Information about Tropical Year
A tropical year (also known as a solar year) is the length of time the Sun, as seen from the Earth, takes to return to the same position along the ecliptic (its path among the stars on the celestial sphere) relative to the equinoxes and solstices. The length of time depends on the point of the ecliptic. Starting from the (northern) vernal equinox, one of the four cardinal points along the ecliptic, yields the vernal equinox year; averaging over all starting points on the ecliptic yields the mean tropical year.
On Earth, the progress of the tropical year seems to slow the Sun from south to north and back. The word "tropical" comes from the Greek tropos meaning "turn". The tropics of Cancer and Capricorn mark the extreme north and south latitudes where the Sun can appear directly overhead. The position of the Sun can be measured by the variation from day to day of the length of the shadow at noon of a gnomon (a vertical pillar or stick). This is the most "natural" way to measure the year in the sense that the variations of insolation drive the seasons.
The vernal equinox moves back along the ecliptic caused by precession. A tropical year is shorter than a sidereal year (in 2000, the difference was 20.409 minutes; it was 20.400 min in 1900).
Astronomers defined a mean tropical year, an average over all points on the ecliptic, with a length of about 365.24219 SI days. Tropical years have been defined for specific points on the ecliptic. The vernal equinox year begins and ends when the Sun is at the vernal equinox. Its length is about 365.2424 days.
Time can be measure in "days of fixed length": SI days of 86,400 SI seconds, defined by atomic clocks or dynamical days defined by the motion of the Moon and planets, or in mean solar days, defined by the rotation of the Earth with respect to the Sun. The duration of the mean solar day, as measured by clocks, is getting longer (or clock days are getting shorter, as measured by a sundial). With the mean solar day, the length of each solar day varies regularly during the year, as the equation of time shows.
Error in Statement of Tropical Year explains using the value of the "mean tropical year" to refer to the vernal equinox year defined above is an error. The words "tropical year" in astronomical jargon refer only to the mean tropical year, Newcomb-style, of 365.24219 SI days. The vernal equinox year of 365.2424 mean solar days is the basis of most solar calendars, but not the "tropical year" of modern astronomers.
The number of mean solar days in a vernal equinox year has been oscillating between 365.2424 and 365.2423 for several millennia and will likely remain near 365.2424 for a few more. This long-term stability is pure chance, because in our era the slowdown of the rotation, the acceleration of the mean orbital motion, and the effect at the vernal equinox of rotation and shape changes in the Earth's orbit, happen to almost cancel out.
In contrast, the mean tropical year, measured in SI days, is getting shorter. It was 365.2423 SI days at about AD 200, and is currently near 365.2422 SI days.
(this value is consistent with the linear change and the other ecliptic years that follow)
or about 5 ms/year, which means that 2000 years ago the tropical year was 10 seconds longer.
Note: these and following formulae use days of exactly 86400 SI seconds. a is measured in Julian years (365.25 days) from the epoch (2000). The time scale is Terrestrial Time which is based on atomic clocks (formerly, Ephemeris Time was used instead); this is different from Universal Time, which follows the somewhat unpredictable rotation of the Earth. The (small but accumulating) difference (called ΔT) is relevant for applications that refer to time and days as observed from Earth, like calendars and the study of historical astronomical observations such as eclipses.
The northern solstice point is now near the aphelion, where the Sun moves slower than average. The time gained because this point approached the Sun (by the same angular arc distance as happens at the southern solstice point) is greater. The tropical year as measured for this point is shorter than average. The equinoctial points are in between, and at present the tropical years measured for these are closer to the value of the mean tropical year as quoted above. As the equinox completes a full circle with respect to the perihelion (in about 21,000 years), the length of the tropical year as defined with reference to a specific point on the ecliptic oscillates around the mean tropical year.
Current values and their annual change of the time of return to the cardinal ecliptic points<ref name="meeus" /> are:
Notice that the average of these four is 365.2422 SI days (the mean tropical year). This figure is currently getting smaller, which means years get shorter, when measured in seconds. Now, actual days get slowly and steadily longer, as measured in seconds. So the number of actual days in a year is decreasing too.
