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The Cosmic Engine
8.5.1
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outline the historical developments of models of the Universe from the time of Aristotle to the
time of Newton
identify data sources, and gather, process and analyse information to assess one of the models
of the Universe developed from the time of Aristotle to the time of Newton to identify limitations
placed on the development of the model by technology available at the time.
Aristotle –
He believes that the Earth was at the centre of the universe and that the Sun, the Moon and the visible planets, as
well as a celestial sphere containing all the stars revolved around the Earth. Aristotle had no technology with which
to examine the heaven, other than his eyes. To the unaided eye it looks as though everything is revolving around
the earth and it does not feel that the Earth is moving at all.
This type of model, with the Earth placed at the centre of the Universe is known as a geocentric model. Aristotle’s
model used a system of 55 transparent concentric spheres rotating around the Earth to explain the observed motion
of the stars and planets.
Aristarchus –
He put forward an alternative view. He suggested that:
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the Sun is much bigger than the Earth
the sun is at the centre of the Universe and the Earth orbits it
the Earth rotates on its axis once per day, producing the apparent motion of the Sun and stars.
A model such as this, with the Sun at the centre of the Universe, is known as a heliocentric model. This model was
however not favoured because it was not sufficiently detailed to allow predictions in the manner of Aristotles
Ptolemy –
Ptolemy was able to develop and refine the geocentric model of the universe by Aristotle into his own geocentric
model. The model he proposed was remarkable in predicting the observed motions of the planets.
This model lasted for over 1400 years because:
1. It worked, that is it could predict the position of a planet to within 2°.
2. It accounted for the observed planetary motions, retrograde motion and variations in brightness.
3. Unlike Aristarchus' model it did not predict the unobserved stellar parallax.
4. It placed the Earth in its natural place at the centre of things, satisfying Aristotelian philosophy.
5. It matched with common sense. We do not feel the Earth move and Ptolemy's model had a static Earth.
Nicholas Copernicus –
He proposed that the sun was stationary and that everything else revolved around circles about it. Due to fear of
the Church, Copernicus did not publish his findings until just before he died; also the belief laid out by the Church
slowed the acceptance of his theories.
There were several advantages of Copernicus' model over that of Ptolemy:
1. It could predict planetary positions to within 2°, the same as that of Ptolemy.
2. Retrograde motion of planets was explained by the relative motion between them and the Earth.
3. Distances between planets and the Sun could be accurately determined in units of the Earth-Sun distance
(ie Astronomical Units).
4. Orbital periods could be accurately determined.
5. It explained the difference between the inferior planets (Mercury and Venus) that were always observed
close to the Sun and the superior ones (Mars, Jupiter and Saturn).
6. It preserved the concept of uniform circular motion
7. It preserved Aristotle's concept of real spheres nestled inside one another.
8. Unlike Ptolemy's model it did not require the Moon to change in size.
Copernicus' model also had several problems which contributed to its failure to immediately supplant Ptolemy's
model:
1. No annual stellar parallax could be detected. Copernicus explained this as due to the fact that the stars were
a vast distance hence any parallax would be very small and difficult to detect.
2. It required a moving Earth, This would contradict Aristotelian physics and Copernicus presented no new laws
of motion to replace Aristotle.
3. By removing the Earth from its natural place it was philosophically and theologically unacceptable to many
scholars.
4. It was no more accurate than Ptolemy's in predicting planetary positions.
5. It was actually more complicated then Ptolemy's model.
Tycho Brahe – Second Dot Point
Tycho Brahe studied and plotted the night sky with meticulous care and accuracy. This was an extraordinary
achievement because he had no telescope to help him. Instead he designed and constructed his own astronomical
measuring instruments. He was able to make measurements as accurate as 0.5 arc minutes (30 arc seconds). He
was also able to record two supernovae during his lifetime.
Copernicus' model was hotly disputed, notably by the best living astronomer, Tycho Brahe. Brahe’s own model of
the universe was a combination of the geocentric and heliocentric models. While Tycho acknowledged that
Copernicus had succeeded in removing equants, he proposed a system which kept Copernicus' best results while
avoiding the serious difficulty of finding an explanation for a moving Earth.
