets, have also been constructed, but most are temporary. There is a

neg: Foucault pendulum vector diagrams time increases because the central axis of the pendulum is aligned with the axis of rotation of the Earth at the North Pole and then the angle of misalignment increases as the latitude decreases to the point of perpendicularity at the Equator. The angular velocity in relation to the rotation of the Earth's axis that is imparted to the pendulum bob decreases with the cosine of the degree of misalignment of the central axis of the pendulum in comparison to the axis of rotation of the Earth. There are zero degrees of misalignment at the North Pole and the cosine

neg: Cardinal direction the Earth, the Celestial Sphere appears to rotate around an axis passing through the North and South poles of the Earth. This axis intersects the Celestial Sphere at the North and South Celestial poles, which appear to the observer to lie directly above due North and South respectively on the horizon. In either hemisphere, observations of the night sky show that the visible stars appear to be moving in circular paths, caused by the rotation of the Earth. This is best seen in a long exposure photograph, which is obtained by locking the shutter open for most of the intensely

neg: 2675 Tolkien an eccentricity of 0.10 and an inclination of 3° with respect to the ecliptic. In the SMASS classification, "Tolkien" is a stony S-type asteroid. In February 2011, photometric observations of "Tolkien" were taken over the course of twenty-three nights. The obtained lightcurve revealed that the body is potentially an extremely slow rotator, that has an outstandingly long rotation period of hours, or 44 days, with a brightness amplitude of magnitude () . An asteroid typically takes only a few hours to rotate once around its axis. In addition, the body is suspected to be in a non-principal axis rotation ("tumbling").

neg: Earth ellipsoid Earth ellipsoid An Earth ellipsoid is a mathematical figure approximating the Earth's form, used as a reference frame for computations in geodesy, astronomy, and the geosciences. Various different ellipsoids have been used as approximations. It is an ellipsoid of revolution whose minor axis (shorter diameter), which connects the geographical North Pole and South Pole, is approximately aligned with the Earth's axis of rotation. The ellipsoid is defined by the equatorial axis "a" and the polar axis "b"; their difference is about 21 km, or 0.335%. Additional parameters are the mass function "J2", the correspondent gravity formula, and the rotation period

neg: Betelgeuse real, due to pulsations in the atmosphere. The star is also a slow rotator and the most recent velocity recorded was 5 km/s—much slower than Antares which has a rotational velocity of 20 km/s. The rotation period depends on Betelgeuse's size and orientation to Earth, but it has been calculated to take 8.4 years to turn on its axis. In 2004, astronomers using computer simulations speculated that even if Betelgeuse is not rotating it might exhibit large-scale magnetic activity in its extended atmosphere, a factor where even moderately strong fields could have a meaningful influence over the star's dust, wind

neg: Space group In 1992, it was suggested to use symbol "e" for such planes. The symbols for five space groups have been modified: A screw axis is a rotation about an axis, followed by a translation along the direction of the axis. These are noted by a number, "n", to describe the degree of rotation, where the number is how many operations must be applied to complete a full rotation (e.g., 3 would mean a rotation one third of the way around the axis each time). The degree of translation is then added as a subscript showing how far along the axis

neg: Euler angles to its intrinsic rotation. It also rotates around its pivotal axis, with its center of mass orbiting the pivotal axis; this rotation is a precession. Finally, the top can wobble up and down; the inclination angle is the nutation angle. The same example can be seen with the movements of the earth. Though all three movements can be represented by a rotation operator with constant coefficients in some frame, they cannot be represented by these operators all at the same time. Given a reference frame, at most one of them will be coefficient-free. Only precession can be expressed in general

neg: True polar wander the axis of low moment of inertia quite near the equator. Such a reorientation changes the latitudes of most points on the Earth by amounts that depend on how far they are from the axis near the equator that does not move. Cases of true polar wander have occurred several times in the course of the Earth's history. The speed of rotation (around the axis of lowest inertia) is thought to have been less than about 1° per million years. Mars, Europa, and Enceladus are also believed to have undergone true pole wander, in the case of Europa by 80°,

neg: Foucault pendulum vector diagrams is still the same force acting on the bob that causes it to rotate (turn) with the Earth. The point of significance is that the same forces imparting an angular velocity to the pre-released bob are still acting on the swinging bob. At the Equator, the relative motion of the Earth is not observable because there is no change in the force imparting an angular velocity to the bob. This is because the central axis of the pendulum is perpendicular with the axis of rotation of the Earth. At intermediate latitudes: The rotation of the Earth is observable in relation

