The regular rise and fall of the water level in the earth’s oceans as a result of the gravitational forces between the earth, moon, and sun. The detailed theory of tides is complex. The moon is approximately twice as effective as the sun in causing tides. In illustration (a) the resultant gravitational forces between the moon and various points on the earth (solid lines) are shown as the vector sums of the tide-generating forces (broken lines) and a constant force (dotted lines) that is the same at all points on the earth and is equal to the moon’s attraction on the earth’s centre. The resultant force when the moon is in zenith (Z in the illustration) is greater than that at nadir (N) because Z is closer to the moon than N and the force is inversely proportional to the square of the distance according to Newton’s law of gravitation. Illustration (b) shows how at full and new moon the sun and moon act together to produce the high-range spring tides, while at quarter moon the forces are at right angles to each other causing the low-range neap tides.
The use of tidal energy, estimated at some 4 × 1018 J per annum at known tidal sites, dates back to medieval tidal mills. Modern tidal power stations use specially designed turbines, operated by tidal waters, to drive generators.
Tidal forces due to Jupiter have large effects on many of its moons.