His model had all of the planets (except Earth) revolving around the Sun, while the Sun revolved around a
stationary Earth. Brahe devised this model because he found it impossible to accept that the Earth moved. Again the
technology of the time failed to show any evidence of a moving Earth.
The evidence sought would have been a slight shift in the positions of some stars as the Earth orbited the Sun. this
affect is called parallax, and the largest parallax of any star is less than one second of an arc, or less than a
thirtieth of Brahe’s best measurements. Brahe had constructed the most sophisticated observatory of his day, and
yet he could detect no parallax effect. Therefore it is not surprising that he found it difficult to totally reject the
geocentric model.
It cannot be overemphasized that an explanation of a moving Earth was not scientifically possible, given the
dominant four-elements theory and the associated, loosely observation-based idea that anything made of the four
elements always fell toward the centre of the universe. There was simply no way, without invoking supernatural
help, to explain how it was that the Earth would not fall to the centre of a heliocentric universe. Thus the idea of a
stationary Earth was deemed to be reasonable.
Johannes Kepler –
Kepler was Brahe’s assistant. After much research and mathematical calculations using Brahe’s observations, Kepler
was able to produce an improved heliocentric model of the universe. His model said that the planets moved around
Sun, in ellipses rather than circles, and the mathematics of this was encapsulated in three laws:
Kepler's 1st Law: The Law of Ellipses:
All planets orbit the Sun in elliptical orbits with the Sun as one common focus.
Kepler's 2nd Law: The Law of Equal Areas:
The line between a planet and the Sun sweeps out equal
areas in equal periods of time.
This effect is very noticeable in comets such as Comet
Halley that have highly elliptical orbits. When in the inner
Solar System, close to the Sun at perihelion, they move
much faster than when far from the Sun at aphelion.
Kepler's Third Law: The Law of Periods or the
Harmonic Law:
The square of a planet's period, T, is directly proportional to the cube of its average distance from the Sun, r.
Mathematically this can be expressed as:
R3 / T2 = k
The implication of Kepler's Third Law is that planets more distant from the Sun take longer to orbit the Sun.
Kepler's laws of planetary motion were empirical, they could predict what would occur but could not account for
why planets behaved in such a manner.
Galileo Galilei –
Galileo was the first person to build a telescope that was used to observe the night sky. When he did this he was
able to see hundreds of stars that were not visible to the naked eye because they were too faint. Even through a
telescope the stars still appeared as points of light. Galileo suggested that this was due to their immense distance
from Earth.
Galileo made many discoveries with his telescope, one of which was that he realized that Jupiter had four
observable moons. He tracked and plotted their rotations around the planet. The significant point, was that the
moons were orbiting Jupiter, not the Earth. This was proof that Ptolemy’s complicated geocentric model was
incorrect.
He published a letter in 1613 announcing his discovery of sunspots in which he also proclaimed his belief in the
Copernican model. Monitoring sunspots showed that the Sun rotated once every 27 days and that the spots
themselves changed. The concept of a perfect, unchanging Sun thus also became untenable. His work however
caused problems with the Holy Inquisition and Galileo was placed under house arrest with minimal visitors allowed.
Sir Isaac Newton –
In 1684, Edmond Halley proposed that the force that acted between the Sun and the planets, whatever its nature
(he didn’t know what the force was), was inversely proportional to the square of the distance of the planet. This
means that a planet that is twice the distance as another would experience just ¼ of the attractive force.
F ∝ 1/d2
Newton used this idea, along with Kepler’s laws to deduce:
Newton's Law of Universal Gravitation
Newton could apply his law of universal gravitation to accurately predict the motions of planets, the orbits of comets
and even account for tides on Earth. His law can be mathematically expressed as follows:
F ∝ m1 m2 / r2
where F is the force between any two objects of masses m1 and m2 respectively and separated by a distance r.