neg: Cosmology in medieval Islam and Varahamihira in his "Ta'rikh al-Hind" (Latinized as "Indica"). Biruni stated that Brahmagupta and others consider that the earth rotates on its axis and Biruni noted that this does not create any mathematical problems. Abu Said al-Sijzi, a contemporary of al-Biruni, suggested the possible heliocentric movement of the Earth around the Sun, which al-Biruni did not reject. Al-Biruni agreed with the Earth's rotation about its own axis, and while he was initially neutral regarding the heliocentric and geocentric models, he considered heliocentrism to be a philosophical problem. He remarked that if the Earth rotates on its axis and moves around

neg: Jupiter As a result, it does not experience significant seasonal changes, in contrast to, for example, Earth and Mars. Jupiter's rotation is the fastest of all the Solar System's planets, completing a rotation on its axis in slightly less than ten hours; this creates an equatorial bulge easily seen through an Earth-based amateur telescope. The planet is shaped as an oblate spheroid, meaning that the diameter across its equator is longer than the diameter measured between its poles. On Jupiter, the equatorial diameter is longer than the diameter measured through the poles. Because Jupiter is not a solid body, its upper

neg: Schoenflies notation for centers of inversion, C for proper rotation axes, σ for mirror planes, and S for improper rotation axes (rotation-reflection axes). C and S are usually followed by a subscript number (abstractly denoted n) denoting the order of rotation possible. By convention, the axis of proper rotation of greatest order is defined as the principal axis. All other symmetry elements are described in relation to it. A vertical mirror plane (containing the principal axis) is denoted σ; a horizontal mirror plane (perpendicular to the principal axis) is denoted σ. In three dimensions, there are an infinite number of point groups,

neg: True polar wander mass distribution of the Earth is not spherically symmetric, and the Earth has three different moments of inertia. The axis around which the moment of inertia is greatest is closely aligned with the rotation axis (the axis going through the Geographic North and South Poles). The other two axes are near the equator. This is similar to a brick rotating around an axis going through its shortest dimension (a vertical axis when the brick is lying flat). But if the moment of inertia around one of the two axes close to the equator becomes nearly equal to that around the

neg: Alpha Ophiuchi is calculated to be and the equatorial temperature . The energy radiated by an oblate star is higher along its axis of rotation because of the larger projected area and the Stefan–Boltzmann law. The axis of rotation of α Ophiuchi is inclined about to the line of sight from the Earth, so that it is being observed from nearly equator-on. The apparent bolometric luminosity seen at this angle is , but the true luminosity of the star is thought to be . Since a star's effective temperature is simply the temperature which would produce its total energy output from a

neg: Tellurion Tellurion A tellurion (also spelled "tellurian", "tellurium", and yet another name is "loxocosm"), is a clock, typically of French or Swiss origin, surmounted by a mechanism that depicts how day, night, and the seasons are caused by the rotation and orientation of Earth on its axis and its orbit around the Sun. The clock normally also displays the age of the Moon and the four-year (perpetual) calendar. It is related to the orrery, which illustrates the relative positions and motions of the planets and moons in the solar system in a heliocentric model. The word tellurion derives from the Latin

neg: Equator Equator An equator of a rotating spheroid (such as a planet) is its zeroth circle of latitude (parallel). It is the imaginary line on the spheroid's surface, equidistant from its poles, dividing it into northern and southern hemispheres. In other words, it is the intersection of the spheroid's surface with the plane perpendicular to its axis of rotation and midway between its geographical poles. On Earth, "the Equator" is about long, of which 78.8% lies across water and 21.3% over land. Indonesia is the country straddling the greatest length of the equatorial line across both land and sea. The name

neg: Polar motion F is a few hundred milliarcseconds (mas) which gives rise to a surface displacement of several meters (100 mas corresponds to 3.09 m) between the figure axis of the Earth and its angular momentum. Using the geometric axis as the primary axis of a new body-fixed coordinate system, one arrives at the Euler equation of a gyroscope describing the apparent motion of the rotation axis about the geometric axis of the Earth. This is the so-called polar motion. Observations show that the figure axis exhibits an annual wobble forced by surface mass displacement via atmospheric and/or ocean dynamics, while the

neg: Letters on Sunspots or we should not. Holding both positions is not tenable. Day 2: Salviati argues that sunspots prove the rotation of the sun on its axis. Aristotelians had previously held that it was impossible for a heavenly body to have more than one natural motion. Aristotelians must therefore choose between their determination that only one natural movement is possible (in which case the sun is static, as Copernicus argued); or they must explain how a second natural motion occurs if they wish to maintain that the sun makes a daily orbit of the earth. This argument is resumed on Day 3

