Sūrya-Grahaṇa: Calculating Solar Eclipses

Why a solar eclipse is a local event, and the parallax correction that pins it to a place

A lunar eclipse is seen by everyone on the night side of the Earth; a solar eclipse is total only along one narrow track, partial around it, and missed entirely farther off. Learn why, and meet lambana, the parallax correction Indian astronomers built to predict exactly where and when the Moon's shadow would fall.

The Eclipse One City Saw and Another Missed

Imagine two astronomers, one at Ujjain and one far to the south, both holding the same tables, both having computed that on a certain morning the Sun and Moon would meet at a node and the Sun would be eclipsed. The morning comes. At Ujjain the Sun is bitten dark, exactly as predicted. Far to the south, the second astronomer waits, and the Sun rises whole and stays whole. Nothing happens. Same numbers, same sky, two different results.

For a lunar eclipse this never happens. When the Moon slides into the Earth's shadow, everyone on the night side of the planet sees the very same darkening at the very same instant, because the shadow really is on the Moon. But a solar eclipse is different, and understanding why is the whole art of predicting one. A solar eclipse is not something that happens to the Sun. It is a line-of-sight alignment, and where you stand decides what you see.

A Shadow With a Narrow Track

In a solar eclipse the Moon passes between us and the Sun, and its small shadow falls on the Earth. But the Moon is small and near, and its shadow touches the Earth only along a narrow track, at most a couple of hundred kilometres wide, sweeping across the globe. Stand inside the track and you see the Sun covered. Stand a few hundred kilometres to the side and you see only a partial bite; go far enough and you see nothing at all. The eclipse is real, but it is local, and to predict it for a given city you must know not just when the Sun and Moon align, but exactly where on the Earth the Moon's shadow will land.

This is what makes a solar eclipse the hardest of the classical predictions, and it turns on a subtle correction the Indian astronomers named lambana.