DIDACTICAL ACTIVITIES ABOUT TIDES

Lidia Nuvoli - Cristina Palici di Suni

Didactic Seminaries Department of General Physics University of Torino.

EAAE Summer School Working Group (Italy)

As for the importance of tides in navigation we propose to analyse the periodical tides

movements using moving paper devices in which different periodical functions may be

compared.

In the discussion we point out that the theory about tides is still a topic of research and that,

from a didactical point of view, it involves teachers of Physics and Science because of a

very stimulating astronomy-link.

If we observe, first, the forces which generate tides by a static approach (it means to

consider the different celestial bodies in their different positions without any consideration

of inertial problems) we can see the difference in acceleration of the solid and liquid part of

our globe. This makes us to understand the level of tides and the moving of the

phenomenon in relation with time. Of course the theory is much more complicated if we

want to go deeper.

Then we consider the time delay in the arrival of a tide wave in a certain place: this cannot

be explained only by a static theory. It involves at first consideration about Coriolis

acceleration of a mass of water which is moving with a velocity of many hundred Km an

hour referring to an observer on the ground of the Earth.

At last we discuss about the dissipative aspect of tides, thus concluding with two different

hypotheses about what could happen, fortunately in a very far away time (!), in our Earth-

Moon and solar system.

After a short introduction about the phenomenon, we propose to analysis the periodical

tides movements using diagrams in which different periodical functions may be compared

in paper-moving devices.

In fact if we consider the forces which generate tides from a static point of view (it means

to consider the different celestial bodies in their different positions without no consideration

of inertial problems) we can see that the difference of the acceleration of the solid and the

liquid part of our globe, in their normal and tangential component let us understand the

level of tides and the moving of the phenomenon in relation with the time (of course the

theory is much more complicated if we want to go deeper). We can also see how the

different level of tides is depending on latitude angle.

The time delete of the arrival of a tide wave in a certain coast-side place cannot be

explained by a static theory: it involves first of all considerations about Coriolis

acceleration of a mass of water which is moving with a velocity of many hundred Km by

hour (referring to somebody fixed in the solid part of the globe) . Also this part can easily

be understood by a three-dimensional paper model of a Cartesian diagram.

At the end, simulating to be old navigator men, we can do an exercise-game which consists

in approaching a coast-side place using a timetable of tides in a decision game about

navigation.

The navigators have always had to take into the greatest consideration the problems of

tides.

We have experimented at various school levels and now we propose an activity to promote

the approach of a physical interpretation of the important phenomenon of tides.

We also prepared a card for the experimental survey but, as Turin is not on the sea (!) we

passed our card to a Nautical Institute for the experimentation on the Adriatic Sea.

Now we propose the activity done in Turin that through handmade devices has allowed to

analyse this complicated phenomenon in a comparatively easy and involving way.

The first step brings us to consider the Moon as the cause of the phenomenon and justifies

the existence of high tides every 12 hours.

The second introduces the action of the solar mass and leads to consider the complications

related to the angles between the orbital planes of the Earth-Moon and the Earth-Sun

system.

The third takes us to consider that the Earth-Moon system is like a handle (a two bodies

bounded system) which twists around its gravity centre and takes us to consider in the tides

phenomenon also the centripetal forces beyond the gravitational.

The building of models is accompanied by cards for the discussion in the classes.

It is possible to go deeper into the problem of the high velocity of propagation of the tide

wave and therefore into the consequences of the Coriolis forces depending on the water

velocity connected to a non inertial observer.

At the end we point out the dissipative aspect of this phenomenon that in the course of

centuries has influenced the duration of the day, opening the mind to hypothesis of possible

future and dramatic scenery.

We made this proposal in two levels: the first basic one as a qualitative description suitable

for 12-15 years students and a second one for oldest students already aware of the

gravitational theory, periodical phenomenon and the cinematic of the solar system. In both

cases we cooperated with the Science teachers.

Paper models

Materials needed:

For all the three of them it is necessary to have cardboard A4 : three rigid ones to be used

as bases and three lighter ones in different colours to produce the forms, glue, scissors,

goniometer, clips, a pin and felt pens.

First model:

Aim: to evidence in a simple way the relation between the tides movements and the

presence of a body external to the Earth.

In an ideal equatorial section our globe is shown in its rigid and liquid components by two

concentric discs of different diameters fixed at the base with a pin.

An observer on the dry land observes that the water level is not constant in time and

believes to be possible to associate this phenomenon to the presence of the moon. This

hypothesis however is too simple because it does not explain the appearance of two tides in

a day (one of these when the moon is not visible).

By using our model and arrows of different length it is possible to give a qualitative

gravitational explanation of both the raisings of the water levels in the moon side and in the

opposite.

We note that the numerical differences of the Earth-Moon attraction corresponding to the

three arrows are very little (around one thousandth of the apparent centrifugal acceleration

by which we justify the shape of the Earth) even compared with the g acceleration due to

the mass of the Earth.

However such differences explain why the liquid masses at the antipodes are less attracted

and therefore stay behind in comparison to the water in front of the Moon.

Second model.

Aims: to examine the combined action of Sun and Moon in the course of the year.

Because of the difference of the ecliptical, lunar orbit and the Earth equator planes and

because of the varying of their reciprocal positions in time we need a three-dimensional

model.

We can obtain this by means of suitable cuts and windows opened on a base representing

the ecliptical plane: in these cuts we insert the plane of the lunar orbit thus underlining the

nodes line, and windows to better discuss the positions of the Moon.

This model is useful in examining how to sum and how to subtract in time the 23 30 and

the 5 9 which influence the vectorial composition of the lunar-solar effects. It is easy to

calculate the ratio between Moon and Sun contribution on the tide wave.

MS / M L = 27 10 5 DS / DL = 390

D=distance Earth Sun and Earth Moon

but 3903 = 59 x 10

5 so that:

as / aL = 27 / 59

In effect comparing 2 r = (m+M)/r

2

We have the relation between the masses

and the cube of the distance.

In building the model, and in order to correctly position our cuts we shall have to consider

also the roughly 19 years period of the nodes line regression. It will also be useful to draw,

on the paper base, an eclipical line overly eccentric in order to point out that the changing

of seasons is strictly depending on the inclination of the Earth axe, whilst the amplitude of

the tides is strongly influenced by the distances between the masses position along the

ecliptic.

The tide wave due by two thirds to the Moon and by one third to the Sun shows its

maximum value in the sigizie (when the Moon is opposite or in line with the Sun position).

To confirm all this, you can find data on experimental tables still in use today. See for

instance the hand book of the Everglades fishermen in the South of Florida.

Third model.

Aim: to examine the movement of the Earth-Moon system and its effect on the tides.

Once we construct a handle Earth-Moon, we discuss the successive positions in a simplified

bi-dimensional model during at least four weeks, shifting its barycentre on a wide arch of

ellipse week by week.

This exercise evidences the winding path of the Moon whilst the Earth is only slightly

twisting along the Keplerian ecliptic.

On the same model we can verify the vectorial composition of the gravitational tides-forces

due to the Sun and to the Moon, and we can also use it to study the centripetal forces

caused by the rotation of the handle in