Sun Declination and Distribution of Natural Beam Irradiance on Earth

The daily path of the Sun across longitude yields night and day, but the Sun also travels across latitude on a belt 47° wide. The solar meridian declination explains the latitudinal budget of natural beam irradiance (NBI), which is defined as the irradiance delivered to the Earth’s surface as a normal projection from the Sun. Data for the Sun meridian declination were obtained from the Spencer model, known as the geometric model. The distribution of NBI was weighed for the latitudinal belt between the Tropics of Cancer and Capricorn. The variation in the parameters of solar meridian declination were found to be analogous to that of pendular motion. The joint distributions of the solar meridian declination against its own velocity, or that of the velocity against the acceleration of solar meridian declination, displayed circular functions. The NBI budget that a particular latitude gathers, fluctuates in inverse proportion to the velocity of solar meridian declination, yielding 18 sun-paths per degree for latitudes above 20°, or 6 sun-paths per degree of latitude for latitudes under 20°. At an average Sun–Earth distance of 1 AU, all sites of the planet, whose latitude coincides, whether within or between hemispheres, accumulate an equivalent budget of NBI.