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Chapter 13: Our Place in the Universe (13.1: Measuring the Solar System…
Chapter 13: Our Place in the Universe
13.1: Measuring the Solar System
Size of the Universe
Some galaxies are 13 billion light-years from Earth
When you look at a picture of an Ultra Deep Field image from the Hubble Space Telescope; you see the universe as it was 13.8 billion years ago, as that is how long it has taken the light from these distant galaxies to reach Earth
Hertzsprung-Russell Diagram
A logarithmic scale which plots the luminosity of stars against their temperature.
Top Left corner shows blue giant stars- they burn through their nuclear fuel at a prodigous rate and wiill finally become supernovae
A blue giant like RIGEL is about 66,000 times brighter than the Sun.
Measuring distance in the Solar System
Modern way to measure distances in the Solar System is to use Radar (Radio Detection Ranging)
Venus was targeted for the first time as a pulse of radio waves was sent out from Earth and the reflected waves detected returning after a delay
Distances between planets can be calculated from the delay and the known speed of EM Radiation
EXAMPLE: With a distance to Venus of 100 milliom km, the out-and-back delay is several minutes and the reflected signal is very weak; there is no hope of measuring the distance to even the nearest star.
How far away is the moon?
Astronomer used trigonometry to obtain a value of about 4x10^8m (centre of Earth to Moon)
This result was obtained using LIDAR ( Light Detection Ranging)
Measuring speeds in the Solar System
To get the relative velocity of the asteroid and Earth you measure the distance
If the out-and-back time has increased,the asteroid is moving away from Earth
If it has decreased, the asteroid is getting closer and we might be in danger of a collision
ASSUMPTIONS
We assume that the speed of the signal was equal both ways
The moment of reflection was just halfway through the time of delay of the pulse as observed on Earth
SPEED OF LIGHT IS CONSTANT
Light-years
1m- light-nanosecond
10^9m- 1 light-second
10^12m- 1 light-hour
10^16m- 1 light-year
10^22m- 1million light-years
10^26m-1000 million light-years
13.2:Measuring the Universe
Techniques for measuring huge distances
Parallax
Hold your hand out in front of you with your thumb up; close one eye and observe where your thumb appears in relation to the background; now try with other eye... You will see a shift...
This is a PARALLAX
Astronomers use this method to measure distance to nearby stars
The angular shift in radians of the position of the star is the ratio of the baseline to the distance
In June, the nearby star lines up with stars in Region A
When 6 months later it is in line with Region B
In practice, this parallax is tiny because the baseline is so small compared to the distance to evem the nearest star
In 1838, the known size of the universe grew when the first parallax star was found ; a star constellation found to be 10.4 light-years distant
We can only use parallax to measure nearby stars
How can greater distances be measured...
Standard Candles
Looking at the night sky, you will see stars of different brightness; how can we know why this is?
Astronomers call this true brightness ABSOLUTE LUMINOSITY of a star
We need a Standard Candle- a star with a known luminosity
If we know this then we can calculate the distance the star by its apparent brightness
A dim star with a high absolute luminosity must be more distant than a star of the same absolute luminosity that appears brighter.
Cepheids (a class of variable star) show a brightness variation that is dependent on their absolute luminosity
Cepheids of greater absolute luminosity vary in brightness over lobger periods
Measuring Speed
As well as the distance to stars, Astronomers were interested in the movement of stars through space
Radar measurements work well for planets, but a different method is required for more distant objetcs
Doppler Shift
Atoms in a distant star absorb and emit light at particular wavelengths that are accurately known from laboratory measurements
If the star is receding: the spectral lines increase
If the star is moving towards Earth: the spectral lines decrease
Receding stars show RED-SHIFT because their spectral lines are shifted towards the red end of the spectrum
Such a change in wavelength is called a DOPPLER SHIFT
Interpeting Red-Shift
Red-Shift, z = Change in wavelength, λ / wavelength λ
When we observe objects of red-shift z=10, we are looking at a time when the universe was about a tenth of its present size; these distant objects show a much younger Universe in which prototype galaxies are forming- the Universe has evolved since then
Hubble's law provides evidence that the Universe is expanding, but doesn't give info about the state of the early Universe
λ= cT
Change inλ= vT
Change in λ/λ= v/c
The Expanding Universe
Hubble's Law
In 1929, Edwin Hubble used red-shift data to plot the speeds of recessions of 24 galaxies against estimates of their distance
These points fell on a more or less straight line; nearly all galaxies seemed to be moving away from us, and the further away they are, the faster they are receding- HUBBLE'S LAW
An idea developed that the universe originated in a very hot, dense state from which it has expanded and cooled
This became known as the Big Bang
The name stuck, but is misleading; the beginning of the Universe was not an explosion in an existing empty space, but the creation of an expanding region of space and time
The bigger the Hubble Constant, the faster the universe must be expanding and the younger it must be to have reached its present size
Recession Velocity, v = constant, H0 x distance, r
Units of H0: speed/distance = 1/time
Cosmic Microwave Background Radiation
In 1965, Arno Penzias and Robert Wilson were calibrating a microwave antenna, they found that wherever the antenna was directed, it detected noise in the signal at microwave lengths
Other Physicists realised where the microwave background came from- it was the predicted cosmic background radiation that was left over from the hot beginnings of the Universe
COSMIC MICROWAVE BACKGROUND has the biggest cosmological red-shift known
It was produced when the Universe became just cool enough for electrons and ions to combine into neutral atoms, emitting photons
That happens at around 3000K, when the typical wavelength of the photons is around 1um.
