Fig. 3

Overlapping area of the Sun occulted by the Earth. a Shows the case where the circle and ellipse intersect, and the center of the solar disk is outside the ellipse; b shows the case where the circle intersects the ellipse, but the center of the circle is inside ellipse; c shows the case where the circle and hyperbola intersect, and the center of the circle is inside of the circle; d shows the case where the circle and the hyperbola intersect, but the center of the circle is inside of the overlapping region. In the figure, P1 and P2 are the intersection points between the circle and the conical curve, Pe and Ps is the projection point of the Earth’s center and the Sun’s center, \({A}_{1}\) and \({A}_{2}\) are the area formed by the intersection points and the conical curve