neg: Earth's rotation based on theory rather than observation. He established the idea of a sphere of fixed stars that rotated about the earth. This was accepted by most of those who came after, in particular Claudius Ptolemy (2nd century CE), who thought the earth would be devastated by gales if it rotated. In 499 CE, the Indian astronomer Aryabhata wrote that the spherical earth rotates about its axis daily, and that the apparent movement of the stars is a relative motion caused by the rotation of the Earth. He provided the following analogy: "Just as a man in a boat going in

neg: Experimental testing of time dilation at rest in S′, so its worldline is the ct′-axis. The upper atmosphere is at rest in S, so its worldline is the ct-axis. Upon the axes of x and x′, all events are present that are simultaneous with A in S and S′, respectively. The muon and Earth are meeting at D. As the Earth is at rest in S, its worldline (identical with the lower atmosphere) is drawn parallel to the ct-axis, until it intersects the axes of x′ and x. Time: The interval between two events present on the worldline of a single clock is called proper

neg: IERS Reference Meridian Thus this IRM is the weighted average (in the least squares sense) of the reference meridians of the hundreds of ground stations contributing to the IERS network. The network includes GPS stations, Satellite Laser Ranging (SLR) stations, Lunar Laser Ranging (LLR) stations, and the highly accurate Very Long Baseline Interferometry (VLBI) stations. All stations' coordinates are adjusted annually to remove net rotation relative to the major tectonic plates. If Earth had only two hemispherical plates moving relative to each other around any axis which intersects their centres or their junction, then the longitudes (around any other rotation axis) of any

neg: Earth orientation parameters Earth orientation parameters In geodesy, earth orientation parameters (EOP) are a collection of parameters that describe irregularities in the rotation of the Earth. The Earth's rotational velocity is not constant over time. Any motion of mass in or on the Earth causes a slowdown or speedup of the rotation speed, or a change of rotation axis. Small motions produce changes too small to be measured, but movements of very large mass, like sea currents or tides, can produce discernible changes in the rotation and can change very precise astronomical observations. Global simulations of atmosphere, ocean, and land dynamics are used

neg: Night a period without night intervening between consecutive days, while part of winter sees a period without daytime intervening between consecutive nights. The phenomenon of day and night is due to the rotation of a celestial body about its axis, creating an illusion of the sun rising and setting. Different bodies spin at very different rates, however. Some may spin much faster than Earth, while others spin extremely slowly, leading to very long days and nights. The planet Venus rotates once every 224.7 days – by far the slowest rotation period of any of the major planets. In contrast, the gas

neg: 44 Nysa they interpreted as indicating the asteroid may actually be a contact binary. In 2003, Tanga "et al." published results obtained from the Fine Guidance Sensor on the Hubble Space Telescope in which high-precision interferometry was performed on Nysa with the goal of a more accurate shape determination. Due to Hubble's orbit around the Earth, hours-long photometry sessions, as are normally used to resolve the asteroid's shape, were not possible. Instead, the team used interferometry on the asteroid at the time in its rotation when it would have its longest axis perpendicular to the Earth. Ellipsoidal shape models were then fit

neg: Léon Foucault to measure the speed of light; it came to be known as the Foucault–Fizeau experiment, and was viewed as "driving the last nail in the coffin" of Newton's corpuscular theory of light when it showed that light travels more slowly through water than through air. In 1851, he provided an experimental demonstration of the rotation of the Earth on its axis (diurnal motion). This experimental setup had been used by Vincenzo Viviani but became well known to the public by Foucault's work. Foucault achieved the demonstration by showing the rotation of the plane of oscillation of a long and heavy

neg: Orientation (geometry) rotation except for those lying on the rotation axis. If the rigid body has rotational symmetry not all orientations are distinguishable, except by observing how the orientation evolves in time from a known starting orientation. For example, the orientation in space of a line, line segment, or vector can be specified with only two values, for example two direction cosines. Another example is the position of a point on the earth, often described using the orientation of a line joining it with the earth's center, measured using the two angles of longitude and latitude. Likewise, the orientation of a plane

neg: Rotation matrix is not commutative) only if they are applied in the specified order (see Ambiguities for more details). Every rotation in three dimensions is defined by its axis (a vector along this axis is unchanged by the rotation), and its angle — the amount of rotation about that axis (Euler rotation theorem). There are several methods to compute the axis and angle from a rotation matrix (see also axis–angle representation). Here, we only describe the method based on the computation of the eigenvectors and eigenvalues of the rotation matrix. It is also possible to use the trace of the rotation matrix.

