Tidal Forces

Introduction

We have all heard of tides, especially those who love sea-based activities like surfing, sailing, scuba-diving, or just regular swimming. We know of high and low tides, and perhaps have even heard of neap and spring tides (if not I will explain them later). But how many of us have ever stopped to wonder why these tides, or variation in the sea level, occur? Most of us know that there is some relationship with the moon. Does the full moon cause a high tide? If so, why are there two high tides and two low tides in 24 hours? Or what exactly does the moon do that creates the tides? And what magical force does it use to move the waters?

 

The answers to these questions are related to what is known as tidal forces. In this article, I will introduce some concepts of tidal forces, and illustrate how these forces work. They work not only on the oceans of our planet Earth, but also on other planets and objects in the Solar System. This force can and will affect our planet in some pretty interesting, if not downright scary ways, and possibly our lives somehow!

What is Tidal Force?

We know that “tide” means the variation of the sea level. It is measured at the shoreline or from a certain point above the sea floor. Typically, the ocean tides are about 1 metre in the open sea. However, what is not so commonly known is that “tide” also means the variation of the land level as well. The land does vary, but much less than the sea – its tide is about 30 centimetres. The difference in land tides when compared with ocean tides is because solids are just not as deformable as liquids. (Pogge, 2007 web)

 

According to Morrison and Owen [1996], a “tide” is “a distortion in the shape of one body induced by the gravitational pull of another nearby object". There are several interesting words worth pointing out in this definition:

 

 

Tidal force then is basically the force that creates the tide. It is the force that distorts a body. It is a force that is the result of gravity from a nearby object (but it is not the same as the gravitational force from that object). Whether tidal forces result in deformations depend on several factors:

 

 

How does tidal force distort a body? Gravitational force is not constant but varies over different parts of a body. It may be a small variation, but is more significant when the body is dimensionally large. Take the Earth and the Moon as an example. The Earth is sufficiently large that the point on the Earth closest to the Moon “feels” a larger force due to gravitational attraction than the point furthest away. So the force varies at each and every point on the Earth. Tidal forces are theoretically present in all bodies, large or small, as long as the body is under the influence of a gravity field that is varying.

 

The actual concepts and calculation of tidal forces is more complicated than one may imagine initially. It is complicated by dynamics in the system, for example, where the Earth and the Moon are orbiting each other. There are many good resources available on the internet that go into the physics and mathematics involved, but an excellent mathematical explanation of tides is given by Paolo Sirtoli (web 2005), in his web resource entitled “Tides and centrifugal force”. His calculations show that the tidal forces acting on the Earth are as depicted in Figure 1 with the moon off to the right.

 

Tidal Forces at work

Here are some examples of tidal forces at work in our Solar System:

Moon’s effect on Earth

When compared to the other planets in the Solar System, the Earth is very unique. There are vast watery oceans on Earth whereas none exist on the other planets. The sea is where the tides are most noticeable. Notice that in Figure 1, there are lines of forces pointing to the right and to the left. This implies that there are 2 tidal bulges at any moment – directly facing the moon, and opposite the moon. Likewise, it also shows where the low points will be. (Sirtoli 2005)

 

The bulges are actually not very much – only one metre in the open seas. But a one metre change in a very large sea results is a huge volume of water. The effect of this movement of water can be very significant at the coasts due to the effect of water having to navigate continents, the sea bed, and other coastline geometries like bays and estuaries.

Earth’s effect on the Moon

Considering the Moon, it too is likewise under the influence of the Earth’s gravity field. As the Earth is much more massive than the Moon, the Tidal Forces are about 20 times stronger than the Moon’s effect on the Earth. But the moon is dimensionally smaller, and is also made of solid material. As such, the Moon has a small tidal bulge due to the tidal forces, and this bulge is roughly aligned towards the Earth.

Sun’s effect on the Earth

The Sun, though it is much further away than the moon, is also more massive. The tidal forces it creates in the Earth are about half that of the Moon’s. During the high tides that the Moon creates, if the Sun also happens to be in the same Earth-Moon line (i.e. it is a new moon or a full moon), then the Sun’s tidal forces will be in addition to the Moon’s, and create higher than normal tides called Spring tides. On the other hand, if the Sun is perpendicular to the Earth-Moon line, the tides are lower than normal, and are called Neap tides. These abnormally high or low tides can affect human lives, e.g. flooding in low lying regions.

