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56-508: A fortnight is a unit of time equal to 14 days (two weeks ). The word derives from the Old English term fēowertīene niht , meaning " fourteen nights " (or "fourteen days", since the Anglo-Saxons counted by nights). In astronomy , a lunar fortnight is half a lunar synodic month , which is equivalent to the mean period between a full moon and a new moon (and vice versa). This

112-642: A = b and A = πr . Kepler's second law states that: A line joining a planet and the Sun sweeps out equal areas during equal intervals of time. The orbital radius and angular velocity of the planet in the elliptical orbit will vary. This is shown in the animation: the planet travels faster when closer to the Sun, then slower when farther from the Sun. Kepler's second law states that the blue sector has constant area. Kepler notably arrived at this law through assumptions that were either only approximately true or outright false and can be outlined as follows: Nevertheless,

168-471: A Proto-Germanic root *dagaz . Several definitions of this universal human concept are used according to context, need, and convenience. Besides the day of 24 hours (86,400 seconds), the word day is used for several different spans of time based on the rotation of the Earth around its axis. An important one is the solar day , the time it takes for the Sun to return to its culmination point (its highest point in

224-532: A décade – the equivalent of a week. 3 décades make a month. Various decimal time proposals which do not redefine the day: Henri de Sarrauton's proposal kept days, and subdivided hours into 100 minutes; in Mendizábal y Tamborel's proposal, the sidereal day was the basic unit, with subdivisions made upon it; and Rey-Pailhade's proposal divided the day 100 cés. The word refers to various similarly defined ideas, such as: Mainly due to tidal deceleration –

280-453: A is the arithmetic mean between r min and r max : The semi-minor axis b is the geometric mean between r min and r max : The semi-latus rectum p is the harmonic mean between r min and r max : The eccentricity ε is the coefficient of variation between r min and r max : The area of the ellipse is The special case of a circle is ε = 0, resulting in r = p = r min = r max =

336-470: A solstice . The current perihelion, near January 4, is fairly close to the solstice of December 21 or 22. It took nearly two centuries for the current formulation of Kepler's work to take on its settled form. Voltaire 's Eléments de la philosophie de Newton ( Elements of Newton's Philosophy ) of 1738 was the first publication to use the terminology of "laws". The Biographical Encyclopedia of Astronomers in its article on Kepler (p. 620) states that

392-481: A reference like "two hours into the day" meant two hours after sunset and thus times during the evening need to be shifted back one calendar day in modern reckoning. Days such as Christmas Eve , Halloween (“All Hallows’ Eve”), and the Eve of Saint Agnes are remnants of the older pattern when holidays began during the prior evening. The common convention among the ancient Romans , ancient Chinese and in modern times

448-603: A small piece of the orbit dx and time to cover it dt . Thus d A d t = 1 2 ( r → × v → ) . {\displaystyle {\frac {dA}{dt}}={\frac {1}{2}}({\vec {r}}\times {\vec {v}}).} d A d t = 1 m 1 2 ( r → × p → ) . {\displaystyle {\frac {dA}{dt}}={\frac {1}{m}}{\frac {1}{2}}({\vec {r}}\times {\vec {p}}).} Since

504-433: A small time d t {\displaystyle dt} the planet sweeps out a small triangle having base line r {\displaystyle r} and height r d θ {\displaystyle r\,d\theta } and area d A = 1 2 ⋅ r ⋅ r d θ {\textstyle dA={\frac {1}{2}}\cdot r\cdot r\,d\theta } , so

560-451: A symmetry principle in the phase space of planetary motion (the orthogonal group O(4) acting) which accounts for the first and third laws in the case of Newtonian gravitation, as conservation of angular momentum does via rotational symmetry for the second law. The mathematical model of the kinematics of a planet subject to the laws allows a large range of further calculations. Kepler's first law states that: The orbit of every planet

616-500: Is an ellipse with the sun at one of the two foci . Mathematically, an ellipse can be represented by the formula: where p {\displaystyle p} is the semi-latus rectum , ε is the eccentricity of the ellipse, r is the distance from the Sun to the planet, and θ is the angle to the planet's current position from its closest approach, as seen from the Sun. So ( r ,  θ ) are polar coordinates . For an ellipse 0 <  ε  < 1 ; in

