A level Physics

Cosmology / Astrophysics

Module 2825, Component 01: Cosmology

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5.5.1 Models of the Known Universe

(a) describe the models of the Universe as proposed by Copernicus and Kepler.

Copernicus' model of the Universe

The Earth-centred model of the Universe of Aristotle and Ptolemy held sway on Western thinking for almost 2000 years. In this model, the apparent temporary reversal of motion of Venus and Mercury (retrograde motion) was explained using the concept of epicycles. Then, in the 16th century a new idea was proposed by the Polish astronomer Nicolai Copernicus . He proposed that the Sun, not the Earth, was the centre of the Solar System. Such a model is called a heliocentric system. The ordering of the planets known to Copernicus in this new system is illustrated in the following figure. This ordering is the same as how we now view it.


In this scheme, Earth is just another planet and the Moon is in orbit around the Earth, not the Sun. The stars are distant objects that do not revolve around the Sun. Instead, the Earth is assumed to rotate once in 24 hours, causing the stars to appear to revolve around the Earth in the opposite direction.

Retrograde Motion and Varying Brightness of the Planets

The Copernican system, by banishing the idea that the Earth was the centre of the Solar System, immediately led to a simple explanation of both the varying brightness of the planets and retrograde motion:

1. The planets in such a system naturally vary in brightness because they are not always the same distance from the Earth.

2. The retrograde motion could be explained in terms of geometry and a faster motion for planets with smaller orbits, as illustrated in the following animation. It is a matter of perspective.

A similar construction to the one shown in the animation can be made to illustrate retrograde motion for a planet inside the orbit of the Earth.

The Copernican model, with its assumption that all planets move in uniform circular motion, still could not explain the details of planetary motion on the celestial sphere, so the idea of epicycles was not given up altogether.

Copernicus' ideas remained rather obscure for about 100 years after his death. But, in the 17th century the work of Kepler, Galileo, and Newton would build on the heliocentric Universe of Copernicus and produce the revolution that would completely sweep away the ideas of Aristotle and replace them with the modern view of astronomy and natural science. This sequence is commonly called the Copernican Revolution.

[Actually, the notion of a Sun-centred Solar System had been proposed by Aristarchus as early as about 200 B.C. - long before Copernicus suggested it. However, it did not survive long under the weight of Aristotle's influence at that time.]

Kepler's model of the Universe

After Copernicus, a Danish nobleman, Tycho Brahe, made important contributions by

In 1600, the German mathematician Kepler went to Prague to become Brahe's assistant. Brahe set Kepler (apparently not with the best of motives) the task of understanding the orbit of the planet Mars, which was particularly troublesome to work out.

After struggling with the problem for some time, Kepler was forced finally to conclude that the orbit of Mars could not possibly be a circle. He realised that the orbit of Mars, and indeed of all the planets, must be ellipses rather circles. The reason that Mars had stood out in not fitting with the existing model of the Solar System was because the orbit of Mars was by far the most elliptical of Brahe's planets.

(b) describe the progress in the understanding of the Universe as a result of the work of Copernicus, Kepler and Galileo.

Galileo

Although Galileo Galilei (1564-1642) did not invent the telescope, he was the first to use this instrument to study the heavens in a systematic way. His little telescope was very poor, but what he observed in the heavens rocked the very foundations of Aristotle's universe. (And it is said that what Galileo saw was so disturbing for some officials of the Church that they refused to even look through his telescope, reasoning that the Devil was capable of making anything appear in the telescope, so it was best not to look through it at all.) Galileo also laid the foundations for a correct understanding of how objects moved on the surface of the earth (dynamics - acceleration, velocity) and of gravity.

So Galileo began, and Newton completed, a synthesis of astronomy and physics in which the former was recognized as but a particular example of the latter, and that would banish the notions of Aristotle almost completely from both. Galileo is sometimes referred to as the "father" of modern astronomy and of modern physics.

Astronomical observations made by Galileo include:

(c) use Newton’s law of Gravitation to derive an expression for the radius of the circular orbit of a planet around the Sun in terms of the period of the orbit.

Set the force of gravity equal to the centripetal force and solve for r:


GMm
=
mrω2
r2
Cancelling m
r3
=
GM
& rearranging:
ω2
so
r3
=
GMT2
2
since
ω
=
T


(d) recall and use Kepler’s laws as applied to circular orbits.

Kepler's Laws

I. The orbits of the planets are ellipses, with the Sun at one focus of the ellipse.

The Sun is not at the centre of the ellipse, but is instead at one focus (generally there is nothing at the other focus). The planet then follows the ellipse in its orbit, so the Earth-Sun distance is constantly changing. The orbit shown in the diagram (right) is more eccentric than most planetary orbits really are.

II. The line joining the planet to the Sun sweeps out equal areas in equal times as the planet travels around the ellipse.

The planet moves faster when it is nearer the Sun. Thus, a planet executes its elliptical motion with constantly changing angular speed. The point of nearest approach of the planet to the Sun is termed perihelion; the point of greatest separation is termed aphelion. Hence the planet moves fastest when it is near perihelion and slowest when it is near aphelion.

III. The ratio of the squares of the revolutionary periods for two planets is equal to the ratio of the cubes of their semimajor axes.

In the equation to the right, P represents the period of revolution for a planet and R represents the length of its semimajor axis. The subscripts "1" and "2" distinguish quantities for planet 1 and 2 respectively. The periods for the two planets are assumed to be in the same time units and the lengths of the semimajor axes for the two planets are assumed to be in the same distance units.

Kepler's Third Law implies that the period for a planet to orbit the Sun increases rapidly with the radius of its orbit. Thus we find that Mercury, the innermost planet, takes only 88 days to orbit the Sun, whereas Pluto (an outer planet) requires 248 years to do the same. Here is an animation illustrating the relative periods of the inner planets. (This, and much of the material in this section, has been fashioned from the website of the University of Tennessee's Dept. of Physics & Astronomy.)

(e) recall how the existence of Neptune was predicted from the orbit of Uranus.

After the discovery of Uranus, it was noticed that its orbit was not as it should be in accordance with Newton's laws. This convinced astronomers that another large planet outside the orbit of Uranus could be tugging Uranus with its gravity and so perturbing Uranus' orbit. On the first night of the search the planet was found just one degree away from the predicted location. This was seen as a tremendous triumph for Newtonian science.

(f) appreciate the significance of Kepler’s third law as evidence of Newton’s law of Gravitation.

Kepler's third law (based on observation) expresses proportionality of (radius of orbit)3 to period2.

This proportionality is also derived from Newton's Law of Gravitation - so Kepler's law corroborates Newton's law.

(g) describe the contents of the Solar System in terms of the Sun, planets, planetary satellites and comets. Details of individual planets are not required.

There are eight planets circling the Sun, the outermost planet being Neptune at 30 A.U. from the Sun. (Pluto, at an average distance of about 80 AU from the Sun, is no longer defined as a 'planet' as of August 2006).

 

 

Acronym for the eight planets of our sun:  My Very Elegant Mum Just Served Us Nosh
- distances not to scale)
Nasa's Magellan spacecraft mapped
98% of Venus' surface with radar


Comets, the Kuiper Belt, the Scattered Disc and the Oort Cloud

A 370kg "impactor" the size of a washing machine, released into the comet Tempel 1's path by the flyby spacecraft, crashed into the comet on 4 July 2005. (NASA)

A comet is a small body in the solar system that orbits the sun and (at least occasionally) exhibits a coma (or atmosphere) and/or a tail - both due primarily to the effects of solar radiation upon the comet's nucleus, composed of rock, dust, and ices. Due to their origins in the outer solar system and their propensity to be highly affected by relatively close approaches to the major planets, comets' orbits are constantly evolving. Some are moved into sun-grazing orbits that destroy the comets when they near the sun, while others are thrown out of the solar system forever.

Comets are believed to originate in a cloud (the Oort cloud) at large distances from the sun consisting of debris left over from the condensation of the solar nebula. The outer edges of such nebulae are cold enough for water to exist as ice.

A Trans-Neptunian Object (TNO) is any object in the solar system that orbits the sun at a greater distance on average than Neptune. The Kuiper belt, Scattered disk, and Oort cloud are names for three divisions of this volume of space. A TNO is an example of a planetoid. The term planetoid loosely refers to a celestial body with some of the characteristics of a planet. Depending on usage, the term may refer to one or more of the following: Trans-Neptunian Object; asteroid; dwarf planet; minor planet; Kuiper Belt Object; and small solar system body.

