Download Week 22

Week 22
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Physics
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Understand that a star is in equilibrium under
the action of two opposing forces, gravitation
and the radiation pressure of the star
Appreciate that nuclear fusion provides the
energy source of a star
Stellar Radiation
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A star like the sun radiates
about 1026 J/s
1,000,000,000,000,000,000,000,00
0,000
The source of this energy is
nuclear fusion in the interior of
the star.
The energy source of stars
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Deuterium – “Heavy Water” formed by two joining
protons, releasing a positron and a neutrino.
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Positron – antiparticle of an electron, positive charge
Neutrino – little or no mass no charge moves at the speed of light.
Helium-3 – formed when a proton bombards a deuterium
nucleus, releasing a photon in the form of a gamma ray.
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photon – a quantum of light (unit of light emission or absorption)
Helium-4 – regular helium atom formed by a helium-3
nucleus bombarding another helium-3 nucleus, releasing
two protons
 These two protons are free to continue the whole process
again.
 https://www.youtube.com/watch?v=-zX-gz1lRt0
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The energy source of stars
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High temperature in the star allows two
protons to fuse.
High pressure ensures a high probability of
collision.
Energy is released in each of the three steps but
most comes out of the third step.
Photons and neutrinos move the energy
outward and collide with protons and
electrons.
This outward motion stabilizes the star against
gravitational collapse.
The energy source of stars
Each time the proton-proton cycle
occurs 3.98 x 10-12 J is released
 0.00000000000398 J
 All of the helium created as a by
product collects at the core of the star
and due to the immense pressure, the
helium is compacted into heavier
elements like nickel and iron.
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The energy source of stars
Give the definitions of luminosity,
L = σAT4 as the power radiated
into space by a star and apparent
brightness, b =L/(4πd2) , as the
power received per unit area on
earth.
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Luminosity - objective
Luminosity is the amount of energy radiated by
the star per second; that is, it is the power radiated
by the star.
 Luminosity depends on the surface temperature
and surface area of the star.
 Luminosity of a star = L
 Imagine a sphere of radius d centered at the
location of the star.
 If the star is assumed to radiate in all directions,
then the energy radiated in 1 s can be thought to
be distributed around this sphere.
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Luminosity
A detector of area-a placed somewhere on
the sphere will detect a small fraction of
the total energy.
 Apparent brightness is the perceived
energy per second per unit area of detector
and is given by…
 b = L/(4πd2)
2
 Measured in W/m
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Apparent Brightness
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The stars energy distributed over an imaginary
sphere of radius equal to the distance between
the star that the observer. The observer only
receives a fraction of the total energy.
The amount of energy per second radiated by
a star of surface area A and absolute surface
temperature T (i.e. the luminosity) is given by
L = σAT4
 σ is sigma and it represents the StefanBoltzmann constant
-8
2 4
 σ = 5.67 x 10 W/m K
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Luminosity
The radius of star A is three times that
of star B and its temperature is
double that of B. Find the ratio of the
luminosity of A to that of B.
 Start with the ratio  LA/LB
 144 times more luminous than B
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Try this
The stars from the last problem have
the same apparent brightness when
viewed from the earth. Calculate
the ratios of their distances.
 Start with the ratio  bA/bB = 1
 12 times the distance to Star B
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And this
The apparent brightness of a star is
6.4 x 10-8 W/m2. If the distance is 15
ly, what is the luminosity?
 1.62 x 1028 W
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Try This
A star half the sun’s surface
temperature and 400 times its
luminosity. How many times bigger is
it?
 Start with this ratio 400 = L/Lsun
 80 times larger
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Try This Too
Black-body Radiation
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A body radiates energy away in the form of
electromagnetic waves according to the StefanBoltzmann law
This Electromagnetic radiation is distributed
over an infinite range of wavelengths
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The spectrum of a
black-body is the
energy radiated per
second per
wavelength interval
from a unit area of
the body.
“Relative intensity”
shows apparent
brightness (W/m2)
Overall intensity is
represented as the
area under the
graph.
Black-Body Radiation Profiles
Peak wavelength (λ0) emits the most
energy
 The color of the star is mainly determined
by the color corresponding to λ0.
 Area under the curve is the total power
radiated from a unit area irrespective of
wavelength and is given by σT4
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Black-Body Radiation
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The Wien displacement law relates wavelength
to temperature.
λ0T = constant = 2.90 x 10-3 K m
The higher the temperature, the lower the
wavelength at which most of the energy is
radiated.
Wien Displacement Law
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The sun has approximate black-body spectrum
with most of the energy radiated at a
wavelength of 5.0 x 10-7 m. Find the surface
temperature of the sun.
T = 5800 K
Try This
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The sun (radius R = 7.0 x 108 m) radiates a total
power of 3.9 x 1026 W. Find its surface
temperature.
T ≈ 5800 K
And This
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A great wealth of information can be
gathered about a star from the
studies of its spectrum.
Temperature
 Chemical composition
 Radial velocity
 Rotation
 Magnetic fields
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Stellar Spectra