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672-469: Is equal to 14.07 days. It gives rise to a lunar fortnightly tidal constituent (see: Long-period tides ). In many languages, there is no single word for a two-week period, and the equivalent terms "two weeks", "14 days", or "15 days" ( counting inclusively ) have to be used. Day A collection of sequential days is organized into calendars as dates , almost always into weeks , months and years . A solar calendar organizes dates based on

728-526: Is for the civil day to begin at midnight, i.e. 00:00, and to last a full 24 hours until 24:00, i.e. 00:00 of the next day. The International Meridian Conference of 1884 resolved That the Conference expresses the hope that as soon as may be practicable the astronomical and nautical days will be arranged everywhere to begin at midnight. In ancient Egypt the day was reckoned from sunrise to sunrise. Prior to 1926, Turkey had two time systems: Turkish , counting

784-505: Is found in Astronomia nova and Epitome Astronomiae Copernicanae . Johannes Kepler 's laws improved the model of Copernicus . According to Copernicus: Despite being correct in saying that the planets revolved around the Sun, Copernicus was incorrect in defining their orbits. Introducing physical explanations for movement in space beyond just geometry, Kepler correctly defined the orbit of planets as follows: The eccentricity of

840-413: Is identical. Kepler's third law states that: The ratio of the square of an object's orbital period with the cube of the semi-major axis of its orbit is the same for all objects orbiting the same primary. This captures the relationship between the distance of planets from the Sun, and their orbital periods. Kepler enunciated in 1619 this third law in a laborious attempt to determine what he viewed as

896-435: Is on average around 7 minutes longer than 12 hours. Daytime is further divided into morning , afternoon , and evening . Morning occurs between sunrise and noon . Afternoon occurs between noon and sunset , or between noon and the start of evening. This period of time sees human's highest body temperature , an increase of traffic collisions , and a decrease of productivity . Evening begins around 5 or 6 pm, or when

952-447: Is the span of time it takes for the Earth to make one entire rotation with respect to the celestial background or a distant star (assumed to be fixed). Measuring a day as such is used in astronomy . A sidereal day is about 4 minutes less than a solar day of 24 hours (23 hours 56 minutes and 4.09 seconds), or 0.99726968 of a solar day of 24 hours. There are about 366.2422 stellar days in one mean tropical year (one stellar day more than

1008-541: Is when the sun is up to 6 degrees below the horizon; nautical when it is up to 12 degrees below, and astronomical when it is up to 18 degrees below. Night is the period in which the sky is dark ; the period between dusk and dawn when no light from the sun is visible. Light pollution during night can impact human and animal life, for example by disrupting sleep. Kepler%27s laws of planetary motion#Second law In astronomy , Kepler's laws of planetary motion , published by Johannes Kepler in 1609 (except

1064-464: The Earth's natural fluctuation of a solar day , and stellar day and sidereal day (using the celestial sphere ) used for astronomy . In most countries outside of the tropics , daylight saving time is practiced, and each year there will be one 23-hour civil day and one 25-hour civil day. Due to slight variations in the rotation of the Earth, there are rare times when a leap second will get inserted at

1120-530: The International Bureau of Weights and Measures (BIPM) redefined a second as "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the caesium -133 atom ". This makes the SI-based day last exactly 794,243,384,928,000 of those periods. Various decimal or metric time proposals have been made, but do not redefine

1176-599: The Jewish religious calendar counts days from sunset to sunset, so the Jewish Sabbath begins at sundown on Friday . In astronomy , a day begins at noon so that observations throughout a single night are recorded as happening on the same day. In specific applications, the definition of a day is slightly modified, such as in the SI day (exactly 86,400 seconds ) used for computers and standards keeping , local mean time accounting of

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1232-561: The Solar System or other parts of the universe , a day is a full rotation of other large astronomical objects with respect to its star. For civil purposes, a common clock time is typically defined for an entire region based on the local mean solar time at a central meridian. Such time zones began to be adopted about the middle of the 19th century when railroads with regularly occurring schedules came into use, with most major countries having adopted them by 1929. As of 2015, throughout