The image above top is an artist's impression of 2003UB313, nicknamed "Xena". The diagram underneath depicts 2003UB313's orbit relative to Pluto's. NASA's Hubble Space Telescope has resolved 2003UB313, finding that it is slightly larger than Pluto and that it has a moon.

The Kuiper Belt is a disc-shaped region past the orbit of Neptune, 30 - 50 AU from the Sun, at inclinations consistent with the ecliptic. It contains many small icy bodies. Over 800 KBOs (Kuiper Belt Objects) - icy bodies orbiting the Sun - have been discovered in the belt, almost all of them since 1992. Among the largest discovered so far are 2003 UB313, Pluto and Charon. They are believed to be remnants of the formation of the Solar System and among the most primitive objects available for study. Beyond the outer boundary of the Kuiper Belt, there is a fairly sharp drop-off in objects. The Kuiper Belt is now considered to be the source of short-period comets.

The scattered disc is a distant region of our solar system, 50-100 AU from the Sun, thinly populated by icy planetoids known as scattered disc objects (SDOs). The innermost portion of the scattered disc overlaps with the Kuiper belt, but its outer limits extend much farther away from the Sun and above and below the ecliptic than the belt proper. While the Kuiper belt is a relatively "round" and "flat" doughnut of space extending from about 30 AU to 44 AU with its member-objects locked in autonomously circular orbits (cubewanos) or mildly elliptical orbits, the scattered disc is by comparison a much more erratic milieu. SDOs can often travel almost as great a "vertical" distance they do relative to what has come to be defined as "horizontal." Orbital simulations show SDO orbits may well be erratic and unstable and that the ultimate fate of these objects is to be permanently ejected from the core of the solar system into the Oort cloud or beyond.

The Oort Cloud (named after Jan Oort) is a postulated spherical cloud of comets situated about 50,000 to 100,000 AU from the Sun. This is approximately 1000 times the distance from the Sun to Pluto or roughly one light year - almost a quarter of the distance from the Sun to Proxima Centauri, the star nearest the Sun.

Although no direct observations have been made of such a cloud, based on observations of the orbits of comets, it is believed to be the source of most or all comets entering the inner solar system (some short-period comets may come from the Kuiper belt).

It is thought that long-period comets reside in the Oort Cloud. Statistics imply that, if it exists, it may contain as many as a trillion comets.

Asteroids and the asteroid belt

This composite image was taken by the Stardust probe during its close approach to Comet Wild 2 in 2004. Several large depressed regions can be seen. Comet Wild 2 is about 5km (3.1 miles) in diameter. (NASA)

Asteroids originate via a different process than do comets, but very old comets that have lost all their volatile materials may come to resemble asteroids.

An asteroid is a small, solid object in our Solar System, orbiting the Sun. It is an example of a minor planet (or planetoid), these being much smaller than what we normally call planets. Most asteroids are believed to be "leftovers" from the proto planetary disc that were not incorporated into planets during the solar system's formation. Some asteroids even have "moons". The vast majority of the asteroids are within the main asteroid belt, with elliptical orbits between those of Mars and Jupiter. It is termed the main belt when contrasted with other concentrations of minor planets, since these may also be termed asteroid belts.

 

 

 

Formation of Solar System

(h) show awareness of the principal contents of the Universe, including stars, galaxies and radiation.

The Universe of visible matter

Sometimes the clusters are grouped in even larger structures called super cluster, which are most probably the largest structures in the Universe.

The following table shows our place in the Universe:

Some stars appear to have planets revolving around them, just like our own Sun. The Earth revolves around the Sun. At least eight other planets orbit the Sun. Pluto's orbit is about 80 AU across. There is some dispute as to whether a recently discovered body (nicknamed Xena), very similar to the outermost planet Pluto but further away and a bit bigger, should be also called a planet - and as to whether we are right in classifying Pluto as a planet!
Stars are grouped into galaxies. The Sun in turn orbits the centre of our galaxy (the Milky Way). The Milky Way is about 100,000 light years (30 kpc) across. It contains 100-600 billion stars. The Sun is towards the edge of the Milky Way on one of the spiral arms. The nearest star to us, at 4.2 light years, is Proxima Centauri, one of three stars in the Alpha Centauri system.
About three-quarters of all galaxies are in clusters. Our galaxy is part of a cluster of galaxies called the Local Group. The Local Group spans about 8 million light years and contains about 30 galaxies. The Milky Way and Andromeda are by far the largest galaxies in this cluster.
Clusters are grouped into superclusters. The Local Group is part of a supercluster of galaxies called the Local Supercluster. The diameter of the Local Supercluster measures roughly 100 million light years and consists of some 50 clusters. The giant Virgo Cluster is at the centre of the Local Supercluster. Superclusters are probably the largest structures in the Universe
Millions of these galaxy superclusters are strung out around the universe - a bit like an unfathomably huge spider's web (see image to the right).   The gaps (or voids) within this 'web' of galaxies fill about 90% of space.

(i) define distances measured in astronomical units (AU), parsecs (pc) and light-years.

Because the distances to stars are so large, it is useful to introduce some large units of distance measure:

The Astronomical Unit (AU) is the average separation of the earth and the sun

The Light Year is the distance that light travels in a single year. Since light is very fast, the light year is a very large distance. We can determine the length of a light year in metres by multiplying the sped of light in a vacuum by the number of seconds in a year.

The Parsec (pc) is short for Parallax-second. Astronomers call it this because it is the method of parallax that gives rise to this natural distance unit. The parsec is defined to be the distance at which a star would have a parallax angle p equal to one second of arc. From basic trigonometry, we find that this distance is equal to 206,265 AU or 3.26 light years. One also commonly uses the kiloparsec (kpc) and the megaparsec (Mpc). Although the light year is often found in popular level discussions, professional astronomers probably use the parsec, kiloparsec, and megaparsec more commonly as units of large distance.

(j) recall the approximate magnitudes, in metres, of the AU, pc and light-year.

Astronomical distance units in metres

Astronomical Unit
~ 1011 m
 
Light Year
~ 1016 m
 
Parsec
~ 3 x 1016 m
also kiloparsec (kpc) and megaparsec (Mpc)

(k) recall the distances involved between objects in the Universe, including distance to nearest stars, distance across a galaxy, size of observable Universe.

(l) appreciate the range of magnitudes of the sizes and masses of objects in the Universe.

5.5.2 Stars and Galaxies

(a) describe the nuclear fusion processes taking place within the Sun.

The Proton-Proton Chain is the principal set of reactions for solar-type stars (i.e. stars like our sun) to transform hydrogen to helium:

The individual nuclear reactions proceed rather slowly, and it is a very small fraction of nuclei in the core of the sun with enough energy to overcome the electrical repulsion. Even so, every second the sun turns 600 million tons of hydrogen into 596 million tons of helium (with 4 million tons transformed into luminous energy via E=mc2).

(b) calculate the energy released as a result of the fusion processes taking place within the Sun.
(c) understand and use the magnitude scales for stars and galaxies.

Because stars can have a very broad range of brightness, astronomers commonly introduce a logarithmic scale called a magnitude scale to classify the brightness.

The apparent magnitude of an object is the "what you see is what you get" magnitude. It is determined using the apparent brightness as observed, with no consideration given to how distance is influencing the observation.

A star's colour is measured by its magnitude, which tells how bright a star or galaxy appears from Earth. Astronomers have used versions of the magnitude scale for thousands of years, so they keep using it even though the scale is a bit confusing. In the magnitude scale, higher numbers correspond to fainter objects, lower numbers to brighter objects; the very brightest objects have negative magnitudes. You could think along the lines: the greater the magnitude of the star, the dimmer it is.

An increase of one number in magnitude corresponds to a decrease in brightness by a factor of about 2.51 - a magnitude five object is 2.51 times fainter than a magnitude four object.

The apparent magnitude (m) of a star, planet or other celestial body is a measure of its apparent brightness as seen by an observer on Earth.

Brighter = more negative / less positive.

Scale of apparent magnitudes (approximate)
App. Mag. Celestial object
  -27 Sun
  -13 Full Moon
  - 4 Venus - brightest planet (at its maximum)
  - 1.5 Sirius - brightest star in northern hemisphere (except for the Sun):
    0 The zero point (this used to be Vega)
    6 Faintest stars observable with naked eye (though not in urban neighbourhood!)
  30 Faintest objects observable with Hubble Space Telescope (at visible wavelengths)

(d) recall and use the equation m = -2.5 lg I + constant, where m is the apparent magnitude and I is the intensity.