neg: Foucault pendulum vector diagrams the force to complete a full circle since it takes one day for the Earth to rotate. At the equator: The central axis of the pendulum is perpendicular with the axis of rotation of the Earth. The central axis of the pendulum is always determined by the force of gravity directed towards the center of the Earth. A pendulum bob at rest at the Equator is still rotating with the Earth and there is no spin on the bob. If the bob is displaced from the central axis of the pendulum in preparation for swinging and held in place, then

neg: Rotation if the axis is replaced with formula_11.) Every proper rotation formula_6 in 3D space has an axis of rotation, which is defined such that any vector formula_13 that is aligned with the rotation axis will not be affected by rotation. Accordingly, formula_14, and the rotation axis therefore corresponds to an eigenvector of the rotation matrix associated with an eigenvalue of 1. As long as the rotation angle formula_5 is nonzero (i.e., the rotation is not the identity tensor), there is one and only one such direction. Because A has only real components, there is at least one real eigenvalue, and

neg: Age of Aquarius diurnal rotation of the Earth on its own axis and the annual revolution of the earth around the sun. Traditionally this 25,800-year-long cycle is calibrated, for the purposes of determining astrological ages, by the location of the sun in one of the twelve zodiac constellations at the vernal equinox, which corresponds to the moment the sun rises above the celestial equator, marking the start of spring in the Northern Hemisphere each year. Roughly every 2,150 years the sun's position at the time of the vernal equinox will have moved into a new zodiacal constellation. However zodiacal constellations are not uniform

neg: Magnetosphere of Jupiter magnetic axis. However, on Jupiter the north pole of the dipole is located in the planet's northern hemisphere and the south pole of the dipole lies in its southern hemisphere, opposite to the Earth, whose north pole lies in the southern hemisphere and south pole lies in the northern hemisphere. Jupiter's field also has quadrupole, octupole and higher components, though they are less than one tenth as strong as the dipole component. The dipole is tilted roughly 10° from Jupiter's axis of rotation; the tilt is similar to that of the Earth (11.3°). Its equatorial field strength is about 776.6

neg: Earth-centered inertial the vernal equinox, the equatorial plane of the Earth, and the ecliptic plane vary according to date and are specified for a particular epoch. Models representing the ever-changing orientation of the Earth in space are available from the International Earth Rotation and Reference Systems Service. One commonly used ECI frame is defined with the Earth's Mean Equator and Equinox at 12:00 Terrestrial Time on 1 January 2000. It can be referred to as "J2000" or "EME2000." The x-axis is aligned with the mean equinox. The z-axis is aligned with the Earth's spin axis or celestial North Pole. The y-axis is

neg: Foucault pendulum vector diagrams or aligned to the Earth's axis and the sine of 90° = 1. At the equator the pendulum axis is perpendicular to the Earth's axis and the sine of 0° = 0. At intermediate latitudes the rotation of the Earth is observable in relation to the plane of the pendulum swing but the time to observe a full rotation depends on the latitude of the location. The time to observe a full rotation is equal to one day at the North Pole with the time increasing with decreasing latitude and not observable at the Equator (infinite length of time). The

neg: Rotation Rotation A rotation is a circular movement of an object around a center (or point) of rotation. A three-dimensional object can always be rotated around an infinite number of imaginary lines called "rotation axes" ( ). If the axis passes through the body's center of mass, the body is said to rotate upon itself, or spin. A rotation about an external point, e.g. the Earth about the Sun, is called a revolution or orbital revolution, typically when it is produced by gravity. The axis is called a pole. Mathematically, a rotation is a rigid body movement which, unlike a translation,

neg: Rotation operator (quantum mechanics) Rotation operator (quantum mechanics) This article concerns the rotation operator, as it appears in quantum mechanics. With every physical rotation "R", we postulate a quantum mechanical rotation operator "D(R)" which rotates quantum mechanical states. In terms of the generators of rotation, formula_3 is rotation axis, and formula_4 is angular momentum. The rotation operator formula_5, with the first argument formula_6 indicating the rotation axis and the second formula_7 the rotation angle, can operate through the translation operator formula_8 for infinitesimal rotations as explained below. This is why, it is first shown how the translation operator is acting on a particle at

neg: Screw axis axis, which defines the displacement D to obtain, A spatial displacement of points q represented as a vector quaternion can be defined using quaternions as the mapping where d is translation vector quaternion and "S" is a unit quaternion, also called a versor, given by that defines a rotation by 2"θ" around an axis S. In the proper Euclidean group E(3) a rotation may be conjugated with a translation to move it to a parallel rotation axis. Such a conjugation, using quaternion homographies, produces the appropriate screw axis to express the given spatial displacement as a screw displacement, in accord

