Celestial equator

Definition and stakes

J. A. Gillet,  The Heavens Above: A Popular Handbook of Astronomy

“ The equality of days and nights when the sun is on the celestial equator is also evident from the following considerations: one-half of the earth is in sunshine all of the time; when the sun is on the celestial equator, it is directly over the equator of the earth, and the illumination extends from pole to pole, as is evident from Figs. 70 and 71, in the former of which the sun is represented as on the eastern horizon at a place along the central line of the figure, and in the latter as on the meridian along the same line. ”
Source: Gutenberg

Gershom Bradford,  The whys and wherefores of navigation (1918)

“ Moreover, a line drawn from this intersection, or terrestrial vernal equinox, through the center of the sun and extended to the celestial sphere would strike the corresponding intersection of the ecliptic and the equinoctial or celestial equator—the celestial vernal equinox. The arrival of the earth at this position is the signal of spring for the northern hemisphere, likewise it announces the advent of autumn to our southern neighbors below the “Line.” The sun this day rises in the east (approximately) and passing through the zenith, sets in the west for those living on the equator. ”
Source: Gutenberg

George C. Comstock,  A Text-Book of Astronomy

“ In those parts of the earth near the equator—the torrid zone—there is no such marked change from cold to warm as we experience, because, as the sun never gets more than 23.5° away from the celestial equator, on every day of the year he mounts high in the tropic skies, always coming within 23.5° of the zenith, and usually closer than this, so that there is no such periodic change in the heat supply as is experienced in higher latitudes, and within the tropics the temperature is therefore both higher and more uniform than in our latitude. ”
Source: Gutenberg

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