The astronomic tide

This website shows the water level at each station due to the astronomic tide.

The astronomic tide is the water level change caused by the motion of the moon and sun, relative to the earth. The gravitational attraction of the moon and sun acts on the world's oceans. These astronomic motions are predictable, thus the resulting tides are predictable.

Gravity

The earth orbits the sun, pulled inward by the sun's gravitational attraction. The moon orbits the earth, pulled inward by the earth's gravitational attraction. The earth, moon and sun are each surrounded by the vacuum of empty space. Gravity accelerates them, and the force is balanced by their inertia. Nothing else connects them, nothing else moves them.

Gravity depends on mass and distance. A more massive body exerts a stronger gravitational attraction. When two bodies are closer, the gravitational force drawing them together is stronger.

The sun

The earth accelerates continuously under the influence of the sun's gravity. The earth has momentum at right-angles to the sun, so the acceleration towards the sun pulls the earth in a curve, forming an orbit.

The earth accelerates towards the sun, nothing constrains it, the earth is free-falling in vacuum. An observer on earth does not feel any of the sun's gravity; to be precise, this is true for an observer at the centre of the earth.

Note that much of what we've said about the sun applies also to the moon, but first we consider the effect of the sun.

The sun from the earth's surface

An observer on the surface of earth experiences a residual of the sun's gravitational force, only a small fraction of the total.

Imagine noon in the tropics, the sun is overhead. The sun is closer to you than it is to the centre of the earth. Thus the gravitational force is stronger. Only by a small fraction, not perceptible to human senses, but measurable with a sufficiently sensitive instrument.

At midnight the sun is further from you than it is from the centre of the earth. Thus the gravitational force is weaker. The sun is beneath your feet, so a weaker attraction towards the sun means a force upwards, outwards from the earth.

Now imagine mid-morning or afternoon, the sun is in the sky, not directly overhead. The sun's gravitational force has a horizontal component as well as a vertical component. The sun's residual gravitational force is present at other times of day, with both a horizontal and vertical component, depending on the angle of the sun above or below the horizon.

A point on the earth's surface experiences this residual; the difference in gravitational force due to the greater or lesser distance from the sun to that point, compared to the distance from the sun to the centre of the earth.

Free fall

Because the earth is in free-fall, we don't feel the tug of the sun's gravity. The total pull of the sun upon the earth is tremendous. Yet we feel nothing of this, or next to nothing.

If gravitational force is resisted, an object experiences the gravitational attraction as a force, equivalent to the force of acceleration. However if the gravitational force is not resisted, the object simply accelerates in response to the gravity, and zero force is experienced.

This is characteristic of free-fall in a vacuum. The gravitational acceleration caused by the sun exactly cancels out the earth's inertial acceleration. Another way to think about it; the earth in it's orbit has angular momentum, so rather than inertial acceleration we can call it centrifugal force, the same thing.

Imagine you are an astronaut in low-earth orbit. Although the earth's gravitational field is present and only a little reduced compared to the surface, you don't feel it, because you free-fall through the vacuum of space. You accelerate in response to the earth's gravitational field, and orbit the earth, but experience no gravity; weightlessness, zero Gs.

If instead you built a tower to the same altitude—about 500km tall—and stood on it, you would be surrounded by the same vacuum of space, but you would feel the earth's gravity pressing up on your feet.

Barycentre

We talked about the earth orbiting the sun. It is more accurate to say: both the earth and the sun orbit the barycentre of the solar system, i.e. the centre of mass of the sun and all the planets combined.

When considering the earth's orbit, it doesn't help us much to make this distinction, and say the earth orbits the barycentre of the solar system, rather than saying the earth orbits the sun. Because the sun is so massive, it makes little difference.

It is, however, helpful to think about the barycentre when considering the moon and the earth.

The moon

We can say the moon orbits the earth, pulled inwards by the earth's gravity. But the moon actually orbits a barycentre, the common centre of mass of the earth and moon combined. The earth is also pulled by the moon's gravity, and orbits this barycentre.

The earth accelerates continuously under the influence of the moon's gravity. The earth has momentum at right-angles to the barycentre (as does the moon) so the acceleration towards the moon pulls the earth in a curve, forming an orbit around the barycentre.

The earth accelerates towards this barycentre, nothing constrains it, the earth is free-falling in a vacuum. The gravitational acceleration caused by the moon exactly cancels out the earth's inertial acceleration. An observer on earth does not feel any of the moon's gravity; to be precise, this is true for an observer at the centre of the earth.

The moon from the earth's surface

From the surface of the earth an observer experiences a fraction of the moon's gravitational attraction. The effect is much the same as for the sun, though the moon's force is comparatively stronger.

When the moon is at it's highest in the sky, the moon is closer to you than it is to the centre of the earth, so the gravitational attraction is stronger. Much as for the sun, the angle of the moon above or below the horizon corresponds to the distance from the moon to you, compared to the distance from the moon to the centre of the earth.

Residual gravity

An observer on the surface of the earth experiences a residual force: the difference between the gravitational force of the moon and sun at their location, and the gravitational force of the moon and sun acting on the earth as a whole.

This difference exists because gravitational force is a function of distance, stronger when the distance between masses is shorter.

Earth's gravity

At the surface of the earth most of the gravitation force we experience is due to the earth itself. The earth's gravity is roughly a million times stronger than the residual force caused by the moon and sun.

The ground under our feet resists the downward pull of earth's gravity. We don't accelerate downward. We remain stationary on the surface, and experience gravity as a force trying to accelerate us downward.

Earth's gravity varies from place to place, a variation too small for our human senses to detect, yet much larger than the residual forces due to the moon and sun. The earth's gravity doesn't change over time—assuming we stay at one place—while the forces due to the moon and sun do change.

Total gravity

A human observer perceives the total gravitational force, but our senses cannot distinguish the tiny residual effect of the moon and sun. We can, though, make a machine that is sensitive enough. This instrument is called a gravimeter, an accelerometer built with sufficient sensitivity.

With one of these instruments we can measure total gravity, subtract earth's unchanging gravity, and see the gravitational effect of the moon and sun, changing over time, as we might expect, following the movement of the sun and moon relative to our location.

The gravitational force is a vector; it has a magnitude and a direction. The earth's gravity always pulls downward, but the forces due to the moon and sun have both a horizontal and vertical component.

Tidal flows

The world's oceans are an exquisitely sensitive natural instrument for detecting small changes in gravitational attraction. Gravity acts on water, as it does on everything else on the surface of the earth. Water contained in a small vessel can't move far, but water in the oceans is free to move over great distances.

We normally define up and down by the direction of gravity. Imagine the gravitational field is fixed and the surface of the earth is tilting. Ocean water flows horizontally, in response to the tilt. The motion is faster in deep seas, slower in the shallows. The sea-bed shapes and modulates the flow of water. Coastlines obstruct and reflect the flow.

The water does not move instantly. Peaks or troughs in tide height occur some time after the moon or sun passes overhead. The timing and height of the tides at any particular location depends on marine topography; the shape of the coast, and the profile of the sea-bed, at both small and large scale.

Tide model

The tidal model used by this website does not directly model marine topography, or it's effect on tidal flows. Rather, this model requires a series of historic observations of water levels at each location.

We do not interpolate the water levels for any location, based on levels at nearby stations. In general this would not be possible without modelling the marine topography and water flow. Two nearby tide stations may have substantially different tides, if the water-ways between them are constricted, or the water is shallow.

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tides last updated 2025-01-09 visit oceantide.io