August 21st 2017, the effulgent glares of the sun are quelled by the shadows of the Moon into a spectacular phenomenon that unites the entire of North America. The sun’s much fainter corona are projected into prominent display and the sky is gradually darkened into an unearthly hue bedecked with bright stars and planets. The clockwork of the universe finds the Earth, Moon, and Sun converging into a synthesis of celestial harmony.

But, this impression of heavenly consonance is all but an accident of nature, a consequence of the correlations which the Earth and the Sun seem to coincidentally but conveniently exhibit. In particular, as the Moon orbits the Earth every 29.5 days, it catches up with the Sun and a ‘New Moon’ occurs. Lunar phases are named with respect to the degree by which the Moon’s disc appears to be illuminated by the Sun. At a New Moon, the hemisphere facing the Earth is unilluminated, making the Moon non-visible.  At this point, the Moon only becomes visible during a solar eclipse, when it blocks out the Sun and is positioned exactly between the Sun and the Earth.

The orbit of the Moon, however, is tipped over 5 % to the ecliptic, the apparent path of the Sun on the celestial sphere. This explains why we do not experience a solar eclipse every New Moon, as one would expect. Because of the inclination in the lunar orbital plane and the fact that this inclination is larger than the apparent diameters of the Moon and the Sun, the Moon’s shadow is regularly too far north or too far south such that it misses the Earth.  It is only when the Moon approaches the ecliptic at one of its two nodes, where a junction between the plane of the ecliptic and the plane of the Moon’s orbit occurs, does a solar eclipse indeed happen. As the Moon orbits around in its tilted plane, it eventually intersects a node going southwards. Two weeks later, it intersects the other node going northwards. Similarly, the Sun moving on its apparent path along the plane of the ecliptic also intersects one of those nodes at one point, followed by the other node six months later. A solar eclipse occurs if the Sun and the Moon happen to intersect the same node at the same time.

In the period of time between two successive New Moons, the Sun moves (29.5 days * 360 degrees / 346.62 days (eclipse year)) or 30.67 degrees across the sky. Such a value is less than the minimum value of the ecliptic limit, 30.70 degrees, which represents the greatest distance of the moon at the node where an eclipse must occur. With the Sun moving along the ecliptic one degree per day, this would give us an eclipse season of 31 days, which would be impossible for a New Moon to miss in its 29.5 day synodic period. As the sun passes through the ecliptic limit, it, therefore, has to be overtaken by a New Moon. This leads to the conclusion that for a solar eclipse to occur, two requirements must be met: the Moon has to be at a New Moon and the moon must lie near its node.

The precession of the lunar nodes, however, presents an extra complexity when it comes to predicting solar eclipses. Owing to the differential gravitational pull exerted by the Sun on the sides of the Moon’s orbit, the nodes precess. As they do, they rotate and the orientation of the lunar orbital plane slightly changes direction over the course of 18.6 years, at which point the nodes return to their original position once again. This allows a certain periodicity of eclipses, in that a geometrical configuration of the Sun, the Moon, and the Earth repeats every 18.031 years and an eclipse occurring at any one time will repeat itself 18.031 years later.  Such a periodicity of 6585.3211 days is more commonly known as the Saros cycle and it is the time it takes for four lunar periods to coincide once again, namely the sidereal period (the time it takes for the Moon to complete one orbital period with respect to the stars), the synodic period (the time between two successive New Moons), the draconitic period (the time between two successive lunar intersections of the ascending node), and finally the anomalistic period (the time between two successive perigees). This cycle is not exact, however. Indeed, due to the lunar precession period of 18.6 years which is not equal to the Saros cycle of 18.931 years, the Moon changes position with respect to the background of fixed stars at each Saros. In addition, each Saros is not an integer number of days but also includes a fraction of about 1/3 of a day. This leads to each successive eclipse occurring 8 hours later, thereby shifting the eclipse track 120° to the west across the surface of the Earth. This shift could be harmonised by waiting three Saros cycles, at which point the eclipse returns back to the same eastwards/westwards location and could be observed in exactly the same part of the world.

Because of the extraordinary coincidence that the Moon is 400 times smaller than the Sun but also 400 times closer, a solar eclipse allows the Moon to block out the Sun almost totally. The Moon’s shadow, cast onto the Earth, has two parts, the umbra and the penumbra. An observer standing in the umbra would see a total solar eclipse, whereas, an individual standing in the penumbra would see a partial solar eclipse. August 2017’s eclipse boasted an umbra covering an area of 115 kilometres, shading the entire horizon into a reddish awe of cosmic wonder.

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