As there are no other variables involved the equation becomes:
F = G m1 m2 / r2
where G is a constant known as the Universal Gravitational Constant.
(G = 6.673 × 10-11 Nm2kg-2)
The law of Universal Gravitation allowed for the derivation of Halley’s inverse square relationship and also Kepler’s
laws, this provided an explanation as to why the planetary orbits are ellipses and not circles. In addition, the
strength of the gravitational field at the surface of a planet can be deduced.
8.5.3
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Gather secondary information to relate the brightness of an object to its luminosity and distance
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Solve problems to apply the inverse square law of intensity of light to relate to the brightness of
a star to its luminosity and distance from the observer
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Describe a Hertzsprung-Russell diagram of a stars luminosity against its colour or surface
temperature
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Process and analyse information using the Hertzsprung-Russell diagram to examine the variety
of star groups including Main Sequence, red giants, and white dwarfs.
Luminosity, Brightness and Distance of a Star –
Luminosity is the total energy radiated by an object per second. This can also be called power output and its SI
units are joules per second, or watts (W). The Sun’s estimated luminosity is 3.83 x 1026 W. This value is
designated as L0 and is often used as a unit to express the luminosity of other stars.
The Brightness of a radiant object is the intensity of the light as seen some distance away from it. It is the
energy received per square metre per second.
Stars vary in their effective temperature and colour. A hot star radiates more energy per second per metre surface
area than a cooler star.
The size of a star. If two stars have the same effective temperature but differ in size then the larger star has a
greater surface area and as it radiates the same amount of energy per unit surface area per second as the smaller
star its total power output or luminosity must be greater.
The distance to the star. All the stars we see in the night sky are at vast distances from us but some are much
closer relatively than others. For two stars of identical size and temperature, the closer one to us will appear
brighter.
Intervening matter. Contrary to common belief interstellar space is not a perfect vacuum. Dust and gas between
stars can absorb and scatter starlight leading to a reduction in brightness and a reddening in colour.
Stars vary enormously in luminosity, ranging from less than 10-4 × that of our Sun to 106 × more luminous.
Brightness depends on :
1) Luminosity
2) Distance ( ie. 1/ distance squared).
The inverse square law –
The star gives off radiation in all directions, and the sum of all the radiation given off in one second is called the
luminosity. The radiation spreads out uniformly and penetrates the whole surface of the sphere. Therefore the
amount of radiant energy per square metre per second received at the surface of the sphere (the brightness) is
given by:
The Sun’s estimated luminosity is 3.83 x 1026 W
Brightness = Luminosity / Surface area of the sphere
Since the surface area of a sphere is 4πr2
Then, brightness = luminosity / 4πr2
This relationship describes how the brightness of a star, a distance r from the observer, depends upon the
luminosity and the distance. In particular, notice that the brightness is inversely proportional to the square of the
distance. This can be written as follows:
Brightness ∝ 1/r2
This relationship means that if the distance, r, were to double, then the brightness would reduce to one-quarter of
its previous value.
New Brightness ∝ 1/ (2r)2
∝ 1/ 4r2
∝ 1/ 4 x 1/r2
= ¼ of previous brightness
Note: 1 light year = 9.46 × 1015 meters
The Sun’s estimated luminosity is 3.83 x 1026 W
Brightness of a star relative to distance
How would the brightness of Procyon change if its distance were three times its distance would be three times its
current value?
The simplest path to a solution would be the inverse square law. So if the distance is multiplied by 3, the brightness
is divided by 3 squared.
The Hertzsprung-Russell Diagram –
A H-R Diagram is a graph of a star’s luminosity (as the vertical axis) plotted against its temperature or colour.
Astronomers use the historical concept of magnitude as a measure of a star's luminosity. Absolute magnitude is
simply a measure of how bright a star would appear if 10 parsecs (one parsec is 3.4 light years) distant and thus
allows stars to be simply compared. Note: the lower or more negative the magnitude, the brighter the star.
Possible axes for a Hertzsprung-Russell Diagram:
Note how the temperature scale is
reversed on the horizontal axis.
