# Tides and tidal forces

The Vela Supernova Remnant – expanding clouds of gas from a supernova which occurred 10,000 years ago. (Image Credit: David Malin, Royal Observatory Edinburgh/Anglo-Australian Observatory.) Tides are due to the gravitational attraction of one massive body on another. We commonly think of the tides as being a phenomenon that we see in the sea. There are other instances of the effects of tidal forces such as the drastic effect that a Black Hole has on matter in its close vicinity.

The effect of the tidal forces of a white dwarf star on its close companion are sufficient to drag matter away from the companion onto the surface of the white dwarf where is can cause a sudden, drastic increase in brightness seen as a Nova explosion. Other binary stars also show the effects of tidal forces and these are also exhibited by close pairs of galaxies where the effects of the gravitational pull are sufficient to distort the shapes of the galaxies into weird and wonderful shapes.

### The Law of Gravity

Isaac Newton showed that the pull of gravity depended on three things; the masses of the two bodies and their distance apart. He showed that the force was inversely proportional to the square of the distance. This means that if we consider the gravitational pull of the Earth on a satellite, the force will be only a quarter if we double the distance from the centre of the Earth. The Sun is far more massive than the Moon yet, because it is much further away, its gravitational pull is less than half the Moon's.

### Ocean tides

The tides which we see in the oceans are due to the pull of the Moon and the Sun. The simplest explanation is that the water on the side of the Earth closest to the Moon is pulled, by the Moon's gravitational force, more strongly than is the bulk of the Earth; whereas the water on the side furthest from the Moon is pulled less strongly than the Earth. The effect is to make bulges in the water on opposite sides of the Earth. The effect of the Sun's pull is similar and the tides that we see are the net effect of both pulls.

When the pull from the Sun adds to that of the Moon the tides are large and we call them Spring tides whereas when the pulls are at 90 degrees the tides are small and we call them Neap tides. The heights of spring tides are governed by the distance of the Moon from the Earth, being largest at Perigee (when the Moon is closest to the Earth) and smallest at Apogee (when the Moon is at its furthest).

The Moon as seen by SMART-1's at a distance of about 60,000km. © ESA/Space-X, Space Exploration Institute Because the Sun's pull is aligned with that of the Moon at New Moon and Full Moon these are the times when Spring Tides occur. The pull of the Sun is less than half that of the Moon and so the frequency of the tides is determined by the apparent passage of the Moon around the Earth which takes just over a day. We, therefore, in most places on the Earth have two tides a day with the time of each becoming later from one day to the next by just under an hour a day. (The actual period is, of course, determined by the rotation of the Earth and the orbit of the Moon.)

The height of the tide at any one place is determined by the shape of the coastline and of the nearby continental shelf. The presence of shelving land masses and bays gives much greater range to the tides than is seen in mid-ocean. A phenomenon which is generally not realised is that the air and solid landmasses also move up and down due to the tidal forces. Although the movement is much less in the land than that in the sea it can amount to a metre of vertical shift. It might be expected that the time of high tide would be when the Moon is on the meridian. This is not so. The reason is that, because of the Earth's rotation and friction, the tidal bulge gets left behind a little. The effects near complex coastlines such as in Britain are very difficult to compute.

### The Earth-Moon system

The long term effect of the tides is that energy is dissipated by friction in the oceans and the land and in the distortion of the Moon by the tidal pull of the Earth. This slows down the rotation speed of the Earth and moves the Moon further away from the Earth. The Earth loses rotational energy which is given to the Moon. Eventually the Earth's rotation rate will be slowed so that it is the same as that of the orbital period of the Moon. The Earth will then always keep the same face towards the Moon in the same way that the Moon already keeps the same face towards the Earth. After that the system will slowly lose energy so that the Moon will come closer to the Earth again.

This is, of course, a very slow effect. The present rate of change is that the Earth's rotation rate is slowing by 16 seconds every million years and the distance of the Moon is increasing by 120 cm each year.

### Satellites of other planets

NAOS-CONICA image of Io obtained on December 5 2001. Many surface features can be identified including volcanoes and lava fields. © European Southern Observatory. In the same way the the tidal forces of the Earth on the Moon have caused it to rotate in synchronism with its orbital period (it keeps the same face towards the Earth as it goes around), almost all of the satellites of the planets do the same. The exceptions are believed to be satellites which are ex-asteroids captured by the planet where the tidal forces have not yet had time to equalise the two periods. Even the planet Mercury has suffered from such tidal forces and its rotational period is two-thirds of its orbital period due to the tidal force of the Sun.

Jupiter's satellite Io has an eccentric orbit. Tidal forces from Jupiter are trying to remove this eccentricity and force the orbit to be circular but the eccentricity is caused by tidal forces from the satellite Europa. This means that Io is suffering considerable distorting forces. These generate heat inside Io which is sufficient to power the active volcanoes that were seen by the Voyager spacecraft.

### Close binary stars

It is believed that at least half the stars, which look to us to be single, are in fact two, or more, stars in binary or multiple systems. It is clear, from analogy with the Earth-Moon system that such pairs of stars will exert tidal pulls on one another. These tidal pulls become very important when we consider pairs of stars which are close together.

If one star is much bigger than the other it is possible to think of situations where the gravitational pull of the smaller star on the closest part of the big star is greater than the pull of the big star. In these circumstances the big star will lose matter towards the small star. We see this happening in many binary systems where the big star has reached the point in its evolution where it increases markedly in size. This leads to many interesting objects, the most notable being when the smaller star is a compact object.

XMM-Newton image of the supernova remnant RCW 103. The central blue dot is probably a neutron star formed when the original star exploded and designated IE161348-5055. Image: ESA/XMM-Newton/A.De Luca (INAF-IASF) Novae are stars that suddenly appear where there was apparently no star, or only a very faint star, before. We know that what has happened is that the tidal forces have stripped material from the larger star of a pair and deposited it onto a smaller white-dwarf companion. This material, when it reaches the surface of the white-dwarf, is 'burnt up' in a very rapid and explosive thermonuclear reaction. This raises the brightness of the white-dwarf to be one of the brightest stars in the whole galaxy, whereas before the explosion it was one of the faintest.

Another example of this phenomenon is where the small companion is a neutron star or a black-hole. Then the matter transferred from the larger star gives up so much energy that it emits intense X-radiation which can be seen by X-ray satellites as an x-ray transient. Such sources are the best way in which we can 'see' evidence for black holes.