The differences between the various types of year are relatively minor for the present configuration of Earth's orbit. On Mars, the differences between the different types of years are an order of magnitude greater: vernal equinox year = 668.5907 Martian days (sols), summer solstice year = 668.5880 sols, autumn equinox year = 668.5940 sols, winter solstice year = 668.5958 sols, with the tropical year being 668.5921 sols [1]. This is due to Mars' considerably greater orbital eccentricity.
Earth's orbit goes through cycles of increasing and decreasing eccentricity over a timescale of about 100,000 years (Milankovitch cycles); and its eccentricity can reach as high as about 0.06. In the distant future, therefore, Earth will also have much more divergent values of the various equinox and solstice years.
Now our current Gregorian calendar has an average year of:
Although it is close to the vernal equinox year (in line with the intention of the Gregorian calendar reform of 1582), it is slightly too long, and not an optimal approximation when considering the continued fractions listed below. Note that the approximation of 365 + 8/33 used in the Iranian calendar is even better, and 365 + 8/33 was considered in Rome and England as an alternative for the Catholic Gregorian calendar reform of 1582.
Moreover, modern calculations show that the vernal equinox year has remained between 365.2423 and 365.2424 calendar days (i.e. mean solar days as measured in Universal Time) for the last four millennia and should remain 365.2424 days (to the nearest ten-thousandth of a calendar day) for some millennia to come. This is due to the fortuitous mutual cancellation of most of the factors affecting the length of this particular measure of the tropical year during the current era.
In the history of solar calendars notably these five rules (approximations) were used, are used or are proposed:
Remarks: The current Gregorian rule matched the mean tropical year measured in SI seconds about 6000 years ago. With respect to the vernal equinox year measured in mean solar days, important for the calendar date of Easter, the Gregorian year is and stays a very good approximation for thousands of years.
When using the Gregorian calendar in constant time scales (TT or TAI), so when ignoring DeltaT, the vernal equinox will inevitably shift to 19-20 March, instead of the traditional 20-21 March. Gregorian common year 2100 will temporally replace vernal equinox to 20-21 March, but shift back to 19-20 March in 2176 (=17x128) according to Meeus' equinox tables. The von Mädler rule would regularly avoid this shift to 19 March for millennia.
On Earth, the progress of the tropical year seems to slow the Sun from south to north and back. The word "tropical" comes from the Greek tropos meaning "turn". The tropics of Cancer and Capricorn mark the extreme north and south latitudes where the Sun can appear directly overhead. The position of the Sun can be measured by the variation from day to day of the length of the shadow at noon of a gnomon (a vertical pillar or stick). This is the most "natural" way to measure the year in the sense that the variations of insolation drive the seasons.
The vernal equinox moves back along the ecliptic caused by precession. A tropical year is shorter than a sidereal year (in 2000, the difference was 20.409 minutes; it was 20.400 min in 1900).
Subtleties
The motion of the Earth in its orbit (and therefore the apparent motion of the Sun among the stars) is not completely regular, caused by gravitational perturbations by the Moon and planets. The time between successive passages of a specific point on the ecliptic, and the speed of the Earth in its orbit vary (because the orbit is elliptical rather than circular). The position of the equinox on the orbit changes because of precession. The length of a tropical year (explained below) depends on the specific point selected on the ecliptic (as measured from, and moving together with, the equinox) that the Sun should return to.Astronomers defined a mean tropical year, an average over all points on the ecliptic, with a length of about 365.24219 SI days. Tropical years have been defined for specific points on the ecliptic. The vernal equinox year begins and ends when the Sun is at the vernal equinox. Its length is about 365.2424 days.
Time can be measure in "days of fixed length": SI days of 86,400 SI seconds, defined by atomic clocks or dynamical days defined by the motion of the Moon and planets, or in mean solar days, defined by the rotation of the Earth with respect to the Sun. The duration of the mean solar day, as measured by clocks, is getting longer (or clock days are getting shorter, as measured by a sundial). With the mean solar day, the length of each solar day varies regularly during the year, as the equation of time shows.
Error in Statement of Tropical Year explains using the value of the "mean tropical year" to refer to the vernal equinox year defined above is an error. The words "tropical year" in astronomical jargon refer only to the mean tropical year, Newcomb-style, of 365.24219 SI days. The vernal equinox year of 365.2424 mean solar days is the basis of most solar calendars, but not the "tropical year" of modern astronomers.
