Measuring Stars Part 1

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Measuring StarsPart 1
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Measuring Stars

• Contents
• Star distances for nearby stars
• Surface temperature
• Luminosity of stars
• The light year

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1. Star distances for nearby stars
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Star distances for nearby stars
There are about 10,000 stars in the Milky Way
whose distance can be measured using
trigonometry. The Greeks first used this method
to measure distances.
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Star distances for nearby stars
Eratosthenes measured the circumference of the
Earth in 270 BC.
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Star distances for nearby stars
The Greeks noticed that close objects appear to
move more than distant ones .
For example
This effect is called parallax.
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Star distances for nearby stars
In 1838 Friedrich Bessel measured the star 61
Cygni by parallax.
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Star distances for nearby stars
He measured the angular position of the star
relative to more distant ones at 6-month
intervals.
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Star distances for nearby stars
The change in angle is called the annual parallax.
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Star distances for nearby stars
The angle that we usually refer to is the
parallax q. This is half the annual parallax.
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Star distances for nearby stars
The modern method of measuring parallax is
described in the following slides
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Star distances for nearby stars
We will end up like this
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Star distances for nearby stars
Measure the angular position of a distant star in
December
Measure the angular position of the star in
December
Measure the angle between these positions q1
Measure the angular position of the distant star
again in June
Measure the angular position of the star again in
June
Measure the angle between these positions q2
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Star distances for nearby stars
The parallax is then the average of q1 and q2
Since we know the Earth-Sun distance, q can be
used to find the star distance
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Star distances for nearby stars
q
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Star distances for nearby stars
Nowadays parallax is found from the thousands of
photographs taken of the sky at different times
of the year.
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Star distances for nearby stars
A star has a parallax of 30. What is its
distance from Earth if the Sun is 150 million km
from Earth?
For small angles, sin q q in radians Since 360
degrees 2p radians, 1 degree 2p/360 radians I
degree 0.0175 radians
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Star distances for nearby stars
A star has a parallax of 30. What is its
distance from Earth if the Sun is 150 million km
from Earth?
30 30/3600 8.33 x 10-3 degrees Which is 1.45
x 10-4 radians From sin q Earth-Sun/Earth-star E
arth-star Earth-Sun/sin q Or Earth-star
Earth-Sun/q (rad) Earth-star 150000000/(1.45 x
10-4) Earth-star 1.03 x 1012 km
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Star distances for nearby stars
Alpha Centauri has a parallax of 0.76. What is
its distance from Earth if the Sun is 150 million
km from Earth?
0.76 0.76/3600 2.11 x 10-4 degrees Which is
3.68 x 10-6 radians From Earth-star Earth-Sun/q
(rad) Earth-star 150000000/(3.68 x
10-6) Earth-star 4.08 x 1013 km
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2. Surface temperature
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Surface temperature
The surface temperature of a star is estimated
from its colour. The hotter a body gets, the
whiter it glows, as shown in the next series of
pictures.
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Surface temperature
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Surface temperature
The maximum energy emission from a hot body is
related to its temperature by Wiens law. It
states that temperature T is inversely
proportional to the wavelength for most radiation
lmax
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Surface temperature
Another way of writing Wiens law is
T lmax 2.898 x 10-3
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Look in the night sky for Orion
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Betelgeuse has a surface temperature of 3700
KSirius A has a temperature of 11000 K
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These lines show the distribution of wavelengths
at different temperatures for stars.

