The solar eclipse occurs at short time before the crescent birth moment when the moon near any one of moon orbit nodes It is important to determine the synchronic month which is used to find Higree date. The 'rules' of eclipses are:
Y= ± 0.997 of Earth radius , the solar eclipse is central and 0.997 < |Y| < 1.026 the umbra cone touch the surface of the Earth, where Y is the least distance from the axis of the moon's shadow to the center of the Earth in units of the equatorial radius of the Earth.
A new model have been designed, depend on the horizontal coordinates of the sun, moon, the distances Earth-Moon (rm), Earth-sun (rs) and |Y| to determine the date and times of total solar eclipse and the geographical coordinates of spot shadow as well as the shadow diameter and the variations with time.
The results are compared with Almanac and others programs are gets a good agreements and the results show the area of eclipse shadow inversely proportional with rm /rs .The Higree month which must be begin after the solar eclipse and the relation were discussed hear.