1288-546: The Solar System , including those farther away from the Sun, also have elliptical orbits. The second law establishes that when a planet is closer to the Sun, it travels faster. The third law expresses that the farther a planet is from the Sun, the longer its orbital period. Isaac Newton showed in 1687 that relationships like Kepler's would apply in the Solar System as a consequence of his own laws of motion and law of universal gravitation . A more precise historical approach

1344-470: The four brightest moons of Jupiter . Godefroy Wendelin also made this observation in 1643. The second law, in the "area law" form, was contested by Nicolaus Mercator in a book from 1664, but by 1670 his Philosophical Transactions were in its favour. As the century proceeded it became more widely accepted. The reception in Germany changed noticeably between 1688, the year in which Newton's Principia

1400-414: The mean motion of the planet around the Sun satisfies And so, d A d t = a b n 2 = π a b T . {\displaystyle {\frac {dA}{dt}}={\frac {abn}{2}}={\frac {\pi ab}{T}}.} S: Sun at the primary focus, C: Centre of ellipse, S': The secondary focus. In each case, the area of all sectors depicted

1456-598: The orbit of the Earth makes the time from the March equinox to the September equinox , around 186 days, unequal to the time from the September equinox to the March equinox, around 179 days. A diameter would cut the orbit into equal parts, but the plane through the Sun parallel to the equator of the Earth cuts the orbit into two parts with areas in a 186 to 179 ratio, so the eccentricity of

1512-409: The " music of the spheres " according to precise laws, and express it in terms of musical notation. It was therefore known as the harmonic law . The original form of this law (referring to not the semi-major axis, but rather a "mean distance") holds true only for planets with small eccentricities near zero. Using Newton's law of gravitation (published 1687), this relation can be found in the case of

1568-451: The 24-hour day. Two effects make daytime on average longer than night. The Sun is not a point but has an apparent size of about 32 minutes of arc . Additionally, the atmosphere refracts sunlight in such a way that some of it reaches the ground even when the Sun is below the horizon by about 34 minutes of arc. So the first light reaches the ground when the centre of the Sun is still below the horizon by about 50 minutes of arc. Thus, daytime

1624-450: The Moon's gravitational pull slowing down the Earth's rotation – the Earth's rotational period is slowing. Because of the way the second is defined, the mean length of a solar day is now about 86,400.002 seconds, and is increasing by about 2 milliseconds per century. Since the rotation rate of the Earth is slowing, the length of a SI second fell out of sync with a second derived from

1680-406: The Sun (due to both its velocity and its axial tilt). In terms of Earth's rotation, the average day length is about 360.9856°. A day lasts for more than 360° of rotation because of the Earth's revolution around the Sun. With a full year being slightly more than 360 days, the Earth's daily orbit around the Sun is slightly less than 1°, so the day is slightly less than 361° of rotation. Elsewhere in

1736-517: The Sun's annual cycle, giving consistent start dates for the four seasons from year to year. A lunar calendar organizes dates based on the Moon 's lunar phase . In common usage, a day starts at midnight , written as 00:00 or 12:00 am in 24- or 12-hour clocks , respectively. Because the time of midnight varies between locations, time zones are set up to facilitate the use of a uniform standard time . Other conventions are sometimes used, for example

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1792-437: The average length of a solar day on Earth has been about 86,400.002 seconds (24.000 000 6 hours). There are currently about 365.2421875 solar days in one mean tropical year . Ancient custom has a new day starting at either the rising or setting of the Sun on the local horizon (Italian reckoning, for example, being 24 hours from sunset, old style). The exact moment of, and the interval between, two sunrises or sunsets depends on

1848-444: The constant areal velocity is d A d t = r 2 2 d θ d t . {\displaystyle {\frac {dA}{dt}}={\frac {r^{2}}{2}}{\frac {d\theta }{dt}}.} The area enclosed by the elliptical orbit is π a b {\displaystyle \pi ab} . So the period T {\displaystyle T} satisfies and