• Blue could be Sirius A
• Yellow could be the Sun
• Red could be Betelgeuse

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Surface temperature
A graph of power v wavelength is called the
Planck distribution of energy
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Surface temperature
This shows how the Planck distribution varies
with temperature
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Surface temperature
T lmax 2.898 x 10-3
Use Wiens law above to calculate the peak
wavelength for a star with a surface temperature
of 106 K.
From T lmax 2.898 x 10-3 lmax 2.898 x
10-3/T lmax 2.898 x 10-3/106 lmax 2.898 x
10-9 m (or 2.898 nm) This is the wavelength for
X-rays
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Surface temperature
T lmax 2.898 x 10-3
Use Wiens law above to calculate the peak
wavelength for a star with a surface temperature
of 100 K.
From T lmax 2.898 x 10-3 lmax 2.898 x
10-3/T lmax 2.898 x 10-3/100 lmax 2.898 x
10-5 m (or 28.98 mm) This is the wavelength for
infrared
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Surface temperature
Stars vary in temperature from 107 K to near
absolute zero
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3. Luminosity of stars
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Luminosity
Consider two metal spheres. They have the same
temperature. Which one will lose more heat and
why?
T
T
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Luminosity
The larger one will lose more heat. It has a
bigger surface area.
T
T
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Luminosity
The rate of loss of heat from a body is
proportional to its surface area.
T
T
Surface area of a sphere 4pr2 So rate of energy
loss or Power a 4pr2
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Luminosity
Now consider two metal spheres of the same size.
They have different temperatures. T1 gt T2 Which
one will lose more heat and why?
T1
T2
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Luminosity
The one with the higher temperature (T1) will
lose more heat. There is a bigger temperature
gradient.
T1
T2
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Luminosity
The rate of loss of heat from a body by radiation
is proportional to the fourth power of its
absolute temperature.
T1
T2
Rate of energy loss or Power a T4
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Luminosity
Rate of energy loss or Power a 4pr2
Rate of energy loss or Power a T4
These two pieces of information are combined into
one equation called the Stefan-Boltzmann equation.
L 4pr2sT4
Where L power or luminosity in watt, s
Stefan-Boltzmann constant
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Luminosity
L 4pr2sT4
s 5.67 x 10-8 W.m2.K-4
The Sun has a surface temperature of 5700K. Its
radius is 6.6 x 108 m. What is its luminosity?
From L 4pr2sT4 4p x (6.6 x 108)2 x 5.67 x
10-8 x (5700)4 L 3.3 x 1026 W
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Luminosity
L 4pr2sT4
s 5.67 x 10-8 W.m2.K-4
Betelgeuse has a surface temperature of 3700K.
Its radius is 3.3 x 1011 m. What is its
luminosity?
From L 4pr2sT4 4p x (3.3 x 1011)2 x 5.67 x
10-8 x (3700)4 L 1.5 x 1031 W
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Luminosity
L 4pr2sT4
s 5.67 x 10-8 W.m2.K-4
Sirius A has a surface temperature of 11000K. Its
luminosity is 8.3 x 1027 W. What is its radius?
From L 4pr2sT4 r2 L/(4psT4) 8.3 x 1027/(4p
x 5.67 x 10-8 x 110004) r2 7.9 x 1017 r 8.9
x 108 m
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4. The light year
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The light year
Speed of light c 3.0 x 108 m.s-1
How far does light travel in a minute in
kilometres?
1 minute 60 seconds Distance 3 x 108 (m) x
60 Distance 1.8 x 1010 m 103 m 1 km Distance
1.8 x 107 km
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The light year
Speed of light c 3.0 x 108 m.s-1
How far does light travel in a day in kilometres?
1 day 60 s x 60 min x 24 hours 1 day 86400
s Distance 3 x 108 (m) x 86400 Distance 2.59
x 1013 m 103 m 1 km Distance 2.59 x 1010 km
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The light year
Speed of light c 3.0 x 108 m.s-1
How far does light travel in a year in kilometres?
1 year 60 s x 60 min x 24 hr x 365 day 1 year
31536000 s Distance 3 x 108 (m) x
31536000 Distance 9.46 x 1015 m 103 m 1
km Distance 9.46 x 1012 km This distance is
called a light year (ly)
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The light year
Speed of light c 3.0 x 108 m.s-1
How long will it take light from the Sun to reach
the Earth if the distance is 150 million
kilometres?
Time distance/speed Time 150 x 106 (km) x 103
(m)/(3 x 108) Time 500 s (or 8.33 minutes)
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The light year
Speed of light c 3.0 x 108 m.s-1
The binary stars of Sirius are 8.6 ly away from
Earth. How many kilometres is that?
Distance 8.6 (ly) x 9.46 x 1012 km Distance
8.14 x 1013 km
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The light year
Speed of light c 3.0 x 108 m.s-1
Earlier we worked out that Alpha Centauri is 4.08
x 1013 km from Earth. How many light years is
that?
1 light year 9.46 x 1012 km Distance 4.08 x
1013/(9.46 x 1012) ly Distance 4.3 ly
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Measuring StarsPart 1