Intensity
Intensity (I) is the power received from a star (its luminosity) per unit area and has the unit, W m-2.
The intensity is the effective brightness of an object, though brightness is a subjective scale of
measurement, meaning it varies depending on the observer.
The intensity of a star follows the inverse square law, meaning it is inversely proportional to the
square of the distance between the star and the observer. It is assumed that light is emitted
equally in all directions from a point, so will spread out (in the shape of a sphere). Therefore, this
can be shown by the equation below:
luminosity
Luminosity (L) is the rate of light energy released or power output of a star.
Trigonometric parallax
Parallax is the apparent change of position of a nearer star in comparison to distant stars in the
background, as a result of the orbit of the Earth around the Sun. The property is measured by the
angle of parallax (0) (also known as parallax angle as in one of the diagrams below). You can find
the angle of parallax by measuring the angle to a star and seeing how this angle changes as the
Earth changes position. The greater the angle of parallax, the closer the star is to the Earth.
Astronomical Unit (AU)
The average distance between the centre of the Earth and the
centre of the Sun.
Parsec (pc)
Parsec (pc) - The distance at which the angle of parallax is 1 arcsecond (1/3600th of a
degree).
Light year (ly)
The distance that EM waves travel a year in a vacuum
Standard candles
You can also determine astronomical distances by measuring the intensity detected from standard
candles, which are objects of known luminosity.
This can be done by measuring the intensity detected from the light source on Earth and using the
inverse square law equation described above to calculate its distance away:
Hertzsprung-Russell diagram (stellar luminosity and temperature)
Stars belong to different spectral classes depending on their temperature. The table below
describes star spectral classes and the temperature range of stars which fall into that class.
Hertzsprung-Russell diagram (life cycle of stars)
The lifecycle of stars depends on their mass, and the diagram below shows the life cycle of
stars depending on their mass in solar masses, however you don’t need to be aware of these exact
amounts.
1.Protostar
Clouds of gas and dust (nebulae) have fragments of varying masses that clump
together under gravity.
2.Main Sequence
The inward force of gravity and the outward force due to fusion are in equilibrium -
the star is stable.
Hydrogen nuclei are fused into helium.
The greater the mass of the star, the shorter its main sequence period because it
uses its fuel more quickly.
3.Red Giant (for a star < 3 solar masses)
Once the hydrogen runs out, the temperature of the core increases and begins
fusing helium nuclei into heavier elements (E.g. Carbon, Oxygen and Beryllium).
The outer layers of the star expand and cool.
4.White Dwarf (for a star < 1.4 solar masses)
When a red giant has used up all its fuel, fusion stops and the core contracts as
gravity is now greater than the outward force.
The core becomes very dense (around 105 - 109 kg m-3).
c A white dwarf will eventually cool to a black dwarf.
5.Red Supergiant (for a star > 3 solar masses)
When a high-mass star runs out of hydrogen nuclei, the same process for a red
giant occurs, but on a larger scale.
6.Supernova (for a star > 1.4 solar masses)
When all fuel runs out, fusion stops and the core collapses inwards very suddenly
and becomes rigid (as the matter can no longer be forced any closer together).
c The outer layers of the star fall inwards and rebound off of the core, launching them
out into space in a shockwave.
As the shockwave passes through surrounding material, elements heavier than iron
are fused and flung out into space.
c The remaining core depends on the mass of the star.
7.Neutron Star (for a star between 1.4 and 3 solar masses)
When the core of a large star collapses, gravity is so strong that it forces protons
and electrons together to form neutrons.
- Black Hole (for a star > 3 solar masses)
When the core of a giant star collapses, the neutrons are unable to withstand
gravity forcing them together.
c The gravitational pull of a black hole is so strong that not even light can escape.
Doppler effect
The Doppler effect is the compression or spreading out of waves that are emitted or reflected by a
moving source. As the source is moving, the wavelengths in front of it are compressed and the
wavelengths behind are spread out as shown in the diagram below. An example of the doppler
effect can be heard in the sound of a car moving past you.
True Sequence
You can observe the life cycle of star by looking at a HR diagram, for example, consider a main
sequence star:
1. The star begins as a protostar, which gradually heats up, moving to the left on the HR
diagram. Once it reaches temperatures which allow fusion to occur, it becomes a main
sequence star.
2. Once the main sequence star uses up all the hydrogen in its core, it will move up and to
the right on the HR diagram as it becomes a red giant. A red giant is brighter and cooler
than a main sequence star.
3. Once the red giant uses up all the helium in its core, it will eject its outer layers and will
move down and to the left on the HR diagram as it becomes a white dwarf. A white dwarf
is hotter and dimmer than a main sequence star.
Red shift
10.162 - Red shift
The Doppler effect causes the line spectra of distant objects to be shifted either towards the blue
end of the visible spectrum when they move towards the Earth (blue-shift) or towards the red
end of the spectrum when they move away from the Earth (red-shift).
Red-shift is used as evidence for the expanding universe, as distant objects are red-shifted. The
more distant the object, the greater its red-shift.
Hubble’s law
Hubble’s law states that a galaxy’s recessional velocity is directly proportional to its distance from
the Earth. It essentially states that the universe is expanding from a common starting point.
This can be summed up in the formula:
The age and ultimate fate of the universe
10.163 - The age and ultimate fate of the universe
The redshift of distant objects shows that they are moving away from us, suggesting that the
universe is expanding. It would be reasonable to assume that the universe began from one point -
a singularity that was infinitely small and infinitely hot. The Big Bang Theory suggests that the
universe began with a huge explosion from this point.
P1
By considering the centripetal force exerted on stars in the outer orbits of a galaxy, you’d expect
them to travel slower than stars closer to the galactic centre (as the centripetal force is inversely
proportional to the distance from the centre), however this is not the case. It has been observed
that all of the stars in the galaxy tend to travel at the same speed regardless of how far away they
are from the centre of the galaxy. This result suggests that the stars have a larger mass than they
appear to, which allows them to travel at the speed that they are. This extra mass is believed to be
caused by dark matter, which is yet to be detected as it does not emit or interact with light.
P2
If the expansion of the universe was slowing down, more distant objects would be observed to be
receding more quickly, since expansion was faster in the past. Note that the light from more distant
objects would take longer to reach us so would appear to be in the past. Objects would also
appear brighter than predicted as they would be closer than expected. However, a certain type of
supernovae have been seen to be dimmer than they were expected to be, meaning they are
more distant than Hubble’s law predicted. This suggests that the expansion of the universe is
accelerating and it is actually older than Hubble’s law estimates.