1904-467: The cross product of the r and dx vectors, for some short piece of the orbit, dx . d A = 1 2 ( r → × d x → ) = 1 2 ( r → × v → d t ) {\displaystyle dA={\frac {1}{2}}({\vec {r}}\times {\vec {dx}})={\frac {1}{2}}({\vec {r}}\times {\vec {v}}dt)} for

1960-513: The current usage of "Kepler's Second Law" is something of a misnomer. Kepler had two versions, related in a qualitative sense: the "distance law" and the "area law". The "area law" is what became the Second Law in the set of three; but Kepler did himself not privilege it in that way. Kepler published his first two laws about planetary motion in 1609, having found them by analyzing the astronomical observations of Tycho Brahe . Kepler's third law

2016-539: The day's boundaries. In the Hebrew Bible , Genesis 1:5 defines a day in terms of "evening" and "morning" before recounting the creation of the Sun to illuminate it: "And God called the light Day, and the darkness he called Night. And the evening and the morning were the first day." The Jewish day begins at either sunset or nightfall (when three second- magnitude stars appear). Medieval Europe also followed this tradition, known as Florentine reckoning: In this system,

2072-431: The day, and use the day or sidereal day as a base unit. Metric time uses metric prefixes to keep time. It uses the day as the base unit, and smaller units being fractions of a day: a metric hour ( deci ) is 1 ⁄ 10 of a day; a metric minute ( milli ) is 1 ⁄ 1000 of a day; etc. Similarly, in decimal time, the length of a day is static to normal time. A day is also split into 10 hours, and 10 days comprise

2128-661: The end of a UTC day, and so while almost all days have a duration of 86,400 seconds, there are these exceptional cases of a day with 86,401 seconds (in the half-century spanning 1972 through 2022, there have been a total of 27 leap seconds that have been inserted, so roughly once every other year). The term comes from the Old English term dæġ ( /dæj/ ), with its cognates such as dagur in Icelandic , Tag in German , and dag in Norwegian , Danish , Swedish and Dutch – all stemming from

2184-413: The final expression is proportional to the total angular momentum ( r → × p → ) {\displaystyle ({\vec {r}}\times {\vec {p}})} , Kepler's equal area law will hold for any system that conserves angular momentum. Since any radial force will produce no torque on the planet's motion, angular momentum will be conserved. In

2240-409: The geographical position ( longitude and latitude, as well as altitude), and the time of year (as indicated by ancient hemispherical sundials ). A more constant day can be defined by the Sun passing through the local meridian , which happens at local noon (upper culmination ) or midnight (lower culmination). The exact moment is dependent on the geographical longitude, and to a lesser extent on

2296-502: The hours from sunset, and French , counting the hours from midnight. Humans have divided the day in rough periods, which can have cultural implications, and other effects on humans' biological processes. The parts of the day do not have set times; they can vary by lifestyle or hours of daylight in a given place. Daytime is the part of the day during which sunlight directly reaches the ground, assuming that there are no obstacles. The length of daytime averages slightly more than half of

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2352-415: The limiting case ε = 0, the orbit is a circle with the Sun at the centre (i.e. where there is zero eccentricity). At θ = 0°, perihelion , the distance is minimum At θ = 90° and at θ = 270° the distance is equal to p {\displaystyle p} . At θ = 180°, aphelion , the distance is maximum (by definition, aphelion is – invariably – perihelion plus 180°) The semi-major axis

2408-489: The number of solar days). Besides a stellar day on Earth , other bodies in the Solar System have day times, the durations of these being: In the International System of Units (SI), a day not an official unit, but is accepted for use with SI . A day, with symbol d, is defined using SI units as 86,400 seconds; the second is the base unit of time in SI units . In 1967–68, during the 13th CGPM (Resolution 1),

2464-399: The orbit of the Earth is approximately which is close to the correct value (0.016710218). The accuracy of this calculation requires that the two dates chosen be along the elliptical orbit's minor axis and that the midpoints of each half be along the major axis. As the two dates chosen here are equinoxes, this will be correct when perihelion , the date the Earth is closest to the Sun, falls on

2520-512: The placement of leap seconds. Leap seconds are announced in advance by the International Earth Rotation and Reference Systems Service (IERS) , which measures the Earth's rotation and determines whether a leap second is necessary. Discovered by paleontologist John W. Wells , the day lengths of geological periods have been estimated by measuring sedimentation rings in coral fossils , due to some biological systems being affected by

