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PHYS-633: Problem set #0 Solutions
PHYS-633: Problem set #0 Solutions

... The cross section of dust of diameter d = 0.1 mm is σ = (π/4)d2 = 7.8−5 cm2 . The optical depth is given in terms of number density n = 20/cm3 , cross section σ, and distance D = 1000 cm, τ = n σ D = 20 × 7.8−5 × 103 = 1.56 . ...
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Tropical year

A tropical year (also known as a solar year), for general purposes, is the time that the Sun takes to return to the same position in the cycle of seasons, as seen from Earth; for example, the time from vernal equinox to vernal equinox, or from summer solstice to summer solstice. Because of the precession of the equinoxes, the seasonal cycle does not remain exactly synchronized with the position of the Earth in its orbit around the Sun. As a consequence, the tropical year is about 20 minutes shorter than the time it takes Earth to complete one full orbit around the Sun as measured with respect to the fixed stars (the sidereal year).Since antiquity, astronomers have progressively refined the definition of the tropical year. The Astronomical Almanac Online Glossary 2015 states:year, tropical:the period of time for the ecliptic longitude of the Sun to increase 360 degrees. Since the Sun's ecliptic longitude is measured with respect to the equinox, the tropical year comprises a complete cycle of seasons, and its length is approximated in the long term by the civil (Gregorian) calendar. The mean tropical year is approximately 365 days, 5 hours, 48 minutes, 45 seconds.An equivalent, more descriptive, definition is ""The natural basis for computing passing tropical years is the mean longitude of the Sun reckoned from the precessionally moving equinox (the dynamical equinox or equinox of date). Whenever the longitude reaches a multiple of 360 degrees the mean Sun crosses the vernal equinox and a new tropical year begins"". (Borkowski 1991, p. 122)The mean tropical year on January 1, 2000, was about 365.2421897 ephemeris days according to the calculation of Laskar (1986); each ephemeris day lasting 86,400 SI seconds. By 2010 this had decreased to 365.2421891 (365 ephemeris days, 5 hours, 48 minutes and 45.14 seconds). This is about 365.242181 mean solar days, though the length of a mean solar day is constantly changing.
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