For every increase of 1 in order of magnitude, there is a 2.5-fold increase in the apparent brightness of a star. Therefore, the equation for apparent magnitude m is:

m = -2.5 log I + constant

where I is the intensity or flux from the star.

Thus that a star of the third magnitude would appear to be 6.31 times as bright as a star of the fifth magnitude, because the difference in apparent magnitude is two.


(e) understand the concept of absolute magnitude M.

Absolute Magnitude

A star that is very bright in our sky could be bright primarily because it is very close to us (the Sun, for example), or because it is rather distant but is intrinsically very bright (Betelgeuse, for example). It is the "true" brightness, with the distance dependence factored out, that is of most interest to us as astronomers. Therefore, it is useful to establish a convention whereby we can compare two stars on the same footing, without variations in brightness due to differing distances complicating the issue.

The problem with apparent magnitudes is that there is no way to differentiate between a bright star that is a long way away, and a dimmer star which is nearer. So astronomers use absolute magnitude M to compare the intrinsic brightness of stars.

The absolute magnitude of a star is defined as being the magnitude a star would have if it were 10 parsecs away from us.

(f) recall and use the inverse square law to derive the relation between apparent magnitude, absolute magnitude and distance: m - M = 5 lg (r/10).

The intensity of light observed from a source falls off as the square of the distance from the object. This is known as the inverse square law for light intensity.

The absolute magnitude M of a star is really a league table of how dim stars are compared to each other. If you could put another star where our sun is right now, you could easily say it was a certain amount dimmer or brighter than our sun.

Astronomers picture a star at a standard distance of 10 parsecs. (Our sun has an absolute magnitude of around +5 when viewed at a distance of 10 pc.)

Deducing a formula for absolute magnitude

Since m = -2.5 log I + constant

For two stars of magnitude mA and mB, and intensity IA and IB respectively:

mA - mB  =  ( -2.5 log IA + constant ) - ( -2.5 log IB + constant )
              =   -2.5 ( log IA - log IB )
              =   -2.5 log ( IA /IB )

Because of the inverse square law relating intensity and distance:

I ∝ 1 / r2

We can write:

mA - mB   =   -2.5 log ( rB /rA )2

Since the absolute magnitude M is defined as the apparent magnitude that a star would have if it were10 parsecs from us, we have:

m - M    =   -2.5 log ( 10 /r )2  =  -2.5 log ( r /10 )-2  =  -2.5 x -2 x log ( r /10 )

i.e.

m - M   =  5 log ( r/10 )

This equation is very useful as it allows astronomers to calculate the distance of stars. By measuring m and M, the distance can easily be found.

(g) recall and use the relationship m - M = 5 lg (r/10).

(h) sketch and interpret a Hertzsprung-Russell diagram of absolute magnitude plotted against temperature in order to recognise and identify different classes of star.

The Hertzsprung-Russell Diagram plots luminosity as a function of temperature for stars. The H-R Diagram is an extremely useful way to follow the changes that take place as a star evolves.

Hertzsprung-Russell diagramAbout 90% of the known stars lie on the Main Sequence, because that is where stars spend most of their lives, burning hydrogen to helium through nuclear reactions. As stars live out their lives, changes in the structure of the star are reflected in changes in stars temperatures, sizes and luminosities, which cause them to move in tracks on the H-R Diagram.

(i) describe how clouds of gas, consisting mainly of hydrogen and helium, form into young Main Sequence stars.

The primordial matter after the Big Bang collapsed into stars and galaxies over a very long period of time.

The stars perform nuclear fusion reactions in their cores, creating "metal" elements heavier than helium, such as carbon and oxygen.

Big stars have short lives and they eventually exploded, seeding space with constituents of new stars and the heavier elements needed to create rocky planets and biological organisms.

Star formation continues today, though clearly at a much lower overall rate than existed in the first generation of star formation.

The hydrogen and helium created in the Big Bang and the much smaller concentrations of "metals" created by stars afterward are now scattered through space. Most of the material is still hydrogen, existing as an exceedingly thin gas known as the "interstellar medium". Light and radiation from stars breaks up molecules and so most of the interstellar medium is in the form of monatomic hydrogen.

Gravitational forces can cause the interstellar medium to collect into much denser clouds of gases and dust. Molecules can also form inside such cold dark clouds, and so they are known as "molecular clouds".

A molecular cloud can remain stable and dark for millions of years, but it will eventually begin to collapse into itself under its own gravity. Hydrogen, the predominant element in such molecular clouds, tends to gather into masses known as "molecular cores" or "dense cores". These dense cores are only at about 10 degrees Kelvin.

These cores become hot spots, or protostars and eventually become main sequence stars.

(j) describe the probable evolution of the Sun into a red giant and represent this evolution on a Hertzsprung-Russell diagram.

Evolution of a star like the Sun

The Sun is a typical star.

(k) recall that the Main Sequence stars may evolve into red giants, white dwarfs, supernovae, neutron stars or black holes.

Death of Stars

The outcome of a star's struggle between gravity and pressure depends entirely on its birth mass.

Binary  system: black hole sucks in its  companion
Black Hole sucks in neighbouring star

(l) recall and understand that the nuclear processes occurring in a star, the time it spends on the Main Sequence and its ultimate fate depends on its mass.

Nuclear energy can be produced by either of two types of reactions: fission, the splitting apart of a massive atomic nucleus, or by fusion of lighter nuclei into a heavier nucleus.

(m) describe the structure of our own Galaxy and the Sun’s position in it.

To the right is a picture of the real Milky Way taken by the satellite COBE. The Sun does not lie near the centre of our Galaxy - the "nuclear bulge". It actually lies about 8 kpc from the centre (towards the outer edge) on what is known as the "Sagittarius" arm of the Milky Way.


Spiral structure of Milky WayThe Milky Way system is a spiral galaxy consisting of 100- 600 billion stars, plus gas and dust arranged into three general components:

The Halo consists of the oldest stars known, including about 146 Globular Clusters, believed to have been formed during the early formation of the Galaxy with ages of 10-15 billion years from their H-R Diagrams. The halo is also filled with a very diffuse, hot, highly-ionized gas. The very hot gas in the halo produces a gamma-ray halo.

Neither the full extent nor the mass of the halo is well known. Investigations of the gaseous halos of other spiral galaxies show that the gas in the halo extends much further than previously thought, out to hundreds of thousands of light years. Studies of the rotation of the Milky Way show that the halo dominates the mass of the galaxy, but the material is not visible, and is now called dark matter.

The disc of the Galaxy is a flattened, rotating system which contains the Sun and other young-to-intermediate stars. The Sun sits about 2/3 of the way from the centre to the edge of the disk (about 25,000 l.y. by the most modern estimates). The Sun revolves around the centre of the galaxy about once every 250 million years. The galaxy about contains atomic (HI) and molecular (H2) gas and dust.

Radio source at centre of our Galaxy.Sagittarius A* is a radio source lying near the centre of the galaxy (right). The evidence is mounting that Sag A* is a black hole 2-3 million times the mass of the sun.

The most common type of galaxy is called a "spiral galaxy." Not surprisingly, spiral galaxies look like spirals, with long arms winding toward a bright bulge at the centre. About 77% of the observed galaxies in the universe are spiral galaxies. Our own galaxy, the Milky Way, is a typical spiral galaxy.

Some spiral galaxies have a bright bar running through them. These are called barred spiral galaxies. 20% of spiral galaxies are barred spiral galaxies. Galaxies without a bar are simply called spiral galaxies.

Since the Earth lies within the plane of the Milky Way disc, dust prevents us from determining the large-scale structure of the Galaxy's spiral pattern beyond a few thousand light-years. It is still not known if our galaxy is a normal spiral like our neighbour Andromeda, or a barred spiral like that shown to the left.


(n) explain qualitatively how other galaxies differ from our own.

Interstellar medium: Although space is very empty and the stars in the Milky Way are very far apart, the space between the stars contains a very diffuse medium of gas and dust astronomers call the interstellar medium (ISM). This medium consists of neutral hydrogen gas (HI), molecular gas (mostly H2), ionised gas (HII), and dust grains. Although the interstellar medium is, by several orders of magnitude, a better vacuum than any physicists can create in the laboratory there is still about of 5-10 billion M of gas and dust out there, comprising approximately 5% of the mass of visible stars in the Galaxy.

