Tides Simulation

The Project

Students are presented with an interactive simulation of the tides.

The cause of tides are discussed including the effect on the tides varying alignment of the Earth with the Sun and the Moon.

Students are asked to take measurements of the tidal variation generated from the simulation, which are then analysed and discussed.

What are Tides?

• In costal areas it can be observed that the sea retreats from the coast before returning at different times throughout the day.

• This is caused by tides.

• Tides are the vertical rise and fall of the Earth’s ocean surface, arising primarily from the gravitational interaction of the Sun, the Earth and the Moon.

Gravity

Gravity is the weakest of the four fundamental forces.

Gravity is responsible for the attraction of massive bodies.

Gravitational force is always attractive and acts along the line joining the centres of mass.

Gravitational force is responsible for the formation of planets, stars and galaxies.

Gravity decides the orbital paths of the planets and moons in our solar system, and the tidal forces that we experience on Earth.

National Schools’ Observatory

Newton’s Law of Universal Gravitation

221

21 rmmGFF

The gravitational force between the two masses m1 and m2 is described by Newton’s Law of Universal Gravitation.

G is the universal gravitation constant.

This relationship is an example of an inverse square law force.

Forces are equal in size but in opposite directions. 2211 /1067.6 kgNmG

National Schools’ Observatory

What causes tides? (1)

• The gravitational field of the Moon causes the Earth’s oceans to bulge. It is the Earth rotating through these ‘tidal bulges’, which causes the tides.

• For the majority of locations, two high tides and two low tides are experienced every day.

• This is due to the presence of a tidal bulge in the Earth’s oceans, which appears on both sides of the planet.

Note : The tidal bulge in this image is

exaggerated for demonstration purposes

What causes tides? (2)

• The gravitational force is not equal over the whole of the planet. This is called a ‘differential gravitational force’.

• Since gravitational force falls away as 1/r2, the force on the near side of the Earth is greater than the force on the far side. i.e. a unit mass on the far side of the Earth feels less of a gravitational pull than a unit mass on the near side.

• This is shown in the image below as force vectors.

What causes Tides (3)

• The tidal bulge which points away from the Moon arises from this imbalance in gravitational force.

• If the forces on the near and far edges of the planet are compared with respect to the force in the middle, we are left with resultant forces pointing outward from the Earth’s surface on both sides of the planet.

• i.e. when the force vectors of the centre are subtracted from the force vectors at either side. The result is forces which, point out from the centre of the Earth.

Tidal Force

• It helps to think of the Earth in simplified terms as a sphere with two layers.

• The outer layer being the oceans, and the inner layer being the solid surface, or the ocean beds.

• If we subtract the force due to gravity on the inner sphere from the force due to gravity on the outer sphere, we have a differential gravitational force.

• This differential gravitational force adds a stress to the oceans.

• The oceans, being made of water, can deform to counter-act this gravitational stress, causing the tides.

Tidal Lag

• The tidal bulges do not line up perfectly, with the line of the Moon.

• This is due to the rotation of the Earth being much faster than the orbit of the Moon.

• Frictional forces between the Earth’s solid surface and the water, cause the tidal bulge to be forced ahead of the Moon.

Note: The above angle is exaggerated for demonstration purposes.

Spring and Neap Tides

• The Earth also lies in the gravitational field of the Sun. The Sun therefore also has an effect on the tides.

• When the Earth, Sun and Moon are in a line (Syzygy), the Sun’s gravity adds to the tidal force increasing the tidal bulges.

• These are called Spring tides.

• When the Moon is at right angle’s to the line of the Sun and the Moon (Quadrature), the solar gravity reduces the Moon’s contribution to the tidal bulge.

• These are called Neap Tides.

Prediction

Which body has the most gravitational pull on the Earth. The Sun or the Moon?

Which body has the most effect on the tides. The Sun or the Moon.

Predict when would you expect the largest tides?

Predict when would you expect the smallest tides?

Setting Up the Experiment

• Load the ‘Tides Simulator’.

• The symbol, will zoom out from the Earth, displaying a ‘not to scale’ interaction of the Sun, the Earth and the Moon.

• The symbol will return to the close up view of the Earth and the Moon.

• The symbol, will allow students to toggle on the ‘day number’, increase or slow down the speed of the Earth’s rotation (close mode only), remove the influence of the Sun and also toggle on the tide height simulation.

Measuring and Recording

• Provide students with a print out of the tides worksheet.

• Ask the students, with the aid of the tides simulation, to sketch the tides on the Earth, which correspond to the position of the Moon and the Sun.

• Ask the students to label, the boxes in which a Spring tide or a Neap tide is present.

Measuring and Recording

• In the simulation, activate the Day Number and Tidal Variation Option.

• The white marker attached to the Earth, represents an observer on a boat.

• The window to the left simulates the change in sea level due to the tides for that observer.

• Record the sea level at high and low tide, for each day until the day Moon has completed a full orbit of the Earth.

Example Chart (Day Vs Tide Height)

• Ask the students to plot Tide Height Vs Days.

• Making sure to only chose one high and low tide a day.

Prediction Compared to Results

• Does the height of the high and low tide vary?

• When do the tides with most variation occur?

• What alignment of the Sun, Moon and Earth generate the highest tides?

Discussion

How many high and low tides are there in one day?

How many days are there between periods of low tidal activity and high tidal activity?

How long does it take the Moon to orbit the Earth?

Questions, Exercises and Tasks

Tidal variation at costal areas can be much higher than out to sea. Why is this?

Does Jupiter have an effect on the tides?

Why is it important to be able to predict the tides?

If the Moon was further away, how would this affect the tides?

Are there tides on the Moon?