The number of mean solar days in a vernal equinox year has been oscillating between 365.2424 and 365.2423 for several millennia and will likely remain near 365.2424 for a few more. This long-term stability is pure chance, because in our era the slowdown of the rotation, the acceleration of the mean orbital motion, and the effect at the vernal equinox of rotation and shape changes in the Earth's orbit, happen to almost cancel out.
In contrast, the mean tropical year, measured in SI days, is getting shorter. It was 365.2423 SI days at about AD 200, and is currently near 365.2422 SI days.
Current mean value
The latest value of the mean tropical year at J2000.0 (1 January 2000, 12:00 TT) according to an incomplete analytical solution by Moisson[1] was:- 365.242 190 419 SI days
(this value is consistent with the linear change and the other ecliptic years that follow)
- 365.242 189 670 SI days.
- difference (days) = −0.000 000 061 62×a days (a in Julian years from 2000),
or about 5 ms/year, which means that 2000 years ago the tropical year was 10 seconds longer.
Note: these and following formulae use days of exactly 86400 SI seconds. a is measured in Julian years (365.25 days) from the epoch (2000). The time scale is Terrestrial Time which is based on atomic clocks (formerly, Ephemeris Time was used instead); this is different from Universal Time, which follows the somewhat unpredictable rotation of the Earth. The (small but accumulating) difference (called ΔT) is relevant for applications that refer to time and days as observed from Earth, like calendars and the study of historical astronomical observations such as eclipses.
Different lengths
As already mentioned, there is some choice in the length of the tropical year depending on the point of reference that one selects. The reason is that, while the precession of the equinoxes is fairly steady, the apparent speed of the Sun during the year is not. When the Earth is near the perihelion of its orbit (presently, around January 3 – January 4), it (and therefore the Sun as seen from Earth) moves faster than average; hence the time gained when reaching the approaching point on the ecliptic is comparatively small, and the "tropical year" as measured for this point will be longer than average. This is the case if one measures the time for the Sun to come back to the southern solstice point (around December 21 – 22 December), which is close to the perihelion.The northern solstice point is now near the aphelion, where the Sun moves slower than average. The time gained because this point approached the Sun (by the same angular arc distance as happens at the southern solstice point) is greater. The tropical year as measured for this point is shorter than average. The equinoctial points are in between, and at present the tropical years measured for these are closer to the value of the mean tropical year as quoted above. As the equinox completes a full circle with respect to the perihelion (in about 21,000 years), the length of the tropical year as defined with reference to a specific point on the ecliptic oscillates around the mean tropical year.
Current values and their annual change of the time of return to the cardinal ecliptic points<ref name="meeus" /> are:
| vernal equinox | 365.242 374 04 + 0.000 000 103 38×a days |
| northern solstice | 365.241 626 03 + 0.000 000 006 50×a days |
| autumn equinox | 365.242 017 67 − 0.000 000 231 50×a days |
| southern solstice | 365.242 740 49 − 0.000 000 124 46×a days |
Notice that the average of these four is 365.2422 SI days (the mean tropical year). This figure is currently getting smaller, which means years get shorter, when measured in seconds. Now, actual days get slowly and steadily longer, as measured in seconds. So the number of actual days in a year is decreasing too.
The differences between the various types of year are relatively minor for the present configuration of Earth's orbit. On Mars, the differences between the different types of years are an order of magnitude greater: vernal equinox year = 668.5907 Martian days (sols), summer solstice year = 668.5880 sols, autumn equinox year = 668.5940 sols, winter solstice year = 668.5958 sols, with the tropical year being 668.5921 sols [1]. This is due to Mars' considerably greater orbital eccentricity.
Earth's orbit goes through cycles of increasing and decreasing eccentricity over a timescale of about 100,000 years (Milankovitch cycles); and its eccentricity can reach as high as about 0.06. In the distant future, therefore, Earth will also have much more divergent values of the various equinox and solstice years.
