A solar eclipse occurs when the moon moves between the sun and the earth, blocking some or all of the sun's light. This can only happen during a new moon when the sun and moon are aligned in a configuration called syzygy. The extent of the eclipse can vary: in a total eclipse, the moon completely covers the sun, while in partial and annular eclipses, only part of the sun is obscured. The coverage of the sun by the moon is represented by the optical coverage parameter (C), which is the ratio of the area of the sun covered by the moon to the total area of the sun. Other important parameters include the ratio of the apparent sizes of the moon and the sun (a) and the impact parameter (p), which measures the closest distance between the centers of the moon and the sun. A total eclipse occurs when a≥1, while an annular eclipse occurs when a<1.

The progress of an eclipse is divided into four stages: first contact, second contact, third contact, and fourth contact, marking the beginning and end of the moon's coverage of the sun. The equations (1) and (3) provide formulas to calculate the coverage (C) based on the apparent separation between the centers of the sun and the moon (d) and the time (t) during the eclipse *,
(1)

where
(2)

and d is the apparent separation between the centers of the sun and the moon (in units of solar radii)
(3)
with t being the time (set to 0 for the point of maximum coverage) and T the time between first and fourth contact.

* M. Narayan, G. Rajasekaran, R. Sinha, C. P. Burgess, Solar neutrinos and the eclipse effect, Phys. Rev. D 60 (1999) 073006