Download Stars, Constellations, and the Celestial Sphere

Stars, Constellations, and the
Celestial Sphere
Constellation - a
region of the sky
with well-defined
boundaries.
Asterism - a group
of stars with a
recognized shape.
Most constellation
names are derived
from the Latin
language.
η
ζ
ε
δ
Alioth = ε Ursae Majoris
γ
The Big Dipper
α
β
Most star names
are derived from
the Arabic
language. The
brightest stars are
also named by
giving the relative
brightness as a
Greek letter (α
being the
brightest),
followed by the
possessive form of
the Latin name of
the constellation.
The stars of the dipper asterism in Ursa Major are a notable exception to this rule. They are
named in alphabetical order, beginning with α at the upper right edge of the bowl of the
di
dipper.
Th
The b
brightest
i ht t off th
these stars
t
iis actually
t ll ε Ursae
U
M
Majoris.
j i
The brightness of a star is usually expressed in terms of a quantity called magnitude, with
smaller magnitudes corresponding to brighter stars. The distance is usually given in light
years or parsecs (1 pc = 3.26 ly)
The stars in a constellation are not all at the same distance. For example, we see the Big
Dipper asterism (part of the constellation Ursa Major) as a projection (onto the plane of the
sky) of a cluster of stars at various distances (100.7 ly, 78.2 ly, 80.9 ly, 81.4 ly, 83.6 ly, 79.4 ly,
123.6 ly).
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09/05/11
9:00 PM
09/05/11
9:00 PM
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Summer Triangle
Measures of Angle
•
•
•
•
•
•
•
•
•
•
360o
= 360 degrees = all the way around a circle
1o =1/360th of a circle
1' = 1 arcminute = 1/60°→ 1o = 60'
1˝ = 1 arcsecond = 1/60' = 1/3600o → 1o = 3600˝
10º ≈ apparent width of fist held at arm’s length
1°≈ apparent width
id h off thumb
h b at arm’s
’ length
l
h
Angular distance between two stars = the angle
between lines from the observer’s eye to the stars.
Angular size of an object = the angle between two lines
from the observer’s eye to the two ends of the object.
½° ≈ angular diameter of the full Moon (or Sun).
The angular distance between δ and α in the Big Dipper
is about the width of a fist held at arm’s length(10°).
δ
90o
α
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The Small Angle Formula
angular diameter linear diameter
=
360°
2π × distance
The Celestial Sphere
The green sphere represents Earth. The
celestial sphere is an arbitrarily large
imaginary sphere with Earth as its center.
The plane determined by the equator intersects the celestial
sphere in a great circle called the celestial equator.
NCP
The vertical line through Earth’s center is its axis of
rotation, which defines the north N and south S poles.
N
The great circle half way between the north and
south poles is the equator.
S
The point on the celestial sphere directly above Earth’s north pole
is called the north celestial pole.
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The horizon for an observer at O is the intersection
of a plane tangent to Earth at O with the celestial
sphere. Everything that the observer can see is
above the tangent plane (represented by the green
line in the figure). The angle between the celestial
equator (yellow line) and the horizon (green line) is
equal to 90° minus the latitude of the observer. For
example, the latitude of an observer at the north pole
is 90°; the tangent plane to this observer’s location
is parallel to the equatorial plane.
NCP
Z
O
The stars are so far away that they appear to the naked
eye to all be at the same distance. They look like they are
embedded
b dd d in
i the
th surface
f
off the
th celestial
l ti l sphere.
h
The point directly above the observer is called the zenith
and is labeled Z in the figure.
NCP
Z
O
Rotate the
diagram so that
the horizon has
its more familiar
orientation.
Z
NCP
O
The Observer at O can see all of the sky above the horizon (green line). Actually, the size of Earth is
negligible compared to the radius of the celestial sphere so we’ll replace the green disk by a point.
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The altitude of the north celestial pole
(denoted by φ in the diagram) is equal to the
latitude of the observer.
Z
NCP
The great circle that passes through the north
celestial pole and the zenith is called the local
celestial meridian.
θ
φ
O
The part of the celestial sphere above the horizon
plane is visible to the observer, so the part of the
sky visible to the observer depends on latitude. At
the North Pole, for example, the stars neither rise
nor set but move in circles parallel to the horizon.
You can verify this by using a desktop
planetariuim program.
