Spatial and temporal patterns of solar eclipses by Phobos on Mars

The spatial and temporal patterns associated with motion of the shadow of Phobos across the surface of Mars are quite different than those associated with solar eclipses on Earth. We present a simple analysis of variations in the position, velocity, size, and shape of the shadow. Simple expressions give reasonably accurate depictions of the shadow motion, which mainly consists of a subdiurnal longitude cycle and an annual latitude cycle. Over most of each year, there are an average of 3.22 shadow transits per day. The duration of the shadow transit depends on latitude. It is maximum at the equator and is then 11.8% of the orbital synodic period. As the subsolar point moves north, the shadow moves south, and vice versa. There is a narrow band, centered on the equator of Mars, within which every point is eclipsed at least once during each semiannual eclipse season. Outside that band, the density of coverage decreases slowly with increasing distance from the equator, until the limiting latitudes are reached. During epochs, like the present, when the obliquity of Mars is in excess of 21.2°, there are portions of each year during which no eclipses occur. As the obliquity increases beyond that transition value, the durations of the eclipse seasons decrease. The minimum possible eclipse season duration, expressed as a fraction of the Mars year, is the same as the maximum shadow transit duration, expressed as a fraction of the Phobos synodic period, since both ratios depend on the same geometry, which is essentially just the radius of the orbit of Phobos, compared to the radius of Mars.