Calendar year
This distinction is relevant for calendar studies. The established Hebrew calendar created a mathematical resolution for the differences that arise between the solar and lunar years so that all Jewish holidays occur at the same season each year. The main Christian moving feast has been Easter. Several different ways of computing the date of Easter were used in early Christian times, but eventually the unified rule was accepted that Easter would be celebrated on the Sunday after the first (ecclesiastical) full moon on or after the day of the (ecclesiastical, not actual) vernal equinox, which was established to fall on 21 March. The church therefore made it an objective to keep the day of the (actual) vernal equinox on or near 21 March, and the calendar year has to be synchronized with the tropical year as measured by the mean interval between vernal equinoxes. From about AD 1000 the mean tropical year (measured in SI days) has become increasingly shorter than this mean interval between vernal equinoxes (measured in actual days), though the interval between successive vernal equinoxes measured in SI days has become increasingly longer.Now our current Gregorian calendar has an average year of:
- 365 + 97/400 = 365.2425 days.
Although it is close to the vernal equinox year (in line with the intention of the Gregorian calendar reform of 1582), it is slightly too long, and not an optimal approximation when considering the continued fractions listed below. Note that the approximation of 365 + 8/33 used in the Iranian calendar is even better, and 365 + 8/33 was considered in Rome and England as an alternative for the Catholic Gregorian calendar reform of 1582.
Moreover, modern calculations show that the vernal equinox year has remained between 365.2423 and 365.2424 calendar days (i.e. mean solar days as measured in Universal Time) for the last four millennia and should remain 365.2424 days (to the nearest ten-thousandth of a calendar day) for some millennia to come. This is due to the fortuitous mutual cancellation of most of the factors affecting the length of this particular measure of the tropical year during the current era.
Calendar rules and vernal equinox
The great interest of the tropical year value is to keep the calendar year synchronized with the beginning of seasons. All the progressive solar calendars since Old Egyptian times are arithmetical calendars. This means an easy rule to try to reach the best possible astronomical value.In the history of solar calendars notably these five rules (approximations) were used, are used or are proposed:
| Calendar rule | |||
| Old Egyptian | 365 | = 365. 000 000 000 | |
| Julian | 365 + ¼ | = 365. 250 000 000 | |
| Gregorian | 365 + ¼ - 3/400 | = 365. 242 500 000 | |
| Khayyam | 365 + 8/33 | = 365. 24 24 24 24 | |
| Mean tropical year at epoch 2000.0 | = 365. 242 190 419 | ||
| von Mädler | 365 + 31/128 | = 365. 242 187 500 | |
| Vernal Equinox from AD 2001 to 2048 in Dynamical Time (delta T to UT > 1 min.) | ||||||||||||||
| 2001 | 20 | 13:32 | 2002 | 20 | 19:17 | 2003 | 21 | 01:01 | 2004 | 20 | 06:50 | |||
| 2005 | 20 | 12:35 | 2006 | 20 | 18:27 | 2007 | 21 | 00:09 | 2008 | 20 | 05:50 | |||
| 2009 | 20 | 11:45 | 2010 | 20 | 17:34 | 2011 | 20 | 23:22 | 2012 | 20 | 05:16 | |||
| 2013 | 20 | 11:03 | 2014 | 20 | 16:58 | 2015 | 20 | 22:47 | 2016 | 20 | 04:32 | |||
| 2017 | 20 | 10:30 | 2018 | 20 | 16:17 | 2019 | 20 | 22:00 | 2020 | 20 | 03:51 | |||
| 2021 | 20 | 09:39 | 2022 | 20 | 15:35 | 2023 | 20 | 21:26 | 2024 | 20 | 03:08 | |||
| 2025 | 20 | 09:03 | 2026 | 20 | 14:47 | 2027 | 20 | 20:26 | 2028 | 20 | 02:19 | |||
| 2029 | 20 | 08:03 | 2030 | 20 | 13:54 | 2031 | 20 | 19:42 | 2032 | 20 | 01:23 | |||
| 2033 | 20 | 07:24 | 2034 | 20 | 13:19 | 2035 | 20 | 19:04 | 2036 | 20 | 01:04 | |||
| 2037 | 20 | 06:52 | 2038 | 20 | 12:42 | 2039 | 20 | 18:34 | 2040 | 20 | 00:13 | |||
| 2041 | 20 | 06:08 | 2042 | 20 | 11:55 | 2043 | 20 | 17:29 | 2044 | 19 | 23:22 | |||
| 2045 | 20 | 05:09 | 2046 | 20 | 11:00 | 2047 | 20 | 16:54 | 2048 | 19 | 22:36 | |||
| Source: Jean Meeus | ||||||||||||||
Remarks: The current Gregorian rule matched the mean tropical year measured in SI seconds about 6000 years ago. With respect to the vernal equinox year measured in mean solar days, important for the calendar date of Easter, the Gregorian year is and stays a very good approximation for thousands of years.
