Tides

Most of us who have ever visited the coast, as well as a great many who have not, will be aware of the phenomenon of tides. At certain times the tide is said to be in, or high, and the beach will likely be covered with water. At other times the tide is said to be out, or low, and the water has receded, sometimes by a great distance, leaving the beach uncovered where only a few hours previously it was covered. Generally, the time between one high tide and the next is somewhat more than twelve hours, so that there are two high tides and two low tides each day, with the times of high tide getting almost an hour later each day. If you got to a particular beach at a particular time one day, and the tide is high; then it will probably be low the same time seven days later, then high at that time after a further seven days, and so on.

The tides are caused by the moon, and to a lesser extent, the sun. The tidal effect results from the law of gravity which states that the gravitational force between two bodies is proportional to the product of their masses, and inversly proportional to the square of the distance between them. Thus the part of the earth which has the moon directly overhead is attracted to the moon with more force than the rest of the earth, resulting in deformation towards the moon. Similarly, the part of the earth exactly opposite, will be attracted to the moon with less force than the rest of the earth, resulting in that part tending to be deformed away from the moon. Thus there is a tendency for a body such as the earth, to become elongated in the presence of another gravitational body. See Figure 1 (which is not to scale - and the tidal effect is shown greatly exaggerated)

Figure 1

The above diagram assumes the earth to be a solid body which is uniform, and would be a sphere if it wasn't for the tidal distortion. As the earth rotates, the distortion alters so that the earth is always elongated towards the moon.

In actual fact, the solid body of the earth would take quite a long time to adjust its shape to an equilibrium position; and as the earth is rotating relative to the position of the moon, the distortion of the solid earth is much less than it would be if the moon were always overhead at the same place - in which case the earth would have had time to adjust to its equilibrium.

Water, however, can flow to a new position much more easily than the solid body of the earth. This means that if the solid body of the earth was a true sphere without significant distortion, then the water covering it would still be distorted in the direction of the moon. See Figure 2 (again much exaggerated and not to scale)

Figure 2

As the diagram shows, the water will be deepest on the part of the earth which is directly under the moon, and also at the opposite place on the earth, and the tides at these places will be high. The water will be shallowest at points at right angles to these, where the tide will be low.

This applies if the solid part of the earth is a perfect sphere, uniformly covered with water, with no land masses to affect the flow of the water from one place to another. Alternatively, if the earth was a uniform sphere with no continents, but only a few very small islands scattered at random around the earth, then each of these islands (except those at high lattitudes) would experience a high tide when the moon was high in the sky, then another just over twelve hours later (12 hours 25 minutes). The tide would be low half way between high tides.

As it is, however, there are large, irregular continents and landmasses; and the depth of the ocean is not uniform. Thus water cannot move as simply as it would without the landmasses and shallow seas. The flow of the water is quite complex, as it flows along various channels, of varying sizes and depths. Thus, at many coasts, the times of high and low tide are not what one would expect from the times of the transit of the moon. That is why, if one looks at the tide tables for British coasts, one will see that the times of high tide at, for example, Morecambe, on the west coast of England, are totally different from the times of high tide at Whitby, which is on the east coast.

The picture is further complicated by the fact that the earth's equator is inclined by 23 1/2 degrees from the plane of the ecliptic. The moon likewise goes round the earth in an orbit inclined to the equator. When the moon and sun are significantly north or south of the equator, the two high tides each day can be of unequal magnitude, or the time between them can be uneven. In certain situations, particularly at high latitudes, high tides occur just once per day rather than twice. The diurnal tide may also dominate over the semi-diurnal component in certain semi-enclosed bodies of water, e.g. the Gulf of Mexico - and Karumba, in the Gulf of Carpentaria, Australia - where, due to the influence of natural resonance periods in the particular bodies of water concerned, there is a single high and a single low tide each day.

Because of the effects of the land masses, the heights of tides vary greatly depending where we are on the earth. In parts of the Mediteranian, for example, the tides are only slight. The Bay of Fundy, Canada, is famous for its extremely high tidal range. There are certain places in the South Pacific where the tide cycle follows the solar day rather than the passage of the moon. High and low tides at such places occur about the same time each day. (Although the magnitude of the tides may vary with the lunar cycle.)

Thus, if one wants to know the tide times for some coast one is considering visiting, one needs to see tide tables for that coast, or at least, one very close to it. One cannot just check details of the moon, and calculate the tide from that alone.

