What is true of two solar eclipses separated by one saros cycle?

Answer: two solar eclipses separated by one Saros cycle will have the same geometric characteristics (they will both be total, or partial or annular).

A Saros is a period of time of about 18 years 11 days and 8 hours and represents the time needed for the system composed by Moon, Earth, and Sun to return to its initial position.

Indeed, this is due to a natural harmony of the Moon’s motion: it takes 29.53 days to complete one orbit around Earth (Synodic Month), it takes 27.21 days to pass from the same node of its orbit (Draconic Month) and it takes 27.55 days to go from perigee to perigee (Anomalistic Month); the composition of these three motions gives one Saros of around 6585.3 days, composed by 223 Synodic Months, 239 Anomalistic Months and 242 Draconic Months (with a precision of few hours).

It has been observed that after one Saros cycle Moon, Earth and Sun are in the same initial position, therefore an eclipse occurring on day 1 of two consecutive Soros cycles would have the same geometric characteristics, which means that one Saros can be considered the periodicity of solar and lunar eclipses.

Due to the fact that a Saros is not composed by a whole number of days (we have a remainder of 8 hours), the two eclipses won’t be visible from the same location on Earth due to the rotation around its axis. It takes about 3 Soros for this to happen.