neg: Pole star the naked eye under ideal conditions) that most closely coincide with the projection of the planet's axis of rotation onto the Celestial sphere. Different planets have different pole stars because their axes are oriented differently. (See Poles of astronomical bodies.) Pole star A pole star or polar star is a star, preferably bright, closely aligned to the axis of rotation of an astronomical object. With regard to planet Earth, the pole star refers to Polaris (Alpha Ursae Minoris), a magnitude 2 star aligned approximately with its northern axis, and a pre-eminent star in celestial navigation. In classical antiquity, Beta Ursae

neg: Equatorial bulge sent to French Guiana, on the northern coast of South America, ran slower than their exact counterparts in Paris. Measurements of the acceleration due to gravity at the equator must also take into account the planet's rotation. Any object that is stationary with respect to the surface of the Earth is actually following a circular trajectory, circumnavigating the Earth's axis. Pulling an object into such a circular trajectory requires a force. The acceleration that is required to circumnavigate the Earth's axis along the equator at one revolution per sidereal day is 0.0339 m/s². Providing this acceleration decreases the effective gravitational

neg: Neutron star Ic supernova, and collapses into a neutron star, it retains most of its angular momentum. But, because it has only a tiny fraction of its parent's radius (and therefore its moment of inertia is sharply reduced), a neutron star is formed with very high rotation speed, and then over a very long period it slows. Neutron stars are known that have rotation periods from about 1.4 ms to 30 s. The neutron star's density also gives it very high surface gravity, with typical values ranging from 10 to 10 m/s (more than 10 times that of Earth). One measure of

neg: Coriolis force the right along with the surface of the Earth). The further north you go, the smaller the "horizontal diameter" of the Earth (the minimum distance from the surface point to the axis of rotation, which is in a plane orthogonal to the axis), and so the slower the eastward motion of its surface. As the object moves north, to higher latitudes, it has a tendency to maintain the eastward speed it started with (rather than slowing down to match the reduced eastward speed of local objects on the Earth's surface), so it veers east (i.e. to the right of its

neg: Foucault pendulum vector diagrams the bob is still rotating (turning) with the Earth with the same angular velocity equal to that of the Earth's angular velocity. This is the same angular velocity when at rest. Since the central axis of the pendulum is perpendicular with the axis of rotation of the Earth this is not the same as the North Pole where the central axis is aligned with the axis of the Earth. The bob is not revolving about the axis of the pendulum when held in place. Once the bob is displaced from the central axis of the pendulum and then released there

neg: Haumea of Earth. Although its shape has not been directly observed, calculations from its light curve indicate that it is a Jacobi ellipsoid, with its major axis twice as long as its minor. Its gravity is thought to be sufficient for it to have relaxed into hydrostatic equilibrium, making it a dwarf planet. Haumea's elongated shape together with its rapid rotation, high density, and high albedo (from a surface of crystalline water ice), are thought to be the consequences of a giant collision, which left Haumea the largest member of a collisional family that includes several large trans-Neptunian objects (TNOs) and

neg: Symmetry operation Identity operation and is denoted by "E" or "I". "C", "n" rotations 360°/"n" is also an Identity operation. These are denoted by "S" and are rotations of 360°/"n" followed by reflection in a plane perpendicular to the rotation axis. "S" is usually denoted as σ, a reflection operation about a mirror plane. "S" is usually denoted as "i", an inversion operation about an inversion centre. When "n" is an even number "S" = "E", but when "n" is odd "S" = "E". Rotation axes, mirror planes and inversion centres are symmetry elements, not operations. The rotation axis of highest order

neg: Moon became tidally locked in this orientation as a result of frictional effects associated with tidal deformations caused by Earth. With time, the energy of rotation of the Moon on its axis was dissipated as heat, until there was no rotation of the Moon relative to Earth. In 2016, planetary scientists, using data collected on the much earlier NASA Lunar Prospector mission, found two hydrogen-rich areas on opposite sides of the Moon, probably in the form of water ice. It is speculated that these patches were the poles of the Moon billions of years ago, before it was tidally locked to

neg: South Pole which is defined based on the Earth's magnetic field. The South Pole is at the center of the Southern Hemisphere. For most purposes, the Geographic South Pole is defined as the southern point of the two points where the Earth's axis of rotation intersects its surface (the other being the Geographic North Pole). However, the Earth's axis of rotation is actually subject to very small "wobbles" (polar motion), so this definition is not adequate for very precise work. The geographic coordinates of the South Pole are usually given simply as 90°S, since its longitude is geometrically undefined and irrelevant. When

