Prediction of the eclipses by the moon (moon solar eclipses) occurring on the geostationary orbit ring

It is necessary to predict moon solar eclipses on GEO-stationed communications satellites in order to select their orbits so their functions will not be necessary when the eclipse occurs. Solar orbital elements are calculated in terms of Newcomb's mean orbital elements (NOE), and the moon's orbital elements are treated as NOEs plus Brownian motion. Perturbation terms are truncated on the 27th order of the true anomaly, the 14th order for the ecliptic latitude, and the 27th order on the geocentric distance. A Besselian coordinate system is devised to obtain the position vector of the sun, moon, and satellite. A total of 55 eclipses are predicted between 1981-1990, and the duration of each is specified. It is shown that a moon solar eclipse can occur twice a day and last for more than 2 hr.