Also take care if using magnitude to
work upwards to negative values.
The effective temperature of a star
is plotted on the horizontal axis of an HR diagram. NOTE: the temperature is
plotted in reverse order, with high
temperature (around 30,000 - 40,000
K) on the left and the cooler
temperature (around 2,500 K) on the
right.
The third possible scale for the
horizontal axis is a star's spectral
class. By splitting the light from a star
through a spectrograph its spectrum
can be recorded and analyzed. Stars of
similar size, temperature, composition
and other properties have similar
spectra and are classified into the same
spectral class. The main spectral classes
for stars range from O (the hottest)
through B, A, F, G, K and M (coolest).
Our Sun is a G-class star. By comparing
the spectra of an unknown star with
spectra of selected standard reference
stars a wealth of information, including
its colour or effective temperature can
be determined.
C
B
A
D
Most stars seem to fall into group A. It shows a general trend from cool, dim stars in the lower right corner up to
hot, extremely bright stars in the top left corner which fits in with our expected relationship between temperature
and luminosity. This group is called the Main Sequence so stars found on it are main sequence stars.
Stars in group B (Red Giants) are mostly 6,000 K or cooler yet more luminous than main sequence stars of the
same temperature. The reason is that these stars are much larger than main sequence stars. Although they emit
the same amount of energy per square metre as main sequence stars they have much greater surface area (area ∝
radius2) the total energy emitted is thus much greater. These stars are referred to as giants.
The stars in group C are even more luminous than the giants. These are the supergiants, the largest of stars with
extremely high luminosities.
The final group of interest are those stars in group D. From their position on the H-R diagram we see that they are
very hot yet very dim. Although they emit large amounts of energy per square metre they have low luminosity
which implies that they must therefore be very small. Group D stars are in fact known as white dwarfs. White
dwarfs are much smaller than main sequence stars and are roughly the size of Earth.
8.5.4
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Describe sunspots as representing regions of strong magnetic activity and lower temperature
Identify data sources, gather and process information and use available evidence to assess the effects of
sunspot activity on the Earth’s power grid and satellite communications
Sunspots –
Sunspots are dark sports seen on the surface of the Sun, varying in size between several hundred to several
thousand kilometers in diameter. Sunspots have been identified since Galileo first observed the Sun using a
telescope. They appear dark because they are about 1500 K cooler than their surroundings. The spots also
represent regions of intense magnetic activity.
It is thought that sunspots are locations of disturbances in the magnetic field lines within the surface of the Sun,
where they have become sufficiently buckles to loop out and then back into the surface. The intense field activity
within a sunspot prevents the convection of heat to the surface, thereby reducing its temperature. Sunspots usually
occur in pairs or groups, lasting for several days or weeks.
All but the smallest spots have two regions; a darker inner part called the umbra which is surrounded by a lighter
region, the penumbra. The reason that sunspots appear dark is due to the fact that they are cooler then the
surrounding photosphere of the Sun. The umbra is about 4,000 K, the penumbra 5,600 K and the granulated
surface on the photosphere is at about 6,000 K. Intense magnetic fields of up to 0.4 tesla in the umbras are thought
to suppress the convection currents that bring up hot gases from deeper down within the Sun.
A sunspot is a dark part of the sun's surface that is cooler than the surrounding area. It turns out it is cooler
because of a strong magnetic field there that inhibits the transport of heat via convective motion in the sun. The
magnetic field is formed below the sun's surface, and extends out into the sun's corona.
Outside a sunspot, you have only gas pressure, which depends on the temperature. In the sunspot you have both
gas pressure and magnetic field pressure combined. Since the pressure must be in balance, magnetic pressure
inside the sunspot allows the gas pressure (and thus the temperature) to remain lower than the areas outside of the
sunspot.
Sunspot cycle –
The sunspot cycle is a cyclical pattern of increasing and decreasing number of sunspots. The solar cycle is an 11
year cyclical pattern of increasing and decreasing frequency of sunspots, flares, prominences and coronal mass
ejections.
