Moray Coast U 3 A Geology The Earths

Moray Coast U 3 A Geology The Earth’s Mass and Structure

Geology A complete introduction By David A Rothery ISBN 978 -473 -60155 -0

This is our text-book for today’s Geology session Today we will be looking at the second part of Chapter 2, The Earth’s Development. In this section the author, David Rothery, tends to gloss over the physics involved. In order to improve our understanding we will be looking at some of the physics involved in a little more detail than is covered in the text. Don’t panic!

How we find the mass of Planet Earth? • The first part of this session is an attempt to indicate how we can find out the mass of the Earth. • We will go through this quickly as this is not something you must learn but you should be satisfied that this is a relatively simple matter and not “magic”. • “Any sufficiently advanced technology is indistinguishable from magic”. – Arthur C Clarke

The Earth’s Mass In everyday language the terms “Mass” and “Weight” are used interchangeably. To a scientist they are not the same. The word “Mass” refers to the quantity of matter in a body. The word “Weight”, when used on Earth, refers to the force by which a body is attracted to the centre of the Earth.

Mass and Weight 1 • For example consider the British astronaut Helen Sharman. • Assume that she has a mass of 60 kg. On Earth she also weighs 60 kg. • Earth’s moon has about one sixth the mass of the Earth and the force due to the gravity of the moon is one sixth of the force due to the of gravity of the Earth.

Mass and Weight 2 • Helen weighs 60 kg on Earth her mass is also 60 kg. • On the moon she would only weigh 10 kg but her mass is still 60 kg. • Between the Earth and the moon she is weightless. Her weight is zero, ( 0 kg ). However she still has a mass of 60 kg.

Finding the mass of The Earth • This next bit is a bit technical but it also illustrates how elegant and beautiful mathematics can be. • I don’t claim to be a mathematician but I know one who will put me right if I make any mistakes.

Calculating the Mass of the Earth Consider a satellite with mass Msat orbiting a central body with a mass of mass Mcentral. The central body could be a planet, the sun or some other large mass capable of causing sufficient acceleration on a less massive nearby object. The satellite could be an artificial satellite or a moon.

Calculating the Mass of the Earth Our Moon has an orbit with an average distance of 384, 800 km from the Earth. (Artificial satellites are much closer. ) The sizes and distance are more or less to scale.

If the satellite moves in circular motion, then the net centripetal force, Fnet, acting upon this orbiting satellite is given by the following relationship Fnet = ( Msat x v 2 ) / R Equation 1 Where R is the radius of the orbit from the centre of the central body; in this case the planet Earth and v is the velocity of the satellite.

Centripetal and Centrifugal Force Consider a ball attached to a piece of string and whirled around someone’s head.

Centripetal and Centrifugal Force The centripetal force is the force directed towards the centre needed to keep the object, (the ball), in a circular path. The centrifugal force is the apparent force outwards on the ball. In this case the centripetal force is equal to the tension on the string.

For a natural or artificial satellite the net centripetal force, Fnet , is equal to the gravitational force, Fgrav, that attracts the satellite towards the central body and can be represented as Fgrav = ( G x Msat x Mcentral ) / R 2 Equation 2 Where G is the Gravitational Constant with a value of 6. 673 x 10 -11 N • m 2/kg 2

Physics Extra! • A newton (N) is the international unit of measure force. • 1 newton of force is the force required to accelerate an object with a mass of 1 kilogram 1 meter per second. • Just in case you wanted to know!

Since Fgrav = Fnet, the above expressions for centripetal force and gravitational force can be set equal to each other. Thus: (Msat x v 2) / R = (G x Msat x Mcentral ) / R 2 Equation 1 Equals (=) Equation 2

Observe that the mass of the satellite is present on both sides of the equation; thus it can be cancelled by dividing through by Msat. Then both sides of the equation can be multiplied by R, leaving the following equation. v 2 = (G x Mcentral ) / R

Rearranging this equation we get a mass for the central body, in this case the Earth as: Mcentral = V 2 x R /G This elegant equation allows one to calculate the mass of the earth using only the velocity of the Moon, its distance from the Earth and the Gravitational Constant which has been well known since the time of Isaac Newton.

Calculating the Mass of Earth Summary Calculating the mass of our Earth is not magic but involves some elegant mathematics. All you need to know is: • The velocity the moon travels around the Earth • The distance of the moon from the centre of the Earth • The Gravitational Constant

The Earth – vital statistics • • Radius: 6, 371 km • Average Density: 5. 51 g/cm³ 24 Mass: 5. 972 × 10 kg • We will now go on to consider the implications of this value of an average density for the Earth.

The Earth’s Interior The density of the rocks on the Earth’s surface averages out at about 2. 7 tonnes per cubic metre or 2. 7 g/cm 3. (The joys of the metric system!) This suggests that there areas of the planet which are much more dense than the rocks on the surface. These denser areas could be arranged in two different possible ways.

Which model? Either the extra dense parts are scattered about as “islands” of denser material throughout the Earth. Or the extra dense parts are all together in the centre of the Earth. Which model is correct?

