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Definitions and Terminology
Published in Frank Vignola, Joseph Michalsky, Thomas Stoffel, Solar and Infrared Radiation Measurements, 2019
Frank Vignola, Joseph Michalsky, Thomas Stoffel
From an Earth-centered point of view, the Sun moves among the other stars in the heavens on the celestial sphere (see Figure 2.3). The observer on Earth is stationary, and the objects in the heavens look as if they are on the celestial sphere rotating at a rate of just under 360 degrees per day (360°/d) or, equivalently, 15 degrees per hour (15°/h). The plane running through the Earth’s equator is designated the celestial equator (or equatorial plane), and the (celestial) polar axis, identical to Earth’s polar axis, is the axis of rotation of the celestial sphere around the Earth. This plane and axis extend to infinity. Similar to the fact that any location on Earth can be specified by the latitude and longitude of the location, the position of any star on the celestial sphere—the Sun in this discussion—can be determined by specifying two parameters: the right ascension and the declination. The difference is that the locations on Earth are fixed while the location of the stars change over the day and over the year as the Earth spins on its axis and takes its journey around the Sun. For the observer on Earth, the stars or Sun look like they are moving in a plane that is parallel to the equatorial plane at a rate of about 15°/h.
Z
Published in Carl W. Hall, Laws and Models, 2018
Sources: Begell, W. 1983; Gillispie, C. C. 1981; Pelletier, A. P. 1994. See also KUTTA-JOUKOWSKY ZIPF LAW OF LEAST EFFORT (1935) An empirical rule that if the words of a sample of spoken language are ranked in terms of the number of times each is used: f(r) = k(1/R) where f(r) = number of times (frequency) a word occurs of rank R R = rank position of the word k = constant As an example, the hundredth most frequent word occurs approximately 1/100th as many times as the most frequent word. Keywords: frequency, language, speech, word ZIPF, George Kingsley, 1903-1950, American psychologist Sources: Allen, T. J., 1977; Considine, D. M. 1976; Watters, C.1992; Pierce, J. R. 1961; Zusne, L. 1987. See also LOTKA; PRICE SQUARE ROOT ZODIACAL LAW The band of 12 constellations passes through the sun in the course of a year, tracing a path of a circle. The ecliptic is the circle traced out by the sun's "apparent" path over the celestial sphere in the course of a year. Keywords: celestial, constellations, ecliptic, sun Source: World Book Encyclopedia. 1990. ZONE LAW OF WEISS In crystallography, the condition that a crystal face (h k l) shall lie in the zone (U V W) as: Uh+Vk+Wl=0 Keywords: crystallography, face, zone WEISS, Pierre, 1865-1940, French physicist and mechanical engineer Sources: Ballentyne, D. W. G. and Lovett, D. R. 1972; Holmes, F.L. 1980; Thewlis, J. 19611964. See also WEISS
Modelling available solar radiation
Published in David Thorpe, Solar Energy Pocket Reference, 2018
Declination (δ) is the angle of an object in the sky with reference to the perpendicular to the celestial equator. The celestial equator is a projection from a point at the centre of the earth of its equator onto the celestial sphere. By convention, angles are positive to the north, negative to the south. The declination angle of the sun in the sky varies throughout the year due to the tilt of the earth on its axis of rotation as it circumnavigates the sun and gives us the seasons. The axial tilt is 23.45° and the declination angle varies plus or minus up to this full amount. At the equinoxes the value is 0°, at the 22 December solstice it is −23.45° and at the 22 June solstice it is 23.45°. It is given by the equation: δ=23.45°⋅sin[360/365⋅(284+N)]
Confessionalization and comets. John Bainbridge on the comet of 1618
Published in Annals of Science, 2022
The astronomical part appears primarily directed to a lay audience, although a highly educated one, not to fellow astronomers or mathematicians, as is clear from the elementary level of his explanations. In particular, there is a very long explanation of the principles of parallax measurements, including a diagram (14–19; the actual observations are described on p. 19–20). Still, Bainbridge emphasizes his mathematical proficiency. At the core of his work is a ‘celestiall Planispheare’ (2), a map of the sky depicting the comet's course. Bainbridge uses a gnomonic projection to depict the celestial sphere, which he calls a ‘new manner’ which he ‘specially invented’. (2–3, 8) Actually, Kepler had already used such a projection in his treatise on the new star of 1604, published at Prague in 1606.15 Given what we know of Bainbridge's intellectual network in London, it is hard to believe that he was not aware of that.
Geometry in Our Three-Dimensional World
Published in Technometrics, 2023
Optics is mostly regarded as a part of physics, earlier known as natural philosophy. However, given the amount of geometry in optics, it is no exaggeration to declare optics as another branch of geometry. Chapter 5 discusses more of optics than anything else. It discusses the shape of the Earth and attempts to explain the reasons why the Earth is not flat. It also talks about the formation of days and nights with a special emphasis on the celestial sphere model. Very interestingly, the chapter contains an account of a formula, involving trigonometric functions, for the length of a day. It also clarifies why there are seasons, phases of the Moon, and eclipses. A formula for the size of the Moon’s shadow is also an engaging part of the chapter.
A technique for evaluation of sky luminance distribution in tropical climate: a case study of Northeastern Thailand
Published in International Journal of Sustainable Energy, 2020
Somporn Hongkong, Jindaporn Jamradloedluk
Development of SLD modelling was generally based on sky luminance data measured by the sky scanner. SLD development without using data from the sky scanner was proposed by Soler and Robledo (Soler and Robledo 2005). Sky luminance data were measured using 35 sensors fixed on a dome to investigate only the overcast sky. One sensor was used to measure the zenith luminance, 34 sensors were positioned with their collimators pointing toward different positions on the celestial sphere. The validation results revealed that the MBE was −1.76% and RMSE was 6.2%. However, intermediate and clear sky types were not included in this study. All literature reviews indicate that the study of SLD for the tropical region in Asia is rather limited.