Text Box: Figure 2 : Comet Shoemaker-Levy 9 Credit H. Weaver (JHU), T. Smith (STScI), NASA Other planets, their moons, comets and asteroids

Tidal forces exist throughout he Solar System. It was most apparent in 1994 when the comet Shoemaker-Levy 9 broke up into more than 21 pieces when it strayed too close to Jupiter (Figure 2). Tidal Forces, which varied over the comet, was enough to break it up.

 

As tides affect liquids and gases more than solids, gaseous planets like Jupiter, Saturn, Uranus, and Neptune would be more easily affected by tidal forces. Their moons would create tidal forces on the planet, and likewise they will experience tidal forces from the planet. Tidal force has been postulated as the cause of several observations in the Solar system, including the cracking of Enceladus, one of Saturn’s icy moons (Dombard 2007). It has also been used to offer explanations as to how planets obtain their spin, as well as how planets like Saturn came to have their rings. The theory is that the rings were formed from the debris of moons or comets which were broken up by tidal forces as they came within the Roche limit of Saturn (Spinrad H, 2004) (Figure 3). The Roche limit is the distance within which any solid object that is purely held together by gravitation, will be torn apart!

Taking tidal forces to an even greater scale, galaxies also exert tidal forces on other astronomical bodies. If two galaxies are relatively close, each galaxy will feel a variation of tidal force due to the other galaxy, and this variation can be the cause of galactic structures that are observed today, including galactic bridges, tails, and spirals.

Implications of Tidal Forces 

Tidal Forces create several very interesting mechanisms for bodies under their influence. Some of these effects include:

 

1)      Tidal heating or friction: As a rigid body undergoes tidal forces, heat is generated due to friction. For example, as the Earth tries to “bulge” due to the Moon’s tidal forces, the land mass resists this bulging, and therefore creates heat in the process.

2)      Tidal coupling, braking or locking: The bulging due to tidal forces creates a redistribution of mass as well as heat. This in turn will gravitationally affect objects near it. For two objects in orbit around each other, and if they are rotating about their own axis, this bulging will tend to resist their rotations. The eventual effect is that the rotations will tend to be synchronized, and once it slows down sufficiently, they will get locked to each other. A way to visualize this is to think of 2 bar magnets, each spinning on a tabletop (ignore the repulsive forces). The attractive forces will tend to slow down their rotation and eventually stop altogether.

3)      Tidal elongation or recession, deceleration or decay: If two orbiting objects are not tidally locked yet, but one is still rotating, tidal bulges will either tend to pull the other ahead or behind, with the net result that the orbital radius will either increase or decrease, and the period of orbit to also vary.

4)      Tidal precession: If the rotational axis of an orbiting object is not exactly normal to its plane of orbit, then tidal forces can cause a “wobble” in the object’s rotation.

 

These effects are observed today in many objects in the Solar System. Some examples:

 

·        Our Moon is tidally locked to Earth, so we are only able to see the same side of the Moon from Earth. Many of the moons of other Solar System planets are also tidally locked to their planet.

·        Tidal heating is responsible for Io, a moon of Jupiter, to be so hot that it is mostly molten and has a lot of volcanic activity.

·        Tidal recession is causing the Earth-moon distance to slowly increase by 4cm per year. A long time ago, there is some evidence that the Earth rotated faster and the Moon was closer to the Earth. (Williams, G, 2000)

·        Tidal precession causes Earth to wobble on its axis, and Polaris, currently the North Star, will eventually not be aligned with the North Pole.

Conclusion

Tidal Forces are caused by variations in a gravity field, and are felt more strongly on dimensionally large objects. As an object under the influence of tidal forces revolves and rotates in its orbit, the forces will alter the object’s behaviour. It may cause it to speed up, slow down, spin faster or slower, or even wobble. Besides the ocean tides, there are many other instances of tidal forces at work in the Solar System today. It has profound influence on moons and also other bodies that are close to planets, like asteroids, comets, satellites and spacecraft. Having a better appreciation of tidal forces will help in our understanding of how our Solar System works.

 

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