Galactic clusters: Most galaxies are found in gravitationally-bound groups called "clusters". Clusters can be rich, with several thousand galaxies, or poor, with only 20 or 30 members. The Local Group, the cluster to which our own Milky Way galaxy belongs, is made up of about 30 galaxies.

(o) recall and use Newton’s law of Gravitation to relate the mass of a galaxy to orbital speed within it.

If you know the size of a satellite's orbit and how quickly it is moving round the star or planet, you can find the mass of the central object. The same principle can be used to calculate the mass of the Galaxy. In this case, the two masses involved are the mass m of the star and the mass M of the part of the Galaxy that is inside the star's orbit. For most orbits, M is much larger than m, so it is safe to ignore the star's mass.

Set the force of gravity equal to the centripetal force and solve for M:


GMm
=
mv2
r2
r
Cancelling m M = rv2
& rearranging: G

 

Thus a galaxy's mass is found by measuring the orbital speed it's stars (or gas clouds) and their distance from the centre of the galaxy.

5.5.3 Structure of the Universe

(a) recall Olbers' paradox.
(b) interpret Olbers' paradox to explain why it suggests that the model of an infinite, static Universe is incorrect.

Olbers' Paradox: why is the sky dark at night?

The paradox can be traced as far back as Kepler in 1610. It was not popularised as a paradox until Heinrich Olbers took it up in the nineteenth century. It goes like this:

Assuming the universe is infinitely large and contains an infinite amount of roughly uniformly distributed stars, then should not the night sky be blazing with light from all these stars? Even if the farther stars are fainter, their number increases with distance, thus there should be an enormous amount of the star light reaching Earth. The reality, though, is that the night sky is quite dark.

OR

In an infinite static universe nearly every line of sight would end on the surface of a star. Thus one would expect that the whole sky would be as bright as the sun, even at night.

One current idea as a solution to the paradox is that the lifetime of a star is about 1010 years. The years for the Universe to reach thermal equilibrium is about 1024 years. Many stars have been born, lived, and died already. Basically at any one time there are not enough stars active to fill the space of the Universe with enough light to brighten the night sky.

Normal matter, dark matter, dark energy

The content of the Universe is widely thought to consist of three types of substance: visible matter, dark matter and dark energy.

Dark matter dominates the Universe and is invisible to current telescope technology. It cannot be detected directly because it emits no light or radiation. Its presence, though, can be inferred from the way galaxies rotate: their stars move so fast they would fly apart if they were not being held together by the gravitational attraction of some unseen material.

For the first time, astronomers have put some real numbers on the physical characteristics of dark matter. A Cambridge team has recently been able to measure its "temperature" and to place limits on how it is packed in space. Using the biggest telescopes in the world, the group has used the movement of stars to "trace" the impression of the dark matter among them and weigh it very precisely. The researchers have been able to establish that the galaxies contain about 400 times the amount of dark matter as they do normal matter.

The apparent speed of dark matter particles (about 9km/s) is a big surprise. Current theory had predicted dark matter particles would be extremely cold, moving at a few millimetres per second, but these observations prove the particles must actually be quite warm (in cosmic terms) at 10,000 degrees.

Now physicists trying to further the understanding of the forces of nature were already starting to believe that new and exotic particles of matter must be abundant in the Universe. These would hardly ever interact with normal matter and many now believe that these particles are the dark matter. At the present time, even though many experiments are underway to detect dark matter particles, none have been successful. Nevertheless, astronomers still believe that somewhere between 30% and 99% of the Universe may consist of dark matter. That it exists is one of the few things on which researchers have been certain.

The most likely candidate for dark matter material is the so-called weakly interacting massive particle, or Wimp. Scientists believe these are relic particles produced in the Big Bang. Their presence would go a long way to explaining the structure and geometry of the Universe we observe.

Experimental crystal detectors placed down the bottom of deep mines are hoping to record the passage through normal matter of these hard to grasp dark matter particles. Researchers would hope also that future experiments in particle accelerators will give them greater insight into the physics of dark matter.

The Cambridge efforts have produced an additional, independent result: the detailed study of the dwarf galaxies has allowed the scientists to weigh our own galaxy more precisely than ever before. It turns out the Milky Way is more massive than we thought. It looks as though the Milky Way is the biggest galaxy in the local Universe - bigger even than Andromeda. It was thought until just a few months ago that it was the other way around.

Dark energy is the latest addition to the contents of the Universe. Originally, Einstein introduced the idea of an all-pervading ‘cosmic energy’; before he knew that the Universe is expanding. The expanding Universe did not need a ‘cosmological constant’ as Einstein had called his energy.

However, in the 1990s observations of exploding stars in the distant Universe suggested that the Universe was not just expanding but accelerating as well. The only way to explain this was to reintroduce Einstein’s cosmic energy in a slightly altered form that we now call ‘dark energy’. No one knows what the dark energy might be.

(c) understand what is meant by the Cosmological principle.

Application of the Theory of General Relativity to the large-scale structure of the Universe leads to various cosmological theories. Of these, the most important are a class of solutions called Friedmann cosmologies that lead to what is termed the hot big bang. The starting point for these theories is what is termed cosmological principle:

Viewed on sufficiently large distance scales, there are no preferred directions or preferred places in the Universe.

Stated simply, this principle means that averaged over large enough distances, one part of the Universe looks approximately like any other part.

This clearly is not true on short distance scales: your classroom probably looks rather different from your dormitory room, and we certainly see distinguishing structure like galactic superclusters and the Great Wall up to at least 100-200 Mpc scales. However, well beyond those distance scales there is strong observational evidence for the cosmological principle.

(d) recall and interpret Hubble’s law for the expansion of the Universe and the size of the observable Universe.

The terms known universe, observable universe, or visible universe are often used to describe the part of the universe that can be seen or otherwise observed by humanity. Due to the fact that cosmic inflation removes vast parts of the total universe from our observable horizon, most cosmologists currently accept that it is impossible to observe the whole continuum.

The Hubble Limit is a concept in cosmology that is related to the Big Bang Theory. It refers to the limit where objects receding from the observer are receding at the speed of light. It is named after the astronomer Edwin Hubble, who was the first to discover that objects on a galactic scale are moving away from us. In the aftermath of the Big Bang, everything in the universe is flying apart and, due to the fact that the speed of light is constant, more distant objects appear to be receding at a greater velocity. Eventually an object will appear to have a velocity that is the speed of light: an object at this point is known to be at the Hubble Limit.

The dominant motion in the universe is the smooth expansion known as Hubble's Law.

V = H0D        or        Recessional Velocity = Hubble's Constant x distance

While in general galaxies follow the smooth expansion, other motions cause slight deviations from the line predicted by Hubble's Law. The diagram to the left shows a typical plot of distance versus recessional velocity, with each point showing the relationship for an individual galaxy. You can se that few of the points fall exactly on the line. This is because all galaxies have some additional residual motion in addition to the pure expansion.

(e) convert Hubble’s ‘constant’ H0 from its conventional units (km s-1 Mpc-1 ) to SI (s-1 )

The constant H0 gives the rate of recession of distant astronomical objects per unit distance away. The fact that more distant objects are receding more rapidly than closer ones is interpreted as implying expansion of the universe and is the main observation which led to the Big Bang theory. H0 changes as a function of time depending on the precise cosmological models as the expansion of the universe slows due to gravitational attraction of the matter within it. Most models give an age of the universe of order H -1 (which has units of time).

The current value of the Hubble constant is hotly debated by opposing camps. Take it to be about 70 (km s-1)/Mpc        {+ or - about 50%}


(f) describe and interpret the significance of the 3 K microwave background radiation.

One of the profound observations of the 20th century is that the universe is expanding. This implies that the universe was smaller, denser and hotter in the distant past.

Cosmic background radiation is the primordial radiation field that filled and still fills the universe, having been created in the form of gamma rays at the time of the big bang. At that time in the very early universe, the radiation temperature was 273 million degrees above absolute zero. At these huge temperatures, there were no atoms, only free protons and electrons. Thus the universe was filled with high frequency electromagnetic radiation and plasma.

