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Astrophysics
Contents
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Lenses & Optical Telescopes
Radio Astronomy
Classification of Stars
Cosmology
Lenses & Optical Telescopes
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Convex Lens: light rays converge
Power (Dioptres, D) = 1 / focal length (m)
Lenses & Optical Telescopes
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Lens Formula:
1/f = 1/v + 1/u
v = image distance, u = object distance
M = v/u
M = magnification (no units)
Lenses & Optical Telescopes
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Refracting Telescope: bends light with lenses
- objective lens: produces small real image
- eyepiece: magnifies image
Angular Magnification:
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M = α/β
α: angle (rads) subtended by the object to the unaided eye
β: angle (rads) subtended by the image to the eye
Reflecting Telescopes
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Disadvantages:
- refract light of different colours by different  distorted image
- do not transmit 100 % of the light; some is lost
- large lenses are complex to make
- for good magnification, the objective lens must have a very
long focal length  telescope becomes very long
Reflecting Telescopes
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Resolving Power: how good a telescope is at distinguishing
between two objects that are close to one another
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Resolving power of eye: angle = 3x10-4 radians
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Observations from Earth: are poor because of atmosphere
turbulence (light is scattered) and light pollution
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Diffraction: As light enters the telescope, a small gap diffracts
the light wave  Fraunhofer Diffraction Pattern
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Overlapping of fringes can occur: θ = λ/D
θ = angular separation (rads), D = aperture width (m)
Reflecting Telescopes
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Recording the Image: Charged Coupled Device (CCD)
- films have fine grain for high resolution
- CCD (size of a stamp) connects to computer
- CCD has millions of pixels on it
The eye has a quantum efficiency of 1%; CCD is approx. 70%:
Radio Telescopes
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Radio Astronomy:
- revealed the existence of radio sources, such as quasars and
pulsars
- analyses chemical elements in stellar objects
- tracks the movement of planets using the Doppler effect
- looked at microwave radiation which gives evidence for the
Big Bang
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Radio waves penetrate dust (nebulae etc.) so radio telescopes
allow us to view inwards, into the centre of the galaxy
Radio telescopes have poor resolution and are absorbed by light
pollution on Earth
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Classification of Stars
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Astronomical Unit (AU):
- Distance between Earth and Sun: 1AU = 1.5 x 1011m
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Light Year (ly):
- Distance travelled by light in 1 year: 1ly = 9.46 x 1015 m
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Parsec (pc):
- An object at 1pc subtends an angle of 1 arc second for a
distance of 1AU: 1pc = 3.086 x 1016m
- 1 pc = 3.26 ly
Classification of Stars
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Apparent Magnitude: apparent brightness of stars on a scale
Very bright stars have negative magnitudes
Magnitude 1 star = 100 times brighter than magnitude 6 star
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Difference in magnitudes = n
- ratio of brightnesses = 2.512n
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Absolute Magnitude: stars at an
arbitrary distance of 10pc
m: apparent magnitude
M: absolute magnitude
d: distance (pc)
Classification of Stars
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Classification by Temperature: spectroscopy
- Balmer lines arise from electron transitions in hydrogen atoms
- As the electron drops from high levels to the second energy
level, photons are emitted
- Emissions of photons appear black  absorption spectrum
Emission
Spectrum
Absorption
Spectrum
Classification of Stars
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Low Temperatures:
- energy levels are rare as electrons remain in ground state
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High Temperatures:
- Electron transitions occur at higher levels so there are
comparatively few Balmer transitions
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Intermediate Temperatures:
- Many electrons perform Balmer transitions, so there are strong
absorption lines
Classification of Stars
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Black Body: an object that absorbs all radiation
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Perfect absorber = perfect emitter (of all radiation… including
visible)
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Stars are approximated to black bodies:
- hot object emits radiation across range of λ
- peak in intensity at a given λ
- hotter object = higher peak
- hotter object = shorter peak λ (λmax)
Wien’s Displacement Law:
λmaxT = constant = 0.00289 mK
Classification of Stars
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Luminosity of Stars: power; energy given out per second
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Stefan’s Law: P = σAT4
σ = 5.67x10-8Wm-2K-4
star = sphere…  A = 4πr2
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For a star…
P = 4πr2σT2
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Observing Stars is difficult due to:
- light pollution which is problematic for viewing dim stars
- poor weather such as clouds
- dust (from pollutants)
- turbulent atmosphere (which is why stars “twinkle”
 put telescope in orbit, or failing that, on a very high mountain
Life & Death of a Star
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Hertzsprung-Russell Diagram:
Life & Death of a Star
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Hertzsprung-Russell Diagram:
- most stars lie along the main sequence
- very bright = blue; very dim = red
- Luminosities: Sun = 1, Betelgeuse = 20 000, Sirius = 0.002
- Surface Temp: Sun = 5800K, Sirius = 20 000K
Life & Death of a Star
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Stage 1: Stars are born in a region of high density Nebula,
which condenses into a huge globule of gas and dust and
contracts under its own gravity. Huge amounts of thermal
energy and IR radiation are emitted
Life & Death of a Star
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Stage 2: A region of condensing matter will begin to heat up
and start to glow forming Protostars. If a protostar contains
enough matter, the internal temperature can reach 15 million
degrees Celsius
Life & Death of a Star
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Stage 3: Ignition temperature is reached… fusion begins.