neg: Letters on Sunspots the ephemeral and irregular sunspots. Showing that the sun rotated had two effects. Firstly, it showed that the traditional Aristotelian model of the universe must be wrong, because that model assumed that the sun had only a diurnal (daily) motion around the earth, and not a rotation on its own axis. Secondly, it showed that there was nothing necessarily unusual about rotation of a body in space. In the Aristotelian system, night and day were explained by the sun moving round a static earth. For Copernicus' system to work, there had to be an explanation for why half the earth

neg: Centrifugal force usual (inertial frame) form, one would conclude that the stone should accelerate in the direction of the net applied force—towards the axis of rotation—which it does not do. The centrifugal force and other fictitious forces must be included along with the real forces in order to apply Newton's laws of motion in the rotating frame. The Earth constitutes a rotating reference frame because it rotates once a day on its axis. Because the rotation is slow, the fictitious forces it produces are small, and in everyday situations can generally be neglected. Even in calculations requiring high precision, the centrifugal force

neg: Dynamo theory astrophysical bodies. The conductive fluid in the geodynamo is liquid iron in the outer core, and in the solar dynamo is ionized gas at the tachocline. Dynamo theory of astrophysical bodies uses magnetohydrodynamic equations to investigate how the fluid can continuously regenerate the magnetic field. It was once believed that the dipole, which comprises much of the Earth's magnetic field and is misaligned along the rotation axis by 11.3 degrees, was caused by permanent magnetization of the materials in the earth. This means that dynamo theory was originally used to explain the Sun's magnetic field in its relationship with that

neg: Prolate rotator galaxy likely objects. They are not to be confused with lenticular galaxies which are spiral galaxies seen edge on and have sometimes been given the name 'spindle' because of their long thin appearance when viewed from this direction , eg NGC 5866. Prolate rotator galaxy A Prolate rotator galaxy is an unusual class of galaxy that is cigar shaped and rotates around its long axis. They are also called Spindle galaxies. A prolate rotator galaxy is an elliptical galaxy in prolate rotation. That is they possess a significant amount of rotation around the major axis. To make a prolate rotator galaxy,

neg: Liquid mirror telescope have the advantage of being easily and rapidly deformable using variations of magnetic field strength. Usually, the mirror of a liquid mirror telescope is rotated around two axes simultaneously. For example, the mirror of a telescope on the surface of the Earth rotates at a speed of a few revolutions per minute about a vertical axis to maintain its parabolic shape, and also at a speed of one revolution per day about the Earth's axis because of the rotation of the Earth. Usually (except if the telescope is located at one of the Earth's poles), the two rotations interact so

neg: Gravity Probe B are "warped" by the presence of the Earth, and by how much the Earth's rotation "drags" space-time around with it. The geodetic effect is an effect caused by space-time being "curved" by the mass of the Earth. A gyroscope's axis when parallel transported around the Earth in one complete revolution does not end up pointing in exactly the same direction as before. The angle "missing" may be thought of as the amount the gyroscope "leans over" into the slope of the space-time curvature. A more precise explanation for the space curvature part of the geodetic precession is obtained by using

neg: Indian influence on Islamic science Hinduism. In sind the idea of the redeemer was closely connected to the incarnations of Vishnu.The dasavatar is considered one of the cannons of modern ismailis. The Indian geographical knowledge that was transmitted and influenced the Arabs included the view of Aryabhata that the apparent daily rotation of the heavens was caused by the rotation of the earth on its own axis,the idea that the proportion of land and sea on the surface of the earth was half and half and the land mass as being dome shaped and covered on all sides by water. The Arabs utilized the Indian

neg: Angular momentum exerts on the Earth. This in turn results in the slowing down of the rotation rate of Earth, at about 65.7 nanoseconds per day, and in gradual increase of the radius of Moon's orbit, at about 3.82 centimeters per year. The conservation of angular momentum explains the angular acceleration of an ice skater as she brings her arms and legs close to the vertical axis of rotation. By bringing part of the mass of her body closer to the axis she decreases her body's moment of inertia. Because angular momentum is the product of moment of inertia and angular velocity,

neg: Rotation around a fixed axis Rotation around a fixed axis Rotation around a fixed axis or about a fixed axis of revolution or motion with respect to a fixed axis of rotation is a special case of rotational motion. The fixed axis hypothesis excludes the possibility of an axis changing its orientation, and cannot describe such phenomena as wobbling or precession. According to Euler's rotation theorem, simultaneous rotation along a number of stationary axes at the same time is impossible. If two rotations are forced at the same time, a new axis of rotation will appear. This article assumes that the rotation is also stable,

