A closed form equation of the time component for the tilt of the earth's axis

摘要

A closed form equation for predicting the Equation of Time component due to the tilt of the earth's axis relative to the ecliptic plane based on geometrical considerations of the earth and sun is presented. The prediction agrees closely with a published model based on Newton's and Kepler's equations. The standard deviation between the published and current model is 9.02 s with a maximum absolute time difference of 12.9 s. The eccentricity of the earth's orbit affects the tilt component of the Equation of Time due to the varying speed of angular rotation of the earth around the sun. The maximum effect of the eccentricity of the earth's orbit on the tilt component of the Equation of Time is 0.11 s.