Spring Tides and Neap Tides

High and low tides will not always be the same, at any particular port. As mentioned above, the tides are caused predominently by the moon, but the sun plays a significant part in addition. When the earth, sun and moon are all in line with each other, as they are at New Moon and Full Moon, the effects of the sun and moon reinforce each other, and the tidal effect is great, thus producing high tides which are very high, and low tides which are very low. When the sun and moon are at right angles to each other as seen from the earth, as at First Quarter and Last Quarter, then the solar and lunar tide oppose each other, and the tides are much less pronounced. In this latter case, the high tide is only moderately higher than the low tide. (As stated above, the lunar tide is stronger than the solar one.)

Tidal Friction

The friction due to the tidal motion of the water on the earth, and also to some extent, the repeated deformation of the solid body of the earth, results in gradual slowing down of the earth's rotation. At the same time, the moon's orbit is very gradually increasing in size.

Tides on Other Bodies

The Moon has no oceans or similar bodies of liquid on its surface. However, the tide brought about by the gravity of the earth (which is 81 times as massive as the moon) has distorted the solid body of the moon. Friction due to the powerful deformation of different parts of the moon as the moon possibly once rotated in its early youth in the geologically far distant past, has slowed the moon's rotation down so that it's period of rotation is the same as the time it takes to move round the earth. Thus the moon keeps the same face to the earth. One side of the moon can never be seen from earth, and nothing was known about it till spacecraft went behind the moon and took photographs of the hidden side (in 1959). For some reason, maria (vast lava plains) are much less prominent on the far side of the moon, than they are on the side facing the earth. Since the moon takes a month to rotate on its axis, an observer on the moon would experience an extremely long period of daylight, followed by an equally long night. Also, if the observer was on the side of the moon facing the earth, the earth would always be at a fixed point in the lunar sky (except for slight wobbling too and fro by a few degrees east and west, and north and south, due to a phenomenon known as libration). An observer on the far side would never see the earth at all!

Many of the moons of other planets, likewise keep the same face towards their primary.

The planet Mercury, much closer to the sun than we are, has had its rotation slowed by the solar tides. At one time it was believed that Mercury kept the same face to the sun, just as the moon does to the earth. If this was the case, one part of Mercury would be in permanent sunlight, with no night, and the opposite side would be in permanent night. In the 1960s however, astronomers found that this is not the case. Mercury's period of rotation on its axis is exactly 2/3 the time it takes to go round the sun. A year on Mercury is 88 of our days, a siderial day (time between successive risings of stars) is rather less than 59 of our days, and a solar day (time between successive corresponding risings of the sun) 176 earth days, or exactly two of Mercury's years. Mercury's distance from the sun varies considerably during the course of its year, and, since the magnitude of the tidal deformation is roughly proportional to the inverse cube of its distance, the force of the solar tides varies a lot. Mercury's rotation and orbital periods are locked into a 2-to-3 resonance, the planet having a permanent deformation which always lines up with the sun at perihelion, when the tidal force is greatest.

Venus rotates very slowly, and its rotation is unusual in being in the opposite direction to the direction of its motion round the sun. On Venus a year is 225 earth days, a siderial day 243 earth days, and a solar day 117 earth days.

In February 2012, the European Space Agency reported a discovery by its Venus Express spacecraft, that Venus appears to rotate a little slower than it did in the 1990s when NASA's Magellan orbiter was in operation around the planet. The planet's siderial day seems currently to be about 6.5 minutes longer than Magellan's measured value. ( http://www.esa.int/Our_Activities/Space_Science/Venus_Express/Could_Venus_be_shifting_gear   -  accessed 27 May 2014)

Jupiter's satellite Io gets much of it's internal heat from immense tidal stresses it experiences as it orbits the planet in a slightly-elliptical orbit. It is one of the most volcanically-active bodies in the Solar System.

Generally the tidal stresses would tend to circularise the orbit with time. However, Io is involved in a triple orbital resonance with Europa and Ganymede, which helps to maintain their slight orbital eccentricities despite tidal friction. Ultimately, the three satellites are between them gradually taking away energy from the giant planet's fast rotation.

 Page composed in 2004 by Kieron Taylor Minor modifications 28 July 2005 Some significant updates and corrections 31 May 2014 (including the removal of some dead external links)