Solar and lunar eclipses
A solar eclipse happens at new moon, when the Moon passes between the Sun and the Earth and its shadow falls on us. Inside the narrow core of the shadow the Sun is completely hidden (total) or, when the Moon is too far to cover it, left as a bright ring (annular); around it, across thousands of kilometres, the Moon takes a bite out of the Sun (partial).
A lunar eclipse happens at full moon, when the Moon passes through the Earth’s shadow. It can be seen from the whole night side of the Earth at the same instant — only the local clock time differs. In a total lunar eclipse the Moon turns copper-red, lit by sunlight bent through the Earth’s atmosphere.
How the times are worked out
Solar eclipse times are computed for each place from NASA’s Besselian elements (Fred Espenak, NASA Goddard Space Flight Center) with the method of the Explanatory Supplement to the Astronomical Almanac: the contacts, the magnitude, the share of the Sun covered and the Sun’s height. Checked against NASA’s own tables, the times agree to within a few seconds.
Lunar eclipse contact times are NASA’s (Espenak and Meeus), converted to UTC with the current difference between atomic and Earth-rotation time (ΔT = 69.2 s), then to each city’s local time; whether the Moon is up comes from its position at each phase.
Watch the Sun safely
Never look at the Sun without certified eclipse glasses (ISO 12312-2) or a solar filter — not during a partial or annular eclipse, and not with sunglasses, smoked glass or an unfiltered camera, binoculars or telescope. Only during the total phase, when the Sun is completely covered, can you look without protection; put the glasses back on as soon as the first bead of sunlight returns. Lunar eclipses are safe to watch with the naked eye.