Today these photons are seen, stretched in wavelength, as microwaves with a wavelength of the order 1mm-1000 times longer
The temperature has fallen by a factor of 1000, to just below 3K
The cosmological expansion z + 1 is the same ratio :
z+1 = radius of Universe Now / radius of Universe then
Satellites have now produced images of the whole Universe that show the microwave background isnt perfectly smooth; it has very small differences in temperature
As the microwave background is the red-shift radiation from the early Universe, this variation must have been present at the early stages of the Universe
13.3: Special Relativity
Relative Motion
When you read on a moving train you are at rest relative to the carriage but not at rest relative to the landscape that speeds past you
Now think about the observing speeds of objects in the Universe; you know that you sit on a moving platform (Earth), orbits the Sun, which moves round the Milky Way
All velocities are relative; from this POV it makes no sense to say which is really moving
We can only detect relative velocity, there is no such thing as 'really moving' or 'really at rest'; so now being at 'rest' simply means 'moving with me'
WE call time that such a clock records 'Wristwatch time', denoted with Greek letter T (Tau)
One observers sate of rest may not be the same as another's, they differ by their relative velocity
These ideas are stated in Einstein's first postulate of SPECIAL RELATIVITY
EINTSEIN'S FIRST POSTULATE
Physical behaviour cannot depend on any 'absolute velocity'; Physical laws must take the same form for all observers, no matter what their state of uniform motion in a straight line
This says that there is nothing special about uniform movement; travelling at uniform velocity relative to another object changes nothing about Physics
Constant Speed of Light
c= 299792458ms-1
Scientists now define the metre as the distance travelled by light in a vacuum in a time of 1/299792458 of a second
This decision to define the S.O.L was taken for reasons to do with precision of measurement
At the same time it was agreed with a fundamental shift in thinking in Physics introduced by Einstein
This was to regard S.O.L as a fixed conversion of units of distance and time
It doesn't matter how fast you move; light will still leave you at 299792458ms-1
EINSTEIN'S SECOND POSTULATE
The S.O.L ,c, is a universal constant. it has the same value regardless of the motion of the platform from which it is observed.
Space-Time diagrams
Space-Time diagrams represent objects moving through space and time, these diagrams have the following features
Distance is shown on the x-axis, in units of x/c (light-seconds)
Every diagram is drawn from the POV of a given platform- this platform moves up the time axis as time passes; observers, clocks and son on are all carried with the platform
Time is conventionally shown on the y-axis
Any other object at rest relative to the platform also moves vertically up the time axis as time passes, staying a constant distance from platform
FIGURE 2 PAGE 300
Lines representing paths of objects through space and time are called Worldlines
An object that moves relative to the observers's platform at a constant velocity moves along a sloping worldlines across the diagram, changing its distance from the observer
A light pulse travels at 1 light-second per second, so it's worldline travels at 45 degrees across the diagram, because the S.O.L is constant, independent of the observer's motion, this is true for every space-time diagram
Time dilation and the relativistic factor y
Clocks moving relative to an observer run slowly as seen by an observer, each second is stretched or dilated- the greater the relative velocity, the greater the the effect
Use the idea of a light clock: a pair of mirrors between which pulses of lgiht bounce back and forth
Imagine sitting on a train, watching your light clock, the wristwatch time for one 'tick' is time taken for a pulse of light to make a return journey between mirrors
But what will an observer outside the train see when the light clock speed past as well as the train; SOL will be same for observer and passenger, but the observer will see the light beam travelling a greater distance
So time taken for one tick will increase
y = 1/ Root 1- v^2/c^2
Time dilation is a consequence of the SOL being constant for all servers
Time Dilation in Action
Relativistic time dilation is not merely an idea confined to gedankenexperiments but used for :
Global positioning system has to allow for the effects of relativistic time dilation to pinpoint locations
Synchronised, accurate clocks record different time intervals when one is placed on an aircraft that makes a round trip whilst the other remains at the airport
The half-life of particles increases when the particles are accelerated to relativistic speeds;the greater the speed, the greater the time dilation
Wristwatch time of a photon is Tua = t/y
For photons, v=c so the relativistic factor is infinite; so whatever the the value of t between the emission and absorption of a photon, even if the photon has travelled across the universe, it sees no time pass by