The cosmic background radiation has now cooled so that its temperature today is about 3K (or 2.725K to be more precise) and its peak wavelength is near 1.1mm, which is in the microwave portion of the electromagnetic spectrum. For this reason the cosmic background radiation we now detect is often called 3K background radiation or cosmic microwave background (CMB) radiation

Cosmic Microwave Background RadiationWhen the visible universe was only one hundred millionth its present size, its temperature was 273 million degrees above absolute zero and the density of matter was comparable to the density of air at the Earth's surface. At these high temperatures, there were no atoms, only free protons and electrons.

Roughly 300,000 years after the Big Bang, when the universe was roughly 1000 times smaller than it is now, the temperature of the Universe had dropped sufficiently for electrons and protons to combine to form neutral hydrogen atoms. From this time onwards, the cosmic radiation photons were only able to interact very weakly with these atoms; they have propagated freely ever since (the Universe effectively became 'transparent', while constantly losing energy - i.e. cooling - because its wavelength is stretched (red-shifted) by the expansion.

Originally, the radiation temperature was about 3000 degrees Kelvin. Today, the CMB radiation is very cold - just under 3° above absolute zero (2.725K to be more accurate). Thus this radiation 'shines' primarily in the microwave portion of the electromagnetic spectrum and is invisible to the naked eye. However, it fills the universe and can be detected everywhere we look. In fact, if we could see microwaves, the entire sky would glow with a brightness that was astonishingly uniform in every direction. The temperature is uniform to better than one part in a thousand! This uniformity is one compelling reason to interpret the radiation as remnant heat from the Big Bang: it would be very difficult to imagine a local source of radiation that was this uniform.

The cosmic microwave background photons easily scatter off electrons. (This process of multiple scattering would produce what is called a “thermal” or “blackbody” spectrum of photon energies - something that has been confirmed through tremendously accurate measurements.) The behaviour of CMB photons moving through the early universe is analogous to the propagation of light through the Earth's atmosphere. Water droplets in a cloud are very effective at scattering light, whereas light moves freely (pretty much in a straight line) through clear air. Thus, on a cloudy day, we can look through the air out towards the clouds, but can not see through the opaque clouds. Cosmologists studying the cosmic microwave background radiation can look through much of the universe back to when it was opaque: a view back to 400,000 years after the Big Bang. This “wall of light“ is called the surface of last scattering since it was the last time most of the CMB photons directly scattered off of matter. When we make maps of the temperature of the CMB, we are mapping this surface of last scattering.

Observers detecting this radiation today are able to see the Universe at a very early stage on what is known as the `surface of last scattering'. Photons in the cosmic microwave background have been travelling towards us for over ten billion years, and have covered a distance of about a million billion billion miles.

Since light - and all other electromagnetic radiation - travels at a finite speed, astronomers observing distant objects are looking into the past. Astronomers observing distant galaxies with the Hubble Space Telescope can see them as they were only a few billion years after the Big Bang. (Most cosmologists believe that the universe is between 12 and 14 billion years old.)

The strongest evidence that something like the Big Bang really happened is the Cosmic Microwave Background radiation (CMB), predicted first, then later discovered in 1965. Gamma-rays are part of the thermal radiation present in the early hot Universe. As the Universe expanded and cooled, the radiation field cooled along with it. When matter and radiation "decoupled" with the formation of atoms a million years after the Big Bang, the radiation had cooled to visible light. Although the matter distribution has become complicated with the formation of galaxies & stars since that time, the light has simply continued to cool with the expansion.

Only with very sensitive instruments can cosmologists detect fluctuations in the cosmic microwave background temperature. By studying these fluctuations, cosmologists can learn about the origin of galaxies and large-scale structures of galaxies and they can measure the basic parameters of the Big Bang theory.

(g) understand that the standard (big bang) model of the Universe implies a finite age for the Universe.

http://cassfos02.ucsd.edu/public/tutorial/Cosmology.html

(h) recall and use the expression t ˜ 1/H0 to estimate the order of magnitude of the age of the Universe.

Hubble's Velocity-Distance relationship

v = Hod

established that the Universe is expanding. Edwin Hubble made a plot of recession velocity vs distance for galaxies that he had observed he found a straight line relationship. The slope of this line, known as the Hubble Parameter, H 20 (km/s)/million l.y., has units of 1/time. It is easy to see that, if the Universe is expanding at the present time, then at some point in the past, all matter was once together. Thus, 1/H, called the Hubble Time is an estimate of the Age of the Universe, about 15 billion years.

If we rewind the motion picture representing the history of the Universe, we can understand a great deal about its early state, just after the Big Bang. In its early stages the Universe was simpler than it has ever been. It was very hot and in a state of Thermal Equilibrium, that is its temperature determined all its other properties. Just after the Big Bang, temperatures were so high that particle pairs could be created purely out of the heat energy present. For example, a pair of thermal photons - which would be gamma-rays at these temperatures - might react to form an electron/positron pair:

+ e+ + e-

During its early phases the Universe was radiation dominated, that is the photons dominated the energy and pressure of the Universe. As the Universe expanded, it cooled, T 1/R, where R is some measure of the "scale of the Universe".

5.5.4 Information from Stellar Observation

(a) understand that stars and galaxies are detected by the electromagnetic radiation which they emit, whilst planets are detected by reflected sunlight.

Stars and galaxies are detected by the electromagnetic radiation which they emit, whilst planets, asteroids and comets are detected by reflected sunlight.

(b) sketch and interpret a graph to illustrate the variation with wavelength of the transparency of the Earth’s atmosphere for the electromagnetic spectrum.

Only a small fraction of the radiation produced by cosmic objects actually reaches our eyes - in part because of the opacity of Earth's atmosphere. Opacity is the extent to which radiation is blocked by the material through which it passes and is the opposite of transparency. There are only a few "windows," at well-defined locations in the electromagnetic spectrum, where the Earth's atmosphere is transparent.

In much of the radio and visible portions of the spectrum, the transparency is high, so we can observe the Universe from the ground using those wavelengths.

Throughout the infrared range, the atmosphere is partially transparent, so we can also make limited infrared observations from the ground. Moving to the tops of mountains, above as much of the atmosphere as possible, improves such observations.

In the rest of the spectrum, however, the atmosphere is opaque. Ultraviolet, x-ray, and gamma-ray observations can be made only from above the atmosphere, mostly from satellites.

(c) explain how the composition of stellar atmospheres may be obtained from stellar spectra.

Large numbers of stars exhibit a small number of distinct patterns in their spectral lines. Classification by spectral features has proved to be a powerful tool for understanding stars.

Continuous, Emision and absorption spectraThe three types of spectrum (continuous, emission and absorption) that can be produced are illustrated to the right.

Radiation by matter
The wavelengths of the radiation emitted by matter depends on temperature. If you turn on your toaster in the dark, you can see it glow: this is the visual spectrum radiated by the hot metal. The hotter the toaster's radiating element, the higher the energy (and frequency) of the radiation it can emit. At low temperatures you see only red, but if you could increase the temperature high enough, the toaster would emit blue and then violet light as well as red. At a million Kelvin it would even emit gamma rays!. At very low temperatures it will also radiate. At room temperature, it radiates infrared. Even in the cold of interstellar space, the toaster would produce radio photons.

As a general rule, as temperature goes up, a body produces ever more radiation at all wavelengths above a limit gets closer and closer to the shortest wavelengths. (A cold body radiates radio, a warmer one infrared and radio, warmer yet visual, infrared, and radio, and so on, all kinds present increasing in amount with increasing temperature.)

A gas under high pressure will radiate as well as a hot solid. Star colours thus reflect temperature: reddish stars cool (3000 to 4000 K), bluish ones hot (over 20,000 K). As a result, we can determine the temperature of a star from its colour - more specifically from the details about how the radiation is distributed throughout its spectrum.

Absorption lines in stellar spectra
The deeper you go into a star, the hotter and denser the gas. The lower layers tend to radiate all the wavelengths rather like a hot solid, while the upper layers act something like the low density gas of the last paragraph through which the radiation passes. Stars are made of the same stuff as found in the Earth (though not in the same proportions) and contain all of nature's chemical elements. As a result, the spectrum of a star displays an extraordinary mixture of absorption lines. Over 100,000 absorption lines are visible in the Sun's spectrum.

