Download parallax in arc seconds

Chapter 19 The Stars
Distances to stars are
measured using parallax.
This is not effective
for very distant stars.
The angle formed by
parallax is measured
in arc seconds.
A circle is divided into
360°. One degree is
divided into 60 minutes,
and one minute is
divided into 60
seconds.
Therefore, one
arc second is
1/(360 x 60 x 60)
of a circle, or
1/1296000
of a circle.
The distance a star must
be to have a parallax of
one arc second is 20,265
18
A.U.’s, 3.1 x 10 cm.
This distance is
called a parsec
(parallax in arc seconds).
The farther away a star
is the smaller the angle
becomes, so:
distance (in parsecs) =
1/parallax (in arc seconds)
One parsec is
approximately
equal to
3.3 light years.
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”.
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.
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.
The next nearest star is
Barnard’s Star at 1.8
parsecs (pc), 6.0 light
years. There are about
30 stars within 4 pc of
Earth.
The annual movement
of a star across the sky,
relative to other stars,
is called proper motion.
It is measured by
angular displacement.
Barnard’s Star moved
227” over 22 years.
This solves to 10.3”/yr.
This is the largest
known proper motion
of any star.
Proper motion is only
the transverse velocity
(perpendicular to Earth).
The other component of
motion is radial velocity
(found from the Doppler
Effect).
True space motion
can be found from the
Pythagorean Theorem.
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.
Another way to find the size
of stars is by using the
Radius-LuminosityTemperature 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.
_________
√ luminosity
radius
is proportional to
---------------------2
temperature
This is used to indirectly
determine stellar size.
Example: Omicron Ceti
temp: 3000K 1/2 Sun’s
Luminosity: 1.6 x 1036 erg/sec
400x Sun’s
√400
Therefore: radius = --------- =
0.52
80X Sun’s radius
80X Sun’s radius would put
the photosphere at
Mercury’s orbit. This
makes Omicron Ceti a
Red Giant. A Giant is
10 to 100x the Sun’s size.
A Supergiant is 1000x the
Sun’s size.
Example: Sirius B
temp: 12,000K 2x Sun’s
Luminosity: 1031 erg/sec
0.002x Sun’s
√0.002
Therefore: radius = ------------ =
22
0.01X Sun’s radius
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.
Luminosity is the rate of
energy emission by a
star. The apparent
brightness of a star is
how bright it appears
from Earth.
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.
The apparent brightness
of a star decreases in
an inverse square
relationship as its
distance from the Earth
increases.
Doubling the distance
from a star makes it
2
appear 2 , or 4 times
dimmer.
Tripling the distance
2
makes it appear 3 , or
9 times dimmer.
The apparent
brightness of a star is
directly proportional to
its luminosity and
inversely proportional
to the square of its
distance.
When comparing the
luminosity of stars,
astronomers imagine
looking at all stars
from a standard
distance of 10 pc.
The apparent
brightness a star
would have at 10 pc
from Earth is called
its absolute
brightness.
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.
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.
The color index of a
luminous object is the
ratio of its B to V
intensities. It is directly
related to the object’s
surface temperature and
to its color.
Color Index
B/V Temp
Color
1.7 30,000K electric blue
1.3 20,000K
blue
1.0 10,000K
white
0.8 8,000K yellow-white
0.6 6,000K
yellow
0.4
4,000K
orange
0.2
3,000K
red
Example
Rigel
Vega, Sirius
Canopus
the Sun,
Alpha Centauri
Arcturus,
Aldebaran
Betelgeuse
This intensity
measurement through a
series of filters is called
photometry. The UBV
system uses Ultraviolet,
Blue, and Visible filters to
determine a star’s
properties.