The period of peak activity is called the solar maximum, while the period of least activity is referred to as the solar
minimum. It has been found that:
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At a solar maximum there is usually over 100 sunspots appearing simultaneously on the surface of the
Sun, while at solar minimum there may be none at all;
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Cycle varies between 7 and 13 years
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An average cycle in not symmetrical, usually takes 4 years from minimum to maximum, and 7 years to
quieten down to the next minimum.
[CME] Coronal mass ejections (which are part of Solar wind) are release by solar flares (sudden explosive burst of
radiation and matter near sunspots). Thus sunspots are the point at which the solar winds are created and released,
this is due to the intense magnetic fields around a sunspot becoming wound up and twisted that they snap. This is
why they are common around sunspots.
Solar winds and the effects of sunspots on the Earth’s power grid and communications –
Solar winds are an outflow of low-density plasma from the corona of the sun. Solar winds take approximately three
to four days to reach the Earth, although high speed gusts can reach us in two days. Near the Earth the solar wind
has a density of approximately five protons and five electrons per cubic centimetre and some helium and heavier
ions. Solar winds are a flow of highly ionised charges carrying the interplanetary magnetic fields with it. The
interplanetary magnetic field couples with the Earth’s magnetic field, allowing the solar wind to interact with the
Earth’s magnetic field. Most of the solar wind flows around and past the Earth, distorting the Earth’s magnetic field
to create a long tail. The region containing a planet’s magnetic field, distorted in this way, is known as a
magnetosphere.
The ions of the solar wind can enter the magnetosphere in three ways:
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Through the cusps, holes in the magnetosphere, over the north and south poles
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Through the magnetotail and then back up towards the Earth
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Through some leakage in the magnetosphere
When the ions are inside, they captured by the Earth’s magnetic field lines. They spiral from one pole to the other
and are then bounced back. Electrical currents are then caused within the ionosphere and Van Allen belts (The Van
Allen belts are two doughnuts-shaped zones of radiation [ions] that wrap around the Earth). These currents produce
their own magnetic field, and the magnetic field of the Earth is disrupted by this.
The magnetosphere offers some protection for our planet from direct exposure to the solar wind, however it is still
vulnerable to major disruptions in the speed, density and temperature of solar wind (known as space weather).
Turbulent solar winds buffet and irregularly distort the magnetosphere, and at the same time a greater than usual
number of charged particles find their way into the magnetosphere to irregularly charge the ionosphere and Van
Allen belts.
The action of stormy space weather on the Earth and it’s magnetosphere produces a range of side effects, including:
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Abnormal heating of the atmosphere causing it to expand slightly and increase drag on low satellites
(which can result in premature decay of their orbits, causing them to re-enter the Earth’s atmosphere
and most probably burn up). As well, extra solar energy can heat the Earth's atmosphere more than
usual, expanding it, and causing extra drag on satellites, pulling them into a lower orbit. To maintain
orbit the satellite must expend valuable fuel to push it to a higher orbit though this is normally at the
expense of shortened mission life
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Electrical failure of communication satellites. Higher levels of radiation can charge up a satellite's
electronics, causing them to fail, through discharge arcs or by building up on insulation. Charged
particles can disrupt computer memories
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Can send huge spikes through power grids, resulting in their failure. Changes in the magnetic fields
around a conducting network such as a power grid, phone lines or even train tracks will induce surges of
current in the conductors, up to hundreds of amperes in magnitude. This can cause vulnerable
components, such as transformers, to fail.
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Fluctuations in the Van Allen belts and the ionosphere resulting in disruptions to normal communication.
The solar wind disrupts radio communications through the way it changes the ionosphere, an
electrically-charged layer of the upper atmosphere, 100-500 km in altitude. For some applications (e.g.
over-the-horizon radar), the ionosphere is used as a mirror. If it is disrupted by 'space weather', it
distorts the reflected signal. The disrupted ionosphere can also affects signals to and from satellites:
GPS navigation signals can lose accuracy or even drop out altogether.