Solar angles revisited using a general vector approach

摘要

Rather than follow the standard technique using direction cosines or major axes vectors to define the angles of the sun, we develop the necessary formulae from a 3-tuple vector based analysis. The direction of the sun with respect to a Cartesian coordinate system is defined as a unit vector, as is the orthogonal to a surface intended to accept solar radiation. The vector formulation is powerful and universal. More importantly, the diagrams used to describe the relative motion of the sun with respect to the Earth are quite simple, leading to less confusion when translating the geometry to algebra. An interesting result on the change in solar angle with time follows.