When using the Gregorian calendar in constant time scales (TT or TAI), so when ignoring DeltaT, the vernal equinox will inevitably shift to 19-20 March, instead of the traditional 20-21 March. Gregorian common year 2100 will temporally replace vernal equinox to 20-21 March, but shift back to 19-20 March in 2176 (=17x128) according to Meeus' equinox tables. The von Mädler rule would regularly avoid this shift to 19 March for millennia.
See also
- Anomalistic year
- Sidereal year
- Tropical astrology
References
1. ^ 365.242190419 days = 365.25 days × 1296000" / (6.28307585085 rad × 180°/π × 1296000"/360° + 50.28796195") from X. Moisson, "Solar system planetary motion to third order of the masses", Astronomy and astrophysics 341 (1999) 318-327, p. 324 (N for Earth fitted to DE405) and N. Capitaine et al., "Expressions for IAU 2000 precession quantities" (685 KB pdf file) Astronomy and Astrophysics 412 (2003) 567-586 p. 581 (P03: pA).
2. ^ Derived from: Jean Meeus (1991), Astronomical Algorithms, Ch.26 p. 166; Willmann-Bell, Richmond, VA. ISBN 0-943396-35-2 ; based on the VSOP-87 planetary ephemeris.
2. ^ Derived from: Jean Meeus (1991), Astronomical Algorithms, Ch.26 p. 166; Willmann-Bell, Richmond, VA. ISBN 0-943396-35-2 ; based on the VSOP-87 planetary ephemeris.
- Jean Meeus and Denis Savoie, "The history of the tropical year", Journal of the British Astronomical Association 102 (1992) 40–42.
The Sun
Observation data
Mean distance
from Earth 1.4961011 m
(8.31 min at light speed)
Visual brightness (V) −26.74m [1]
Absolute magnitude 4.
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Observation data
Mean distance
from Earth 1.4961011 m
(8.31 min at light speed)
Visual brightness (V) −26.74m [1]
Absolute magnitude 4.
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EARTH was a short-lived Japanese vocal trio which released 6 singles and 1 album between 2000 and 2001. Their greatest hit, their debut single "time after time", peaked at #13 in the Oricon singles chart.
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ecliptic is the apparent path that the Sun traces out in the sky, as it appears to move in the sky in relation to the stars, this apparent path aligns with the planets throughout the course of the year.
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celestial sphere is an imaginary rotating sphere of "gigantic radius", concentric and coaxial with the Earth. All objects in the sky can be thought of as lying upon the sphere.
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equinox can have two meanings:
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- The moment when the Sun is positioned directly over the Earth's equator and, by extension, the apparent position of the Sun at that moment - see below.
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solstice occurs twice a year, whenever Earth's axis tilts the most toward or away from the Sun, causing the Sun to be farthest north or south at noon. The name is derived from Latin sol (sun) and sistere
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equinox can have two meanings:
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- The moment when the Sun is positioned directly over the Earth's equator and, by extension, the apparent position of the Sun at that moment - see below.
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A year (from Old English gēr) is the time between two recurrences of an event related to the orbit of the Earth around the Sun. By extension, this can be applied to any planet: for example, a "Martian year" is the time in which Mars completes its own orbit.
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Greek}}}
Writing system: Greek alphabet
Official status
Official language of: Greece
Cyprus
European Union
recognised as minority language in parts of:
European Union
Italy
Turkey
Regulated by:
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Writing system: Greek alphabet
Official status
Official language of: Greece
Cyprus
European Union
recognised as minority language in parts of:
European Union
Italy
Turkey
Regulated by:
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Tropic of Cancer, or Northern tropic, is one of the five major circles of latitude that mark maps of the Earth. It is the most northerly latitude at which the sun can appear directly overhead at noon.
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Tropic of Capricorn, or Southern tropic, is one of the five major circles of latitude that mark maps of the Earth. It lies 23° 26′ 22″ south of the Equator, and marks the most southerly latitude at which the sun can appear directly overhead at noon.