neg: Gyrocompass fixed point in outer space (not to a fixed point on Earth). Since our planet rotates, it appears to a stationary observer on Earth that a gyroscope's axis is completing a full rotation once every 24 hours. Such a rotating gyroscope is used for navigation in some cases, for example on aircraft, where it is known as heading indicator or directional gyro, but cannot ordinarily be used for long-term marine navigation. The crucial additional ingredient needed to turn a gyroscope into a gyrocompass, so it would automatically position to true north, is some mechanism that results in an application of

neg: Foucault pendulum vector diagrams The central axis of the pendulum aligns with the axis of rotation of the Earth. The central axis of the pendulum is always determined by the force of gravity directed towards the center of the Earth. A pendulum bob at rest at the North Pole still has spin on the bob. The Foucault pendulum connection is constructed such that the pendulum is free to swing in any direction. If the bob is displaced from the central axis of the pendulum in preparation for swinging and held in place, then the bob will revolve about the central axis of the pendulum

neg: Foucault pendulum vector diagrams deduce that the time to observe a full rotation of the Earth increased by the inverse of the sine of the latitude. formula_7 = formula_8 = formula_9 The Pendulum Sine Law also defines that the ratio of the observed Earth's rotation time at two separate latitudes in relation to a pendulum swing is equal to the inverse ratio of the sine of the two latitudes. formula_10 = formula_11 = formula_12 The sine of the latitude also indicates the degree of alignment of the pendulum central axis to the Earth's axis of rotation. At the poles the pendulum axis is parallel

neg: Operation of computed tomography with photomultiplier tubes excited by (typically) cesium iodide crystals. Cesium iodide was replaced during the 1980s by ion chambers containing high-pressure xenon gas. These systems were in turn replaced by scintillation systems based on photodiodes instead of photomultipliers and modern scintillation materials (for example rare-earth garnet or rare-earth oxide ceramics) with more desirable characteristics. Initial machines would rotate the X-ray source and detectors around a stationary object. Following a complete rotation, the object would be moved along its axis, and the next rotation started. Newer machines permitted continuous rotation with the object to be imaged slowly and smoothly slid through

neg: Habitability of natural satellites true of red dwarf systems, where comparatively high gravitational forces and low luminosities leave the habitable zone in an area where tidal locking would occur. If tidally locked, one rotation about the axis may take a long time relative to a planet (for example, ignoring the slight axial tilt of Earth's moon and topographical shadowing, any given point on it has two weeks – in Earth time – of sunshine and two weeks of night in its lunar day) but these long periods of light and darkness are not as challenging for habitability as the eternal days and eternal nights

neg: Grand Gulf Mound the mound. The beginning stage is believed to have been a rectangular earthen platform in height, wide on its east–west axis and long on its north–south axis. After a period of use, this platform was covered with a mantle of earth in height and wide along its east–west axis, with an extremely hard cap of earth covering the mound. During a third stage another mantle of earth was added to the mound, bringing it to a height of and to approximately in width on its east–west axis. Grand Gulf Mound The Grand Gulf Mound (22CB522) is an Early Marksville culture

neg: Moment of inertia - both characterize the resistance of a body to changes in its motion. The moment of inertia depends on how mass is distributed around an axis of rotation, and will vary depending on the chosen axis. For a point-like mass, the moment of inertia about some axis is given by formula_1, where formula_2 is the distance of the point from the axis, and formula_3 is the mass. For an extended rigid body, the moment of inertia is just the sum of all the small pieces of mass multiplied by the square of their distances from the axis in question. For

neg: North African climate cycles abrupt shifts back and forth from the "green Sahara" to the "desert Sahara" are not entirely explained by long term changes in the insolation cycle. Precession of the equinoxes on Earth can be divided up into two distinct phases. The first phase is created by a wobbling of the Earth's axis of rotation and is known as axial precession. While the second phase is known as procession of the ellipse and is related to the slow rotation of the Earth's elliptical orbit around the sun. When combined these two phases create a precession of the equinoxes that has a strong

neg: Omega Orionis is 179 km/s – involves a period of 1.37 days rotation. However, actual rotation speed can reach 450 km / s, it estimated that its axis is inclined 24° relative to the line of sight. The star has a mass 7.0 times that of the Sun, just below the limit beyond which stars explode as supernovas. Its age is estimated at 43.6 million years. As a result of its rapid rotation, Omega Orionis is a Be class star. Among the stars of this class, Omega Orionis was the first where the magnetic field was measured and found to be 1000

