Fundamental Astronomy

If the source were at rest, the wavelength of its radiation
would be λ0 = cT. The motion of the source changes
the wavelength by an amount
∆λ = λ − λ0 = cT + vT − cT = vT ,
and the relative change ∆λ of the wavelength is
∆λ
=
λ0
v
. (2.37)
c
This is valid only when v ≪ c. For very high velocities,
we must use the relativistic formula
∆λ 1 + v/c
= − 1 . (2.38)
λ0 1 − v/c
In astronomy the Doppler effect can be seen in stellar
spectra, in which the spectral lines are often displaced
towards the blue (shorter wavelengths) or red (longer
wavelengths) end of the spectrum. A blueshift means
that the star is approaching, while a redshift indicates
that it is receding.
The displacements due to the Doppler effect are
usually very small. In order to measure them, a reference
spectrum is exposed on the plate next to the
stellar spectrum. Now that CCD-cameras have replaced
photographic plates, separate calibration exposures of
reference spectra are taken to determine the wavelength
scale. The lines in the reference spectrum are produced
by a light source at rest in the laboratory. If the reference
spectrum contains some lines found also in the stellar
spectrum, the displacements can be measured.
Displacements of spectral lines give the radial velocity
vr of the star, and the proper motion µ can be
measured from photographic plates or CCD images. To
find the tangential velocity vt, we have to know the distance
r, obtainable from e.g. parallax measurements.
Tangential velocity and proper motion are related by
vt = µr . (2.39)
If µ is given in arc seconds per year and r in parsecs
we have to make the following unit transformations to
get vt in km/s:
1rad= 206,265 ′′ , 1 year = 3.156 × 10 7 s ,
1pc= 3.086 × 10 13 km .
Hence
vt = 4.74 µr , [vt]=km/s ,
[µ]= ′′ (2.40)
/a , [r]=pc .
2.11 Constellations
The total velocity v of the star is then
v = v2 r + v2 t . (2.41)
2.11 Constellations
At any one time, about 1000–1500 stars can be seen in
the sky (above the horizon). Under ideal conditions, the
number of stars visible to the naked eye can be as high as
3000 on a hemisphere, or 6000 altogether. Some stars
seem to form figures vaguely resembling something;
they have been ascribed to various mythological and
other animals. This grouping of stars into constellations
is a product of human imagination without any physical
basis. Different cultures have different constellations,
depending on their mythology, history and environment.
About half of the shapes and names of the constellations
we are familiar with date back to Mediterranean
antiquity. But the names and boundaries were far from
unambiguous as late as the 19th century. Therefore
the International Astronomical Union (IAU) confirmed
fixed boundaries at its 1928 meeting.
The official boundaries of the constellations were established
along lines of constant right ascension and
declination for the epoch 1875. During the time elapsed
since then, precession has noticeably turned the equatorial
frame. However, the boundaries remain fixed with
respect to the stars. So a star belonging to a constellation
will belong to it forever (unless it is moved across
the boundary by its proper motion).
The names of the 88 constellations confirmed by the
IAU are given in Table C.21 at the end of the book.
The table also gives the abbreviation of the Latin name,
its genitive (needed for names of stars) and the English
name.
In his star atlas Uranometria (1603) Johannes Bayer
started the current practice to denote the brightest stars
of each constellation by Greek letters. The brightest
star is usually α (alpha), e. g. Deneb in the constellation
Cygnus is α Cygni, which is abbreviated as α Cyg.
The second brightest star is β (beta), the next one γ
(gamma) and so on. There are, however, several exceptions
to this rule; for example, the stars of the Big
Dipper are named in the order they appear in the constellation.
After the Greek alphabet has been exhausted,
Latin letters can be employed. Another method is to use
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