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equator divides the planet into a Northern Hemisphere and a Southern Hemisphere, and has a latitude of 0. Latitude, usually denoted symbolically by the Greek letter phi, , gives the location of a place on Earth north or south of the equator.
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gnomon is the part of a sundial that casts the shadow. Gnomon is an ancient Greek word meaning "indicator", "one who discerns," or "that which reveals."
In the northern hemisphere, the shadow-casting edge is normally oriented so that it points north and is parallel to the
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In the northern hemisphere, the shadow-casting edge is normally oriented so that it points north and is parallel to the
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Insolation (from INcoming SOLar radiATION) is a measure of solar energy received on a given surface area in a given time. It is commonly expressed in kilowatt-hours per square meter per day (kW•h/m²/day).
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The precession of Earth's axis of rotation with respect to inertial space is also called the precession of the equinoxes. Like a wobbling top, the direction of the Earth's axis is changing; while today, the North Pole points roughly to Polaris, over time it will change.
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The sidereal year is the time taken for the Sun to return to the same position with respect to the stars of the celestial sphere. It is the orbital period of Earth, equal to 365.25636042 mean solar days (31,558,149.540 seconds), that is 365.25636042 earth rotations or sidereal days.
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ORBit is a CORBA compliant Object Request Broker (ORB). The current version is called ORBit2 and is compliant with CORBA version 2.4. It is developed under the GPL license and is used as middleware for the GNOME project.
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Gravitation is a natural phenomenon by which all objects with mass attract each other. In everyday life, gravitation is most familiar as the agency that endows objects with weight.
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Perturbation is a term used in astronomy to describe alterations to an object's orbit caused by gravitational interactions with other bodies. For example, the orbits of comets are often perturbed, particularly by the gravitational fields of the giant planets - Jupiter's
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Moon
The Moon as seen by an observer on Earth
Orbital characteristics
Periapsis: 363,104 km
0.0024 AU
Apoapsis: 405,696 km
0.0027 AU
Semi-major axis: 384,399 km
0.
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The Moon as seen by an observer on Earth
Orbital characteristics
Periapsis: 363,104 km
0.0024 AU
Apoapsis: 405,696 km
0.0027 AU
Semi-major axis: 384,399 km
0.
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planet, as defined by the International Astronomical Union (IAU), is a celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, not massive enough to cause thermonuclear fusion in its core, and has cleared its neighbouring region of
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Si, si, or SI may refer to (all SI unless otherwise stated):
In language:
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In language:
- One of two Italian words:
- sì (accented) for "yes"
- si
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day (symbol: d) is a unit of time equivalent to 24 hours. It is not an SI unit but it is accepted for use with SI.[1] The SI unit of time is the second. The term comes from the Old English dæg.
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second (SI symbol: s), sometimes abbreviated sec., is the name of a unit of time, and is the International System of Units (SI) base unit of time.
SI prefixes are frequently combined with the word second to denote subdivisions of the second, e.g.
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SI prefixes are frequently combined with the word second to denote subdivisions of the second, e.g.
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equation of time is the difference, over the course of a year, between time as read from a sundial and a clock. The sundial can be ahead (fast) by as much as 16 min 33 s (around November 3) or fall behind by as much as 14 min 6 s (around February 12).
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day (symbol: d) is a unit of time equivalent to 24 hours. It is not an SI unit but it is accepted for use with SI.[1] The SI unit of time is the second. The term comes from the Old English dæg.
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Definitions
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Terrestrial Time (TT) is the modern time standard for time on the surface of the Earth. It is the proper time experienced by a clock located on the geoid. In astronomy it is used as the time coordinate for apparent ephemerides for an Earthbound viewer.
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Julian year (symbol: a) is a unit of measurement of time defined as exactly 365.25 days of 86,400 SI seconds each, totalling 31,557,600 seconds. That is the average length of the year in the Julian calendar used in Western societies in previous centuries, and for which the
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Ephemeris Time (ET) is a now obsolete time scale used in ephemerides of celestial bodies, in particular the Sun (as observed from the Earth), Moon, planets, and other members of the solar system.
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Universal Time (UT) is a timescale based on the rotation of the Earth. It is a modern continuation of Greenwich Mean Time (GMT), i.e., the mean solar time on the meridian of Greenwich, England, which is the conventional zero meridian for geographic longitude.
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