Emission lines
What goes up must come down. Electrons, like anything else, will attempt to seek their lowest energies. If electrons in an atom, molecule or ion gain energy by the absorption of photons, or perhaps by collisions, they must eventually lose it again. They can lose it in collisions or they can, instead of absorbing photons, radiate them. The emission wavelengths, like the absorption wavelengths, are tightly defined.

If we look at a heated low-density gas that has no bright source behind it, we will see bright lines of colour at the same spectral wavelengths at which we before saw dark absorptions. For any given atom, ion or molecule, the emission spectrum is a simple reversal of the absorption spectrum. Emission lines are radiated by street lamps (the orange ones radiating sodium lines, the blue ones mercury lines), neon signs, and fluorescent bulbs. They are also radiated by clouds of interstellar gas that are heated and ionized by nearby hot stars. Examples are the great Orion Nebula (a cloud of interstellar gas), planetary nebulae and remnants of supernova. (Under some special circumstances, stars can produce emission lines too.)

Analysis of absorption lines
The absorption lines in the Sun and stars can be identified with individual chemical elements or molecular compounds by comparing their positions in the spectrum (their wavelengths) with those observed from pure sources in the laboratory. Some absorptions are very weak, just shallow dips in the spectrum, whereas others are completely black. The "strength" of an absorption line -- the amount of energy removed from the spectrum -- depends on the amount of the particular chemical element in the star causing the line and on the efficiency of absorption. The efficiency is crucial. Hydrogen dominates the Sun, yet absorption lines of ionized calcium dominate the solar spectrum even though there is 440,000 times as much hydrogen as calcium. Hydrogen has a low efficiency of absorption, whereas that of ionized calcium is very high. The efficiency depends on the availability of electrons to move to higher energies and on atomic factors, namely the likelihood of absorption in the presence of a passing photon. The efficiencies depend critically on temperature and can be calculated from theory or measured in the laboratory. Once they are known, we can calculate the abundances of the atoms from the strengths of the absorption lines and therefore calculate the chemical composition of the outer part of a star. Relative absorption line strengths can also be used to find temperatures and densities. Similar rules can be developed to analyse the emission lines radiated by interstellar gas clouds, from which we learn the compositions of the nebulae, including those of the planetary nebulae.

The spectral sequence
Because the efficiencies of absorption depend on temperature, so do the appearances of the spectra of the stars. Stellar spectra were first observed in the middle of the 19th century. To the great confusion of the astronomers of the time, most spectra looked nothing like the solar spectrum. Some, like that of Vega, had powerful hydrogen lines, whereas others had none at all and displayed what were later shown to be molecular lines of titanium oxide. It looked as though different stars were made of different elements. As an aid to understanding, astronomers began classifying the spectra, the schemes culminating about 1890 in the one still used today, in which stars are lettered according to the strengths of their hydrogen lines. The result was the classic seven-group sequence OBAFGKM. A bit over a century later, as a result of new technologies, astronomers added another two classes whose spectra contained molecules, L and T. About the first thing any astronomer wants to know about a star is its class. The Sun is class G.

In the modern spectral sequence, OBAFGKMLT, the hydrogen absorption lines weaken in both directions away from class A. Various other absorptions round out the picture. It was noted very early that the spectral sequence in this form correlates with colour, ranging from a blue tint for O and B stars to reddish for class M. Since colour depends on surface temperature, so must the spectral class. Stars of class T and cool L radiate only in the infrared and are invisible to the eye.

THE SPECTRAL SEQUENCE
Class Spectrum Colour Temperature (K)
O ionised and neutral helium, weakened hydrogen bluish 31,000-49,000
B neutral helium, stronger hydrogen blue-white 10,000-31,000
A strong hydrogen, ionised metals white 7400-10,000
F weaker hydrogen, ionised metals yellow-white 6000-7400
G still weaker hydrogen, ionised and neutral metals yellowish 5300-6000
K weak hydrogen, neutral metals orange 3900-5300
M little or no hydrogen, neutral metals, molecules reddish 2200-3900
L no hydrogen, metallic hydrides, alkali metals red-infrared 1200-2200
T methane bands infrared under 1200

(d) understand what is meant by the Doppler effect.

The Doppler Effect

Remember how the an ambulance siren's pitch changed as the vehicle raced towards, then away from you? First the pitch became higher, then lower.

Originally discovered by Christian Doppler (1800s), this change in pitch results from a shift in the frequency (and so wavelength) of the sound waves, as illustrated in the picture to the left.

As the ambulance approaches, the sound waves from its siren are compressed towards the observer. The intervals between waves diminish, which translates into an increase in frequency or pitch. As the ambulance recedes, the sound waves are stretched relative to the observer, causing the siren's pitch to decrease. By the change in pitch of the siren, you can determine if the ambulance is coming nearer or speeding away. If you could measure the rate of change of pitch, you could also estimate the ambulance's speed.

By analogy, the electromagnetic radiation emitted by a moving object also exhibits the Doppler effect. The radiation emitted by an object moving toward an observer is squeezed: the wavelength is shortened and the frequency appears to increase. In contrast, the radiation emitted by an object moving away is stretched: the wavelength shortens and the frequency increases.

(e) recall and use Δλ/λ = v/c.

The velocity v of an electromagnetic-radiation-emitting source relative to an observer is given by the equation:

Δλ/λ = v/c              where c is the speed of light, λ is the wavelength of the radiation and Δλ is the shift in its wavelength.

(f) understand what is meant by red-shift and by blue-shift and appreciate simple differences between red-shift and terrestrial Doppler effects.

As in the ambulance analogy, shifts in the wavelengths, and thus frequencies, exhibited by the electromagnetic radiation from stars, galaxies and gas clouds also indicate their motions with respect to the observer.

In astronomy, the Doppler effect was originally studied in the visible part of the electromagnetic spectrum. So a shift towards the longer wavelength (red) end of the visible spectrum is referred to as a red shift. The less commonly observed shift towards the short wavelength (blue) end of the spectrum is referred to as a blue shift.

Today, the term Doppler shift, as it is also known, is used not only for the visible part of the spectrum, but also for electromagnetic waves in all portions of the spectrum. Radiation is red shifted when its wavelength increases, and blue shifted when its wavelength decreases.

Astronomers use Doppler shifts to calculate precisely how fast stars and other astronomical objects move toward or away from Earth. For example, the spectral line emitted by hydrogen gas in distant galaxies is often observed to be considerably red shifted. The spectral line emission, normally found at a wavelength of 21 centimetres on Earth, might be observed at 21.1 centimetres instead. This 0.1 centimetre red shift would indicate that the gas is moving away from Earth at over 1,400 kilometres per second.

Shifts in frequency result not only from relative motion. Gravity itself can affect the frequency of electromagnetic radiation. Also, the phenomenon called O Cosmological Red shift results not from motion through space, but rather from the expansion of space itself following the Big Bang.

5.5.5 How the Universe may evolve

(a) appreciate that there is no direct experimental evidence for the physics involved at the energies prevailing during the evolution of the Universe before about l ms.

There is no direct experimental evidence for the physics involved at the energies prevailing during the evolution of the Universe before about l ms.

(b) outline the difficulties involved in projecting the evolution of the Universe back before 0.01s.
(c) describe qualitatively the evolution of the Universe from 0.01s after the big bang to the present, including the production of an excess of matter over antimatter, the formation of light nuclei, the recombination of electrons and nuclei and the formation of stars, galaxies and galactic clusters.

About 11 to 15 billion years ago all of the matter and energy in the Universe was concentrated into an area the size of an atom. At this moment, matter, energy, space and time did not exist. Then suddenly, the Universe began to expand at an incredible rate and matter, energy, space and time came into being (the Big Bang). As the Universe expanded, matter began to coalesce into gas clouds, and then stars and planets. Our solar system formed about 5 billion years ago when the Universe was about 65 % of its present size. Today, the Universe continues to expand.

Assuming the validity of the Big Bang theory - a theory, albeit one that has a lot of evidence going for it - the universe can be defined in terms of time, space, and temperature. At the actual start of the Big Bang, there is no size (only a point) and temperature is infinite. This is another way of saying what we have here is a Singularity, a point at which the known laws of the universe no longer apply. As the universe expanded it went through various phases and stages, referred to as "eras" although most only lasted for a trillionth of a second or so.

Why do Most Scientists Accept the Big Bang Theory?

