Tides and the moon

Although the relationship between the moon and the ocean tides was suspected by ancient mariners, the mechanism remained obscure until Newton's Principia provided a quantitative account. Gravity, Newton showed, acts not only on the body of the Earth as a whole but differentially across its volume. The waters on the side of the Earth facing the moon are pulled slightly more strongly than the solid Earth beneath them; the waters on the opposite side are pulled slightly less. The result is two bulges of water, one on each side of the planet, with the Earth rotating beneath them. Any given coastline therefore passes through two high tides and two low tides each day. The sun produces a similar but weaker effect; when the sun and moon are aligned, near the new and full moon, the tides are amplified — these are the spring tides. When the sun and moon are at right angles relative to Earth, the effects partially cancel, producing the smaller neap tides. The explanation is elegant, but the actual heights of tides at any given port depend on local geometry: the shape of the seabed, the orientation of the coastline, and the resonant frequencies of bays and estuaries can amplify a modest astronomical tide into the dramatic surges seen, for example, in the Bay of Fundy.