Hydrogen fuses into Helium
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Stage 4: Energy is released which prevents the star from
collapsing further. Star stabilises and shines
 main sequence lasts approx. 10 billion years
Life & Death of a Star
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Stage 5: Helium core contracts and reactions occur in a shell
around the core
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Stage 6: Core is hot enough for the Helium to fuse to form
Carbon. Outer layers begin to expand, cool and shine less
brightly. Expanding star is now called a Red Giant
Life & Death of a Star
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Stage 7: Helium core runs out, and the outer layers drift away
from the core as a gaseous shell. This gas that surrounds the
core is called a Planetary Nebula
Life & Death of a Star
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Stage 8: Approx. 20% of original star mass has been lost.
Remaining mass (core) becomes a White Dwarf as the star
cools and dims. Once it ceases shining  Black Dwarf. It is
believed that up to ½ the mass of the galaxy is due to Black
Dwarfs
White Dwarf
Black Dwarf
Life & Death of a Star
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Novae & Supernovae: With massive stars, electrons & protons
will combine to form neutrons. The inner core will
spontaneously collapse (approx. 1 sec duration) as neutrinos
are ejected at which point  Neutron Star. The outer layers
then collapse onto the core, which cannot be compressed
further. The pressure of this outer layer collapse causes the
wave of movement to reverberate and a violent shock wave
outwards occurs. This explosion is called a Supernova
Life & Death of a Star
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Black Hole: With very massive stars, the inner core collapses
but continues to do so until it becomes nothing more than a
point mass. Point mass  singularity, and this breaks the laws
of Physics. The strength of gravity inside a black hole is so
massive that nothing can escape, not even light (which is why
they are not visible). The perimeter at which light can/cannot
escape is called the Event Horizon, but far away from this
point, everything else is sucked in. Black holes are invisible,
but they can be found, as nearby stars will be sucked in
Cosmology
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Doppler Effect: shift in frequency and wavelength of waves that
causes its properties to change
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Objects that travel with v<<c obey this law:
and
- Moving towards observer = positive speed; away = negative
- Moving away  frequency decreases  wavelength increases
- Moving towards  frequency increases  wavelength
decreases
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Moving away = red shift
Moving towards = blue shift
Cosmology
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Big Bang: age of universe = 1/H0
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If galaxies are moving away from us, they must have been
closer together millions of years ago. If Hubble’s graph is
used, the origin of this movement = approx. 10 000 million
years old
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Earth = approx. ½ age of universe (5 000 millions years old)
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The universe will either:
Continue to expand forever
Return in on itself back to its origin (Big Crunch)
1)
2)
Cosmology
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Quasars: Extremely bright objects that are most distant from
us that we know of. Smaller than a galaxy, they are more
luminous and contain elements we do not know exist. They
have a huge red shift
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They could be:
massive black holes?
responsible for consuming 10 solar masses per year
responsible for ejecting jets of matter at high velocity
1)
2)
3)
(Several hundred light years is probably a safe distance!)
Summary
Lenses & refracting telescopes
 Reflecting telescopes
 Radio telescopes
 Classification of stars
 Life & death of a star
 Cosmology
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