The acceptance of this theory by the scientific community is based on a number of observations. These observations confirm specific predictions of the Big Bang theory. In a previous section, we learned that scientists test their theories through deduction and falsification. Predictions associated with the Big Bang theory that have been tested by this process are:

  1. If the Big Bang did occur, all of the objects within the Universe should be moving away from each other. In 1929, Edwin Hubble documented that the galaxies in our Universe are indeed moving away from each other.
  2. The Big Bang should have left an "afterglow" from the explosion. In the 1960s, scientists discovered the existence of cosmic background radiation, the so-called "afterglow" after the Big Bang explosion. Our most accurate measurements of this cosmic radiation came in 1989. These measurements indicated that the spectrum of the cosmic radiation varied agreed with what was predicted to a high level of accuracy.
  3. If the Universe began with a Big Bang, extreme temperatures should have caused 25 % of the mass of the Universe to become helium. This is exactly what is observed.
  4. Matter in the Universe should be distributed homogeneously. Astronomical observations from the Hubble Space Telescope do indicate that this is indeed the case.

How will the Universe End?

Cosmologists have postulated two endings to the Universe:

  1. If the Universe is infinite or has no edge, it should continue to expand forever.
  2. A Universe that is finite or closed is theorized to collapse when expansion stops because of gravity. The collapse of the Universe ends when all matter and energy is compressed into the high energy, high-density state from which it began - the Big Crunch. Some theorists have suggested that the Big Crunch will produce a new Big Bang and the process of an expanding Universe will begin again. This idea is called the Oscillating Universe Theory.

Nucleosynthesis in the Early Universe

The term nucleosynthesis refers to the formation of heavier elements, atomic nuclei with many protons and neutrons, from the fusion of lighter elements. The Big Bang theory predicts that the early universe was a very hot place. One second after the Big Bang, the temperature of the universe was roughly 10 billion degrees and was filled with a sea of neutrons, protons, electrons, anti-electrons (positrons), photons and neutrinos. As the universe cooled, the neutrons either decayed into protons and electrons or combined with protons to make deuterium (an isotope of hydrogen). During the first three minutes of the universe, most of the deuterium combined to make helium. Trace amounts of lithium were also produced at this time. This process of light element formation in the early universe is called “Big Bang nucleosynthesis” (BBN).

Nucleosynthesis in Stars

Elements heavier than lithium are all synthesized in stars. During the late stages of stellar evolution, massive stars burn helium to carbon, oxygen, silicon, sulphur, and iron. Elements heavier than iron are produced in two ways: in the outer envelopes of super-giant stars and in the explosion of a supernovae. All carbon-based life on Earth is literally composed of stardust.


(d) understand that the Universe may be ‘open’, ‘flat’, or ‘closed’, depending on the mean density of matter in the Universe.

What is meant by an "open," "flat," or "closed" Universe?

These different descriptions concern the future of the Universe: whether it will continue to expand forever or to expand up to a point and then contract. The future of the Universe hinges upon its density - the denser the Universe is, the more powerful the effect of gravity.

Closed universe. If the Universe is sufficiently dense, the Universe will cease to expand at some point in the distant future and begin to contract. This is termed a closed Universe. If this is the case, the Universe is finite in size, though unbounded. (Its geometry is, in fact, similar to the surface of a sphere. One can walk an infinite distance on a sphere's surface, yet the surface of a sphere clearly has a finite area.)

Graph of open, flat & closed universesOpen universe. If the Universe is not sufficiently dense, then the expansion will continue forever. This is termed an open Universe. One often hears that such a Universe is also infinite in spatial extent. This is possibly true; recent research suggests that it may be possible for the Universe to have a finite volume, yet expand forever.

Flat universe. One can also imagine a Universe in which the gravity effects and expansion effects exactly cancel each other out. The Universe stops expanding only after an infinite amount of time. This Universe is also (possibly) infinite in spatial extent and is termed a flat Universe, because the sum of the interior angles of a triangle sum to 180 degrees - just like in the plane or "flat" geometry (Euclidean geometry) at school. For an open Universe, the geometry is negatively curved s,o that the sum of the interior angles of a triangle is less than 180 degrees; in a closed Universe, the geometry is positively curved and the sum of the interior angles of a triangle is more than 180 degrees.

The critical average density that separates an open Universe from a closed Universe is 1.0 x 10-29 g/cm3. Current observational data are able to account for about 10-30 % of this value, suggesting that the Universe is open. However, motivated by inflationary theory, many theorists predict that the actual density in the Universe is essentially equal to the critical density and that observers have not yet found all of the matter in the Universe.

-------

The Fate of the Universe

The three possible types of expanding universes are called open, flat, and closed universes. If the universe were open, it would expand forever. If the universe were flat, it would also expand forever, but the expansion rate would slow to zero after an infinite amount of time. If the universe were closed, it would eventually stop expanding and re-collapse on itself, possibly leading to another big bang. In all three cases, the expansion slows, and the force that causes the slowing is gravity.

A simple analogy to understand these three types of universes is to consider a spaceship launched from the surface of the Earth:

For the last eighty years, astronomers have been making increasingly accurate measurements of two important cosmological parameters: Ho - the rate at which the universe expands (the Hubble Constant); and ω - the average density of matter in the universe. Knowledge of both of these parameters will tell us which of the three models describes the universe we live in, and thus the ultimate fate of our universe.

The Heavier Elements

Astronomers are not only interested in the fate of the universe; they are also interested in understanding its present physical state. One question they try to answer is: why is the universe composed mainly of hydrogen and helium? A related question: what is responsible for the relatively small concentration of the heavier elements?

It has been calculated that helium could well have been be formed in a substantial quantity the primordial Universe. However, the heavier elements are still being synthesized within the cores of stars or during supernovae.

If the universe were hotter and denser in the past, radiation should still be left over from the early universe. This radiation would have a well-defined spectrum (called a blackbody spectrum) that depends on its temperature. As the universe expanded, the spectrum of this light would have been red-shifted to longer wavelengths, and the temperature associated with the spectrum would have decreased by a factor of over one thousand as the universe cooled.

The Cosmic Microwave Background Radiation

While two scientists in New Jersey scientists were testing a new satellite's antenna in 1963, they found mysterious microwaves coming equally from all directions. After rigorously checking to see if anything was wrong with the antenna, they realized that what they were detecting was the radiation - called the Cosmic Microwave Background Radiation - predicted years earlier. This discovery convinced most astronomers that the Big Bang theory was correct.

After this discovery, astrophysicists began to study whether they could use its properties to study what the universe was like long ago. According to Big Bang theory, the radiation contained information on how matter was distributed over ten billion years ago, when the universe was only 500,000 years old.

At that time, stars and galaxies had not yet formed. The Universe consisted of a hot soup of electrons and nuclei. These particles constantly collided with the photons that made up the background radiation, which then had a temperature of over 3000 K.

Soon afterwards, the Universe expanded enough, and thus the background radiation cooled enough for the electrons and nuclei to combine to form atoms. Because atoms were electrically neutral, the photons of the background radiation no longer collided with them.

When these first atoms formed, the universe had slight variations in density, which grew into the density variations we see today - galaxies and clusters. These density variations should have led to slight variations in the temperature of the background radiation, and these variations should still be detectable today. Scientists realized that they had an exciting possibility: by measuring the temperature variations of the Cosmic Microwave Background Radiation over different regions of the sky, they would have a direct measurement of the density variations in the early universe, over 10 billion years ago.

Density Variations in the Early Universe

Map of the sky as scanned by COBE,
emphasising the minute temperature variations of the background radiation

In 1990, a satellite called the Cosmic Microwave Background Explorer (COBE) measured background radiation temperatures over the whole sky. COBE found minute density fluctuations in the early universe. These initial density variations would be the seeds of structure that would grow over time to become the galaxies, clusters of galaxies, and superclusters of galaxies observed today. With the data available today, astronomers will be able to reconstruct the evolution of structure in the universe over the last 10 to 15 billion years. Using this information, we will have a deep understanding of the history of the universe - an amazing scientific achievement.

But measuring the evolution of the density variations in the universe still does not answer the most important question: why does the universe contain these differences in density in the first place? To answer this question, astronomers and astrophysicists ned to construct theories of the origin of the universe that would explain these variations.

(e) appreciate that, until the mean density of matter in the Universe is known accurately, its age cannot be determined from the Hubble constant.
(f) understand that the ultimate fate of the Universe depends on the mean density of matter in the Universe.
(g) recall that it is currently believed that the mean density of matter in the Universe is close to, and possible exactly equal to, the critical density needed for a ‘flat’ cosmology.
(h) use Newton’s law of Gravitation to derive the expression expression ρ0 = 3H02/ G, and recognize that relativity is needed for a strict derivation.
(i) use the expression ρ0 = 3H02/ G.


