Always introduce the celestial sphere with a companion Earth-Sun figure

Abstract

Contemporary authors of basic astronomy textbooks introduce the celestial sphere in less than ideal ways. It is suggested that an early discussion of the celestial sphere should make reference to a companion figure showing the Earth-Sun relation with explicit attention to the equinoxes, solstices, and other major features.

Warm wall in autumn: how to use the solar irradiation in full? *

“…To clarify the geometry of the Sun's and Earth's relative motion, we shall additionally use the ecliptic and equatorial reference frames with their origins located in the center of the Earth (see figures 2(b) and (c)), as is shown in references [3,4,[14][15][16][17]. First, let us express the declination δ in terms of the ecliptic longitude λ of the Sun and the obliquity ε.…”

“…It should be noted that throughout the paper we consider the Earth as a sphere, since the corresponding flattening ratio is ≈ 1:298. The simple scheme (14) was used earlier [3,4] to calculate insolation of horizontal surfaces for arbitrary latitudes, taking into account the atmospheric attenuation of the Sun irradiation. Thus, one of the main factors, which determines the climate per se was analyzed.…”

“…For example, figure 2(a) represents, for the latitude of Dresden (Germany), two extreme Sun paths corresponding to the days of winter solstice (thick solid arc) and summer solstice (dotted arc) together with the Sun path on days of vernal and autumnal equinoxes (thin solid arc). It is easy to see from equation (14), that the Sun possesses its highest daily position and the highest altitude at solar noon instant (t = 720), which is equal to (90°− j) + ε and (90°− j) − ε for the days of summer and winter solstice, respectively (figures 3(a), (b)). Thus, the sunlight at the midday of summer solstice strikes the horizontal plane at a large angle of (90°− j) + ε, whereas it falls onto the south-faced vertical plane with a smaller angle of (j − ε) (figure 3(c)).…”

“…The first vector corresponds to the solar vector described here by equation ( 14) and the second one describes the normal to the selected plane. Particularly, for the south-faced vertical plane, it has the coordinates of (0, 1, 0) in the selected coordinate system and therefore the value of sinγ can be easily found as y in equation (14).…”

“…The Sun 'orbits' the Earth once per year in the plane of the ecliptic along the orange circle. (c) The Northern hemisphere and rotating horizon (x, y, z) reference frame described by set of equations(14). The horizontal dotted circle shown here describes the diurnal motion of the point on the Earth's surface at the latitude of Dresden (j = 51°03′) (the hour angle ω varies from 0°to 360°).…”