neg: Axis–angle representation to obtain the rotated vector is For the rotation of a single vector it may be more efficient than converting and into a rotation matrix to rotate the vector. There are several ways to represent a rotation. It is useful to understand how different representations relate to one another, and how to convert between them. Here the unit vector is denoted instead of . The exponential map effects a transformation from the axis-angle representation of rotations to rotation matrices, Essentially, by using a Taylor expansion one derives a closed-form relation between these two representations. Given a unit vector representing the

neg: Axes conventions called rolling, rotation about the "Y"-axis is called pitching, and rotation about the "Z"-axis is called yawing. For satellites orbiting the earth it is normal to use the Equatorial coordinate system. The projection of the Earth's equator onto the celestial sphere is called the celestial equator. Similarly, the projections of the Earth's north and south geographic poles become the north and south celestial poles, respectively. Deep space satellites use other Celestial coordinate system, like the Ecliptic coordinate system. If the goal is to keep the shuttle during its orbits in a constant attitude with respect to the sky, e.g. in

neg: Neptune 1.77° compared to that of Earth. The axial tilt of Neptune is 28.32°, which is similar to the tilts of Earth (23°) and Mars (25°). As a result, Neptune experiences similar seasonal changes to Earth. The long orbital period of Neptune means that the seasons last for forty Earth years. Its sidereal rotation period (day) is roughly 16.11 hours. Because its axial tilt is comparable to Earth's, the variation in the length of its day over the course of its long year is not any more extreme. Because Neptune is not a solid body, its atmosphere undergoes differential rotation. The

neg: Psi Persei equator and extending out to about 11 times the radius of the star. As a result of this disc, the spectrum of this star shows emission lines (as indicated by the 'e' in the stellar class) and its magnitude varies over a period of about a day. Psi Persei is rotating rapidly with a projected rotational velocity ("v" sin "i") along the equator of 390 km/s or more. The axis of rotation is inclined about to the line of sight from the Earth, so this velocity is close to the actual azimuthal velocity along the star's equator. It is expelling

neg: North African climate cycles monsoon circulations in the northern hemisphere. On the opposite end of the spectrum, when the Northern Hemisphere is pointed toward the sun during aphelion, there is a minimum in insolation and the North African Monsoon is at its weakest. Obliquity, otherwise known as tilt, refers to the angle that Earth's axis of rotation makes with a line that is perpendicular to Earth's orbital plane. The current tilt of Earth's axis is roughly 23.5°. However, over long periods of time the tilt of Earth's axis of rotation changes because of the uneven distribution of mass across the planet and gravitational interactions

neg: Gyrocompass NS-axis by formula_3. We establish coordinates attached to this observer as so that the unit formula_5 versor formula_6 is mapped to the point formula_7. For the 2-O neither the Earth nor the barycenter of the gyroscope is moving. The rotation of 2-O relative to 1-O is performed with angular velocity formula_8. We suppose that the formula_9 axis denotes points with zero longitude (the prime, or Greenwich, meridian). We now rotate about the formula_10 axis, so that the formula_11-axis has the longitude of the barycenter. In this case we have With the next rotation (about the axis formula_13 of an angle

neg: Retrograde and prograde motion with retrograde rotation – are Venus and Uranus. Venus's axial tilt is 177°, which means it is rotating almost exactly in the opposite direction to its orbit. Uranus has an axial tilt of 97.77°, so its axis of rotation is approximately parallel with the plane of the Solar System. The reason for Uranus's unusual axial tilt is not known with certainty, but the usual speculation is that during the formation of the Solar System, an Earth-sized protoplanet collided with Uranus, causing the skewed orientation. It is unlikely that Venus was formed with its present slow retrograde rotation, which takes 243

neg: Commentariolus 2 and 3 months. The Moon's sphere, however, revolves around the Earth in a period of one month, and moves with it around the Sun like an epicycle. This section explains how the apparent motion of the Sun could arise from three separate motions of the Earth. The first motion is a uniform revolution, with a period of one year, from west to east along a circular orbit whose centre is offset from the Sun by 1/25 of the orbit's radius. The second motion is the daily rotation about an axis which passes through the Earth's centre and is inclined

neg: Earth's rotation given in mean solar time above to obtain their lengths in SI seconds (see Fluctuations in the length of day). The angular speed of Earth's rotation in inertial space is radians per SI second (mean solar second). Multiplying by (180°/π radians) × (86,400 seconds/mean solar day) yields 360.9856°/mean solar day, indicating that Earth rotates more than 360° relative to the fixed stars in one solar day. Earth's movement along its nearly circular orbit while it 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