At any given latitude (except at the Equator),
Equator)
there are some constellations that never go
below the horizon. These constellations are
called circumpolar.
North Point
South Point
θ=
90o
- latitude
φ = latitude
Motions of Earth
• Relative to the most distant galaxies, Earth rotates once in 23.93 hours.
• It revolves around the Sun once in 365.25
365 25 days.
days
• The angle between the plane of Earth’s equator the plane of its orbit is
23½°.
Rotation Axis
Equatorial Plane
23½°
Ecliptic Plane
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Earth’s orbital motion and the angle between the ecliptic plane and the
equatorial plane cause the seasons.
June 20
December 20
December 20
June 20
Sunlight strikes Earth’s surface at a steeper angle in the summer than in the
winter. The sunlight is more concentrated (spread out over a smaller area),
so it heats up the ground faster and to a higher temperature.
The celestial equator (red line), the
horizon (green line), and the ecliptic
(orange line) are great circles on the
celestial sphere. As Earth moves around
the sun, the sun appears to move along
the ecliptic on the celestial sphere.
As Earth rotates once in 24 hours,
the sun and other celestial objects
seem to move once around the
celestial sphere in circles parallel to
the celestial equator (red line).
Z
Around June 20,, the sun is at
the position labeled SS
(summer solstice) in the
diagram. Its path during one
day is indicated by the yellow
dotted line.
Around December 20, the sun is at the
position labeled WS (winter solstice).
Its path is indicated by the blue dotted
line.
Notice that the Sun is above the horizon
for a shorter time on December 20.
Consequently, the sunlight is heating the
ground for a shorter time than on June 20.
This is another reason why June 20 is
warmer than December 20 in the northern
hemisphere. This situation is reversed in
the southern hemisphere.
Celestial Equator
Ecliptic
NCP
WS
Horizon
SS
Around March 20 and September 20, the sun is on the celestial
equator. Its path during the day is along the celestial equator in the
diagram. These days, and the corresponding points in the sky are
called the vernal equinox and the autumnal equinox, respectively.
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Precession
The motion of the spinning top in the figure is called precession. It is a result of
the force of gravity that tends to tip the top over.
over
Because Earth spins around an axis through its north and south poles and is
not perfectly spherical, the gravitational forces of the Moon, Sun, and planets
cause it to precess. The precession period is about 26,000 years.
As a result, the position of the north celestial pole changes with a period of
26,000 years.
The Milankovitch Hypothesis
1. Eccentricity of Earth’s orbit varies with a period of
100,000 years
2. With a period of 26,000 years, precession of Earth’s axis
of rotation changes the locations in its orbit where the
seasons occur
3. The inclination of Earth’s equator to its orbit varies
between 22º and 24º with a period of 41,000 years.
Ice ages occur with a period of about 250 million years. Within any given ice age,
cycles of glaciation occur with a period of about 40,000 years. Oceanographic evidence
shows ocean temperature variations that support the Milankovitch hypothesis.
Nevertheless, this hypothes is not universally accepted by climatologists.
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This coordinate
system is defined
by giving a
reference line (the
celestial equator)
and a reference
point (the vernal
equinox).
Celestial
Equatorial
Coordinates
The direction
toward any object
in the sky can be
given
i
by
specifying its
celestial equatorial
coordinates.
The vernal
equinox (green
dot) is the point
where the sun
crosses the
celestial equator
on its way
northward in the
spring. The path
of the sun on the
celestial sphere is
called the ecliptic
(orange line).
The celestial equator (red
line) is the great circle
halfway between the
north and south celestial
poles.
Lines of right
ascension are
semicircles from pole
to pole, analogous to
longitude on Earth.
The semicircle from
pole to pole through
the vernal equinox is
d fi d tto h
defined
have a
right ascension of 0
hours. The unit of
right ascension is the
hour of angle and is
equal to the angle
that Earth rotates
through in 1 hour of
time. Right ascension
increases eastward.
1 hour = 15º.
Declination lines are
circles parallel to the
celestial equator,
analogous to latitude
on Earth. The unit of
declination is the
degree.
75º
60º
Declinations south of
the celestial equator
are negative.
45º
30º
20h
15º
4h
21h
3h
22h
23h
0h
-15º
-30º
1h
2h
The celestial
equatorial
coordinates of an
object tell you the
direction in which to
point a telescope in
order to see the
object through the
telescope.
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