# The Physics, Astronomy and Mathematics of the Solar System

## The Mathematical Dynamics of Celestial Navigation and Astronavigation

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## GLOSSARY

UT0 is Universal Time determined at an observatory by observing the diurnal motion of stars or extragalactic radio sources, and also from ranging observations of the Moon and artificial Earth satellites. It is uncorrected for the displacement of Earth's geographic pole from its rotational pole. This displacement, called polar motion, causes the geographic position of any place on Earth to vary by several meters, and different observatories will find a different value for UT0 at the same moment.[7]

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UT1 is the principal form of Universal Time. It is computed from the raw observed UT0 by correcting UT0 for the effect of polar motion on the longitude of the observing site. UT1 is the same everywhere on Earth, and is proportional to the true rotation angle of the Earth with respect to a fixed frame of reference. Since the rotational speed of the earth is not uniform, UT1 has an uncertainty of plus or minus 3 milliseconds per day. The ratio of UT1 to mean sidereal time is defined to be 0.997269566329084 − 5.8684×10−11T + 5.9×10−15T², where T is the number of Julian centuries of 36525 days each that have elapsed since JD 2451545.0 (J2000).[7]

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UT1R
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is a smoothed version of UT1, filtering out periodic variations due to tides. It includes 62 smoothing terms, with periods ranging from 5.6 days to 18.6 years.[7]

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UT2
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is a smoothed version of UT1, filtering out periodic seasonal variations. It is mostly of historic interest and rarely used anymore. It is defined by the equation:

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UT2 = UT1+0.0220•sin(2Πt)-0.0120•cos(2Πt)-0.0060•sin(4Πt)+0.0070•cos(4Πt)
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seconds, where t is the time as fraction of the Besselian year.[7]

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UT2R is a smoothed version of UT1, incorporating both the seasonal corrections of UT2 and the tidal corrections of UT1R. It is the most smoothed form of Universal Time. Its non-uniformities reveal the unpredictable components of Earth rotation, due to atmospheric weather, plate tectonics, and currents in the interior of the Earth.[7]

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UTC
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(Coordinated Universal Time) is an atomic timescale that approximates UT1. It is the international standard on which civil time is based. It ticks SI seconds, in step with TAI. It usually has 86400 SI seconds per day, but is kept within 0.9 seconds of UT1 by the introduction of occasional intercalary leap seconds. As of 2007 these leaps have always been positive, with a day of 86401 seconds. When an accuracy better than one second is not required, UTC can be used as an approximation of UT1. The difference between UT1 and UTC is known as DUT1.[7]

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UTC-SLS
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(UTC with Smoothed Leap Seconds) is a modified form of UTC that avoids unequal day lengths. It usually ticks the same as UTC, but modifies the length of the second for the last 1000 UTC seconds of a day containing a leap second so that there are always 86400 seconds in the UTC-SLS day.[7]

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UTS
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(Smoothed Universal Time) is an obscure form of UT used internally at IERS. The same abbreviation was for a time used to refer to UTC-SLS.[7]

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STUDENT'S BIBLIOGRAPHY

[1] Latitude Hooks and Azimuth Rings, by Dennis Fisher, An International Marine/McGraw-Hill Companies Book, 1995, Camden, Maine.

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