Chapter 19 The Stars Distances to stars are measured using parallax.

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Chapter 19 The StarsDistances to stars are
measured using parallax.
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This is not effective for very distant stars.
The angle formed by parallax is measured in arc
seconds.
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A circle is divided into 360. One degree is
divided into 60 minutes, and one minute is
divided into 60 seconds.
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Therefore, one arc second is 1/(360 x 60 x 60)
of a circle, or 1/1296000 of a circle.
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The distance a star must be to have a parallax of
one arc second is 20,265 A.U.s, 3.1 x 1018 cm.
This distance is called a parsec (parallax in
arc seconds).
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The farther away a star is the smaller the angle
becomes, sodistance (in parsecs) 1/parallax
(in arc seconds)
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One parsec is approximately equal to 3.3 light
years.
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The closest star to Earth is Proxima Centauri. It
is a member of a triple star system called the
Alpha Centauri System.Proxima Centauri has the
largest known stellar parallax at 0.76.
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1/0.76 1.3 parsecs 4.3 light years, or
270,000 A.U.s. This is a typical interstellar
distance in the Milky Way galaxy.
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If the Earth were a grain of sand orbiting a golf
ball sized Sun at a distance of 1 meter, Proxima
Centauri would be another golf ball over 100 km
distant.
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The next nearest star is Barnards Star at 1.8
parsecs (pc), 6.0 light years. There are about
30 stars within 4 pc of Earth.
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The annual movement of a star across the sky,
relative to other stars, is called proper motion.
It is measured by angular displacement.
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Barnards Star moved 227 over 22 years. This
solves to 10.3/yr. This is the largest known
proper motion of any star.
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Proper motion is only the transverse velocity
(perpendicular to Earth). The other component of
motion is radial velocity (found from the Doppler
Effect).
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True space motion can be found from the
Pythagorean Theorem.
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Finding Stellar Size One way is by speckle
interferometry. Many short exposure images of a
star are pieced together producing a high
resolution map of the star.
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Another way to find the size of stars is by
using the Radius-Luminosity-Temperature
Relationship. Energy flux is the energy emitted
by a star per unit area per unit time. Energy
flux increases proportional to increases in
temperature and stellar radius.
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_________ v
luminosityradius is proportional to
---------------------- temperature2This
is used to indirectly determine stellar size.
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Example Omicron Cetitemp 3000K 1/2
SunsLuminosity 1.6 x 1036 erg/sec 400x
Suns v400Therefore radius
--------- 0.52 80X Suns radius
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80X Suns radius would put the photosphere at
Mercurys orbit. This makes Omicron Ceti a Red
Giant. A Giant is 10 to 100x the Suns size. A
Supergiant is 1000x the Suns size.
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Example Sirius Btemp 12,000K 2x
SunsLuminosity 1031 erg/sec 0.002x
Suns v0.002Therefore radius
------------ 22 0.01X Suns radius
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Sirius B is much hotter and much smaller than our
Sun. It is roughly the size of Earth. It is a
white dwarf star. Any star smaller than our Sun
is called a dwarf.
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Luminosity is the rate of energy emission by a
star. The apparent brightness of a star is how
bright it appears from Earth.
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A bright star is a powerful emitter, is near
Earth, or both. A dim star is a weak emitter, is
far from Earth, or both.
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The apparent brightness of a star decreases in an
inverse square relationship as its distance from
the Earth increases.
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Doubling the distance from a star makes it appear
22, or 4 times dimmer. Tripling the distance
makes it appear 32, or 9 times dimmer.
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The apparent brightness of a star is directly
proportional to its luminosity and inversely
proportional to the square of its distance.
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When comparing the luminosity of stars,
astronomers imagine looking at all stars from a
standard distance of 10 pc.
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The apparent brightness a star would have at 10
pc from Earth is called its absolute brightness.
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A star closer than 10 pc from Earth will have an
absolute brightness less than its apparent
brightness. A star greater than 10 pc will have
an absolute brightness greater than its apparent
brightness.
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The surface temperature of a star can be
determined from measurements of its brightness at
different frequencies. This is usually measured
at a certain frequency of blue light (B) and a
certain frequency of visible light (V) to which
human vision is most sensitive.
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The color index of a luminous object is the ratio
of its B to V intensities. It is directly
related to the objects surface temperature and
to its color.
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Color IndexB/V Temp Color Example
1.7 30,000K electric blue 1.3 20,000K
blue Rigel 1.0 10,000K white
Vega, Sirius 0.8 8,000K yellow-white
Canopus 0.6 6,000K yellow the
Sun, Alpha Centauri 0.4 4,000K
orange Arcturus, Aldebaran 0.2
3,000K red Betelgeuse
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This intensity measurement through a series of
filters is called photometry. The UBV system
uses Ultraviolet, Blue, and Visible filters to
determine a stars properties.
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