2576-413: The result of the Second Law is exactly true, as it is logically equivalent to the conservation of angular momentum, which is true for any body experiencing a radially symmetric force. A correct proof can be shown through this. Since the cross product of two vectors gives the area of a parallelogram possessing sides of those vectors, the triangular area dA swept out in a short period of time is given by half

2632-409: The rotational period. This arose the need for leap seconds , which insert extra seconds into Coordinated Universal Time (UTC) . Although typically 86,400 SI seconds in duration, a civil day can be either 86,401 or 86,399 SI seconds long on such a day. Other than the two-millisecond variation from tidal deceleration, other factors minutely affect the day's length , which creates an irregularity in

2688-506: The sky). Due to an orbit's eccentricity, the Sun resides in one of the orbit's foci instead of the middle. Consequently, due to Kepler's second law , the planet travels at different speeds at various positions in its orbit, and thus a solar day is not the same length of time throughout the orbital year. Because the Earth moves along an eccentric orbit around the Sun while the Earth spins on an inclined axis, this period can be up to 7.9 seconds more than (or less than) 24 hours. In recent decades,

2744-418: The sun sets, and ends when one goes to bed. Twilight is the period before sunrise and after sunset in which there is natural light but no direct sunlight. The morning twilight begins at dawn and ends at sunrise, while the evening twilight begins at sunset and ends at dusk . Both periods of twilight can be divided into civil twilight , nautical twilight , and astronomical twilight . Civil twilight

2800-447: The terminology of scientific laws for these discoveries was current at least from the time of Joseph de Lalande . It was the exposition of Robert Small , in An account of the astronomical discoveries of Kepler (1814) that made up the set of three laws, by adding in the third. Small also claimed, against the history, that these were empirical laws , based on inductive reasoning . Further,

2856-440: The third law, and was fully published in 1619), describe the orbits of planets around the Sun. These laws replaced circular orbits and epicycles in the heliocentric theory of Nicolaus Copernicus with elliptical orbits and explained how planetary velocities vary. The three laws state that: The elliptical orbits of planets were indicated by calculations of the orbit of Mars . From this, Kepler inferred that other bodies in

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2912-431: The tide. The length of a day at the Earth's formation is estimated at 6 hours. Arbab I. Arbab plotted day lengths over time and found a curved line. Arbab attributed this to the change of water volume present affecting Earth's rotation. For most diurnal animals, the day naturally begins at dawn and ends at sunset. Humans, with their cultural norms and scientific knowledge, have employed several different conceptions of

2968-401: The time of the year. The length of such a day is nearly constant (24 hours ± 30 seconds). This is the time as indicated by modern sundials. A further improvement defines a fictitious mean Sun that moves with constant speed along the celestial equator ; the speed is the same as the average speed of the real Sun, but this removes the variation over a year as the Earth moves along its orbit around

3024-545: The world, 40 such zones are now in use: the central zone, from which all others are defined as offsets, is known as UTC+00 , which uses Coordinated Universal Time (UTC) . The most common convention starts the civil day at midnight : this is near the time of the lower culmination of the Sun on the central meridian of the time zone. Such a day may be called a calendar day . A day is commonly divided into 24 hours, with each hour being made up of 60 minutes, and each minute composed of 60 seconds. A sidereal day or stellar day

3080-448: Was published and was taken to be basically Copernican, and 1690, by which time work of Gottfried Leibniz on Kepler had been published. Newton was credited with understanding that the second law is not special to the inverse square law of gravitation, being a consequence just of the radial nature of that law, whereas the other laws do depend on the inverse square form of the attraction. Carl Runge and Wilhelm Lenz much later identified

3136-457: Was published in 1619. Kepler had believed in the Copernican model of the Solar System, which called for circular orbits, but he could not reconcile Brahe's highly precise observations with a circular fit to Mars' orbit – Mars coincidentally having the highest eccentricity of all planets except Mercury. His first law reflected this discovery. In 1621, Kepler noted that his third law applies to

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