Earthquakes • The subject matter of earthquakes will be dealt with in detail later in the course. • Earthquakes are natural occurrences that send out shock waves over very large distances. • Large earthquakes can make the whole Earth vibrate, or ring, like a bell. • Sensitive instruments, called seismometers, can detect even very weak earthquakes.

Seismic Waves • Earthquakes generate Seismic Waves. • A Seismic Wave is a wave of energy that is generated by an earthquake or other earth vibration and that travels within the earth or along its surface. • An “other earth vibration” could be a nuclear explosion or the impact of a significant meteorite.

Seismic Waves • There are several different kinds of seismic waves, and they all move in different ways. The two main types of waves are body waves and surface waves • Body waves can travel through the earth's inner Body waves layers, but surface waves can only move along the surface of the planet like ripples on water. Earthquakes radiate seismic energy as both body and surface waves.

Body Waves • Travelling through the interior of the earth, body waves arrive before the surface waves emitted by an earthquake. • Body waves are of a higher frequency than surface waves. • Two types of body wave have been identified, Primary Waves and Secondary Waves.

Primary Waves • The first kind of body wave is the P wave or primary wave. This is the fastest kind of seismic wave, and, consequently, the first to 'arrive' at a seismic station. • The P wave can move through solid rock and fluids, like water or the liquid layers of the earth. It pushes and pulls the rock it moves through just like sound waves push and pull the air. • A big clap of thunder can be heard and make windows rattle at the same time The windows rattle because the sound waves were pushing and pulling on the window glass much like P waves push and pull on rock.

Primary Waves Continued • P waves are also known as compressional waves, because of the pushing and pulling they do. • Subjected to a P wave, particles move in the same direction that the wave is moving in, which is the direction that the energy is travelling in, and is sometimes called the 'direction of wave propagation'.

Primary Waves

Secondary Waves • The S wave, or secondary wave, is the second wave you may feel in an earthquake. • An S wave is slower than a P wave and can only move through solid rock, not through any liquid medium. • S waves move rock particles up and down, or side-to-side, perpendicular to the direction that the wave is travelling in or the direction of wave propagation.

Secondary Waves

An Experiment A “slinky” spring can be used as a model to illustrate p waves and s waves P wave S wave

Surface Waves Surface waves are not important at this point • Surface waves travel only through the crust. • Surface waves are of a lower frequency than body waves, and are easily distinguished using a seismometer as a result. • Although they arrive after body waves, it is surface waves that are almost entirely responsible for the damage and destruction associated with earthquakes. This damage and the strength of the surface waves are reduced in deeper earthquakes.

Seismic waves - a quick summary • Earthquakes form surface waves and body waves. • Surface waves travel only through the crust. They cause damage but don’t give us much information about the structure of the earth. • Body waves are of two types. • P waves travel through solids and liquids (fluids). • S waves travel through solids only.

Seismometers • A seismometer is a scientific instrument used to detect seismic waves. • There are seismometers placed in many locations on the earth. • Information from this network can be collated to give information about the structure of the earth deep below its surface.

A seismometer This is what a simple, amateur built, seismometer looks like. Most seismometers are not much to look at but are delicate, precision, You can get instructions to build one on the internet. instruments.

Seismograph A seismograph is the paper, or electronic, record of seismic waves obtained from a seismometer.

Seismic Waves Bend • Seismic body waves, (p & s), to not travel in straight lines like light. • The deeper a rock is the greater the pressure and the more denser it becomes. • Also the deeper a solid rock is the more rigid it becomes. • These changes affect the speed of travel of seismic waves and cause the path of a seismic wave to curve slightly.

The earthquake sends out body and surface waves. Consider an earthquake at the Note what happens to the s and p body waves North Pole Earthquake here S – waves are in red P– waves are in blue

Consider an earthquake at the North Pole 2 • Note that both S and P waves can travel through the solid mantle they can’t both travel through the outer core which must be liquid. • This leaves a S wave shadow zone. • The size of this shadow zone can be used to determine the size of the molten outer core. Molten Outer Core “Solid” mantle

The Inner Core • A more detailed analysis of the s and p waves over many seismic events provided evidence that the earth’s inner core is solid. • The Earth was discovered to have a solid inner core distinct from its liquid outer core in 1936, by the Danish seismologist Inge Lehmann, who deduced its presence by studying seismograms from earthquakes in New Zealand. She observed that the seismic waves reflect off the boundary of the inner core and can be detected by sensitive seismographs on the Earth's surface. • In 1940, it was hypothesized that this inner core was made of solid iron; its rigidity was confirmed in 1971.

Inge Lehmann Danish geophysicist

Summary • The mass of the earth is easier to measure than you might think • From its mass and size one can work out the average density of the earth ( d = m/v ) • The surface rocks are much less dense than the earth as a whole. • The centre must be very dense • A careful analysis of seismic data from earthquakes has revealed the inner structure of the earth.

End of Chapter 2, part two Any Questions?