DETERMINATION OF THE POSITION AND VELOCITY OF THE NATURAL SATELLITE’S SHADOW ON THE ILLUMINATED PART OF THE SPHERICAL PLANET’S VISIBLE DISK

Abstract

This study introduces a simple analytical method for determination of the rectangular coordinates of the natural satellite’s (or the moon’s) shadow cast on the illuminated part of the spherical planet’s visible disk and projected onto the sky plane, as well as the rates of change of those coordinates when the shadow is moving. The analytical method’s formulae, derived in two approximations of the Earth’s and the Sun’s positions relative to the planet’s rotation axis, provide an accurate solution for each approximation at any phase angle values that enables to apply them to simulate processes associated with the satellite’s shadow passing across the illuminated part of the planet’s visible disk.