5.5.6 Relativity

(a) recall and explain the postulates of special relativity to include the invariance of the speed of light.

Later to become known as the Special Theory of Relativity, there ar two postulates:

  1. the speed of light is the same for all observers, regardless of their motion relative to the source of the light;
  2. all observers moving at constant speed should observe the same physical laws.

Putting these two ideas together, Einstein showed that the only way this can happen is if time intervals and/or lengths change according to the speed of the system relative to the observer's frame of reference. This flies against our everyday experience, but has since been demonstrated to hold in a number of very solid experiments. For example, scientists have shown that an atomic clock travelling at high speed in a jet plane ticks more slowly than its stationary counterpart.

(b) describe a thought experiment, involving a vehicle carrying a clock, to illustrate time dilation.

(c) outline an experiment, involving the extended half-life of muons, to illustrate time dilation.
(d) describe a thought experiment to demonstrate length contraction.
(e) use the factor √{1 - (v2/c2)} in calculations for time dilation and length contraction.

Observed length l = l0 ÷ γ      
Observed   time t = t0 x γ where and is always ≥ 1 ;  c is the speed of light;
and v is the speed of the object in question
relative to the observer
Observed mass m = m0 x γ      

l0 , t0 and m0 above are the length, time and mass from the frame of reference moving with velocity v relative to the observer.

(f) appreciate that, if mass increases with speed, there is a maximum speed to which a body can be accelerated.
(g) appreciate the significance of the principle of equivalence of inertial and gravitational forces.

The General Theory of Relativity is an expansion of the Special Theory to include gravity as a property of space.

The Principle of Equivalence as applied to general relativity can be stated:

Experiments performed in a uniformly accelerating reference frame with acceleration a are indistinguishable from the same experiments performed in a non-accelerating reference frame which is situated in a gravitational field of strength g,   i.e. a = g.

Another way of stating this fundamental principle is to say that:

Gravitational mass is identical to inertial mass.

http://cassfos02.ucsd.edu/public/tutorial/GR.html


(h) explain the effect of gravity on time in terms of a thought experiment based on the principle of equivalence.
(i) describe a thought experiment to illustrate that light passing through an accelerating glass spacecraft appears to follow a curved path to an observer within the craft.

One of the implications of the principle of equivalence is that because photons have momentum they must also have an inertial mass; and having this inertial mass they must also have a gravitational mass. Thus photons should be deflected by gravity. They should also be impeded in their escape from a gravity field, leading to the gravitational red shift and the concept of a black hole. It also leads to gravitational "lens effects".

The Principle of Equivalence applied to light travelling across a freely falling elevator suggests that light will follow a curved path in a gravitational field.


(j) appreciate the significance of observations made during the 1919 solar eclipse, and the measured precession of Mercury’s perihelion, in supporting the general theory of relativity.

Astronomical observations in support of the general theory of relativity.

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THE MATERIAL THAT FOLLOWS IS ADDITIONAL TO THE OCR SYLLABUS

 

Stellar evolution 1: http://cassfos02.ucsd.edu/public/tutorial/StevI.html

Stellar evolution 2: http://cassfos02.ucsd.edu/public/tutorial/StevII.html

Supernovae, Neutron Stars & Pulsars: http://cassfos02.ucsd.edu/public/tutorial/SN.html

Spectral classes: http://www.bbc.co.uk/dna/h2g2/A337312 & http://freespace.virgin.net/gareth.james/3__objects/Classes_of_Stars/classes_of_stars.html

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Gamma-ray detectors for detecting ultrahigh-energy cosmic rays. (Hess Collaboration)
Neutrino telescopes deep underground for detecting ultrahigh-energy cosmic rays. (NSF)
Hubble's map: Dark matter may be invisible but it accounts for most of the Universe's mass. Its gravitational attraction acts as a template, pulling normal matter - the stars in their galaxy groupings – into the large-scale structures we can see through telescopes. Hubble's new 3D map shows the "clumpy" nature of dark matter. Dark matter is invisible, so only the luminous galaxies can be seen directly. The new images are equivalent to seeing a city, its suburbs and country roads in daylight for the first time. The map shows about 1/20000th of the sky.
Supersonic gales may gust on three "gas giant" planets that orbit their stars at distances far less than that of Mercury's from the Sun. (Artist's Impression)
The helix nebula was photographed by the Spitzer Space Telescope Nasa/JPL-Caltech/K. Su (University of Arizona). The Spitzer Space Telescope, an infrared space-based observatory, was able to pick up the glow of a dusty disk circling around the stellar corpse at a distance of about 35 to 150 astronomical units. the favoured explanation is that the dust is being freshly churned up by comets that survived the death of their sun smashing into each other in the outer fringes of the white dwarf's system. The dead white dwarf star lies at the centre of the Helix nebula.

Eventually, our own Sun will turn into a white dwarf. Stars of medium or low mass become white dwarfs after they have exhausted the hydrogen which powers their thermonuclear reactions. Near the end of the nuclear burning stage, such a star expels most of its outer material, creating a planetary nebula. Only the hot core of the star remains.

Radiation from the dead star's hot core heats the expelled material, causing it to fluoresce with vivid colours.

A few million years ago, when the star was still lively like our sun, its comets - and possibly planets - would have been in stable orbits, travelling harmoniously around the star. But when the star died, any inner planets would have been burned up or engulfed as the star expanded. Outer planets, asteroids and comets would have been thrown into each other's paths. Our own Solar System is expected to undergo a similar transformation in about five billion years.Like the Helix nebula, it will sparkle with colours. Our sun, which will have become a white dwarf, will be circled by a band of surviving outer planets and colliding comets.

Material in the dusty disk surrounding the white dwarf might be falling on to the star and triggering the X-ray outbursts that are observed.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Twin Nasa spacecraft have returned panoramic images that will help scientists to study solar explosions capable of causing havoc on Earth. Stereo's Extreme Ultraviolet Imager took this close up image of the Sun.

 

 

 

 

 

 

 

 

 

 

 

 

 

The discovery in 2005 of water vapour spewing from geysers at Enceladus' south pole into space took scientists by surprise. Enceladus is an icy satellite of Saturn. How this tiny, ice-covered moon generated the amounts of heat needed to fuel these eruptions was a puzzle. Scientists now say a short-lived burst of radioactivity early in its history kicked off a "slow cooking" of its core. Scientists need to view astronomical objects at different wavelengths to fully understand them.

Hubble has concentrated on the visible spectrum - seeing the Universe as our eyes do. Chandra is sensitive to X-rays, Compton imaged gamma-rays. Spitzer (formerly known as SIRTF) specialises in infrared observations, seeing objects as they radiate at longer wavelengths.

 

The light from the star Fomalhaut was blocked to allow the planet to be seen

The HR 8799 system. Three exoplanets orbiting the same star have been imaged directly. Christian Marois and his team used the Keck and Gemini telescopes in Hawaii to view the ifraraed part of the spectrum. The star is just visible to the naked eye.

An exoplanetary system comprising three planets has been directly imaged, circling a star in the constellation Pegasus. The difficulty for astronomers imaging exoplanets has until now been that their parent stars' light swamps them - like trying to spot a match next to a floodlight at a distance of a mile.

But advances in optics and image processing have allowed astronomers to effectively subtract the bright light from stars, leaving behind light from the planets. That light can either come in the infrared, caused by the planets' heat, or be reflected starlight.

Paul Kalas of the University of California led an international group that used the Hubble Space Telescope to image the region around a star called Fomalhaut.

The star has a massive ring of dust surrounding it that appears to have a cleanly groomed inner edge.

That is in keeping with what is known as accretion theory - that young planets gather up dust and matter as they orbit.

The team estimates that the planet, dubbed Fomalhaut b, is 11bn miles away from its star, about as massive as Jupiter and completes an orbit in about 870 years. It may also have a ring around it.

According to a theoretical model that accounts for the light coming from the planets, they range in size from five to 13 times the mass of Jupiter and are probably only about 60 million years old.

The trio have similarities with our own solar system. Their orbits are comparable in size to those of the outer planets, and the smaller planets are those closest to the sun - again suggesting a system that formed through accretion.