Tides Simulator
The Moon and Sun pull on the Earth’s oceans, creating tidal bulges on opposite sides of the planet. As the Earth rotates, a point on the coast sweeps through these bulges, creating the rise and fall of tides. When the Moon and Sun align, spring tides surge; when they’re at right angles, neap tides barely move.
Spring tides
When the Moon and Sun are aligned (new moon or full moon), their tidal forces add together, producing the largest tidal range — spring tides. The name has nothing to do with the season; it comes from the Old English springan, to surge.
When the Moon and Sun are at right angles (first or third quarter), their forces partially cancel, producing the smallest tidal range — neap tides. The Moon’s tidal effect is about 2.2 times stronger than the Sun’s, because tidal force depends on the cube of distance.
How tides work
Tidal forces arise from the difference in gravitational pull across the diameter of the Earth. The Moon pulls harder on the near side than the center, and harder on the center than the far side. The result is a stretching force that creates two bulges: one facing the Moon and one opposite.
The tidal force
The tidal acceleration at a point on Earth’s surface is the difference between the gravitational
acceleration there and at the center: a_tidal ≈ 2GMr/d³, where G is the gravitational
constant, M is the mass of the attracting body, r is Earth’s radius, and d is the distance to the body.
The d³ dependence explains why the Moon (closer) dominates the Sun (more massive but far away).
Spring and neap tides
The Moon completes one orbit in about 29.5 days. At new moon and full moon, the Sun and Moon align (syzygy), and their tidal bulges reinforce each other — spring tides. At first and third quarter, they’re perpendicular (quadrature), and the bulges partially cancel — neap tides. The spring-to-neap ratio is about (1 + 0.46)/(1 − 0.46) ≈ 2.7.
Why two bulges?
The near-side bulge is intuitive: the Moon pulls water toward it. The far-side bulge is less obvious. In the Earth-Moon system’s rotating reference frame, the centrifugal force at the far side exceeds the Moon’s gravitational pull, pushing water outward. Equivalently, in an inertial frame, the Earth’s center accelerates toward the Moon more than the far-side water does, leaving the water behind.