Transcript Intro To Astronomy PowerPoint 2

2. Motions on the sky:
The celestial sphere
Slide 1
Star trails
Slide 2
The diurnal motion
Slide 3
The diurnal motion
The entire sky appears to turn around
imaginary points in the northern and southern
sky once in 24 hours. This is termed the daily or
diurnal motion of the celestial sphere, and is in
reality a consequence of the daily rotation of
the earth on its axis. The diurnal motion affects
all objects in the sky and does not change their
relative positions: the diurnal motion causes the
sky to rotate as a whole once every 24 hours.
Superposed on the overall diurnal motion of the
sky is "intrinsic" motion that causes certain
objects on the celestial sphere to change their
positions with respect to the other objects on
the celestial sphere. These are the "wanderers"
of the ancient astronomers: the planets, the
Sun, and the Moon.
Slide 4
The celestial sphere
We can define a useful coordinate system
for locating objects on the celestial sphere
by projecting onto the sky the latitudelongitude coordinate system that we use on
the surface of the earth.
Slide 5
The stars rotate around the North and South Celestial Poles. These are
the points in the sky directly above the geographic north and south pole,
respectively. The Earth's axis of rotation intersects the celestial sphere at
the celestial poles. The number of degrees the celestial pole is above
the horizon is equal to the latitude of the observer. Fortunately, for
those in the northern hemisphere, there is a fairly bright star real close to
the North Celestial Pole (Polaris or the North star). Another important
reference marker is the celestial equator: an imaginary circle around the
sky directly above the Earth's equator. It is always 90 degrees from the
poles. All the stars rotate in a path that is parallel to the celestial
equator. The celestial equator intercepts the horizon at the points
directly east and west anywhere on the Earth.
Slide 6
Latitude
Slide 7
Slide 8
Slide 9
The arc that goes through the north point on the horizon, zenith, and south point
on the horizon is called the meridian. The positions of the zenith and
meridian with respect to the stars will change as the celestial sphere rotates and
if the observer changes locations on the Earth, but those reference marks do
not change with respect to the observer's horizon. Any celestial object crossing
the meridian is at its highest altitude (distance from the horizon) during that night
(or day).
The angle the star paths make with respect to the horizon =
90 degrees - (observer's latitude).
During daylight, the meridian separates the morning and afternoon positions of
the Sun. In the morning the Sun is ``ante meridiem'' (Latin for ``before
meridian'') or east of the meridian, abbreviated ``a.m.''. At local noon the Sun is
right on the meridian. At local noon the Sun is due south for northern
hemisphere observers and due north for southern hemisphere observers. In the
afternoon the Sun is ``post meridiem'' (Latin for ``after meridian'') or west of the
meridian, abbreviated ``p.m.''.
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Slide 11
If you are in the northern hemisphere, celestial objects north of the celestial
equator are above the horizon for more than 12 hours because you see more
than half of their total 24-hour path around you. Celestial objects on the
celestial equator are up 12 hours and those south of the celestial equator are
above the horizon for less than 12 hours because you see less than half of their
total 24-hour path around you. The opposite is true if you are in the southern
hemisphere.
Notice that stars closer to the NCP are above the horizon longer than those
farther away from the NCP. Those stars within an angular distance from the
NCP equal to the observer's latitude are above the horizon for 24 hours---they
are circumpolar stars. Also, those stars close enough to the SCP (within a
distance = observer's latitude) will never rise above the horizon. They are also
called circumpolar stars.
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Slide 13
Slide 14
p. 16
Star trails around South Celestial Pole (Gemini Observatory, Chile)
Slide 15
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Slide 17
Here is a summary of the positions of the celestial reference marks (note that
``altitude'' means the number of degrees above the horizon):
• Meridian always goes through due North, zenith, and due South points.
• Altitude of zenith = 90° (straight overhead) always.
• Altitude of celestial pole = observer's latitude. Observers in northern
hemisphere see NCP; observers in southern hemisphere see SCP.
• Altitude of celestial equator on meridian = 90 - observer's latitude.
• Celestial equator always intercepts horizon at exactly East and exactly West
points.
• Angle celestial equator (and any star path) makes with horizon =
90 - observer's latitude.
• Stars move parallel to the celestial equator.
Slide 18
This angle = 90o – Latitude!
Slide 19
Measuring distances on the sphere
Slide 20
To measure distances on the imaginary celestial sphere, you use ``angles on
the sky'' instead of meters or kilometers. There are 360 degrees in a full circle
and 90 degrees in a right angle (two perpendicular lines intersecting each
other make a right angle). Each degree is divided into 60 minutes of arc. A
quarter viewed face-on from across the length of a football field is about 1 arc
minute across. Each minute of arc is divided into 60 seconds of arc.
The ball in the tip of a ballpoint pen viewed from across the length of a football
field is about 1 arc second across. The Sun and Moon are both about 0.5
degrees = 30 arc minutes in diameter. The pointer stars in the bowl of the Big
Dipper are about 5 degrees apart and the bowl of the Big Dipper is about 30
degrees from the NCP. The arc from the north point on the horizon to the point
directly overhead to the south point on the horizon is 180 degrees, so any
object directly overhead is 90 degrees above the horizon and any object
``half-way up'' in the sky is about 45 degrees above the horizon.
1 degree = 60 arcmin = 3600 arcsec
180 degrees =  radian
Slide 21
p. 17
The "Road of the Sun" on the Celestial Sphere
1.
2.
Slide 22
Diurnal motion from east to west due to the earth’s
spinning around its axis, with ~ 24 h period
Drift eastward with respect to the stars ~ 1 degree per
day with the period of ~ 365.25 days
Slide 23
Ecliptic and Zodiac
Sun travels 360o/365.25 days ~ 1o/day
Slide 24
axis
Celestial
equator
As a result, planes of the ecliptic and celestial equator make an angle 23.5o
Slide 25
Slide 26
p. 22
The ecliptic and celestial equator intersect at two points: the
vernal (spring) equinox and autumnal (fall) equinox. The Sun
crosses the celestial equator moving northward at the vernal
equinox around March 21 and crosses the celestial equator
moving southward at the autumnal equinox around September
22.
When the Sun is on the celestial equator at the equinoxes,
everybody on the Earth experiences 12 hours of daylight and
12 hours of night for those two days (hence, the name
``equinox'' for ``equal night'').
The day of the vernal equinox marks the beginning of the
three-month season of spring on our calendar and the day of
the autumn equinox marks the beginning of the season of
autumn (fall) on our calendar. On those two days of the year,
the Sun will rise in the exact east direction, follow an arc right
along the celestial equator and set in the exact west direction.
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Slide 28
When the Sun is above the celestial equator during the seasons of spring and
summer, you will have more than 12 hours of daylight. The Sun will rise in the
northeast, follow a long, high arc north of the celestial equator, and set in the
northwest. Where exactly it rises or sets and how long the Sun is above the
horizon depends on the day of the year and the latitude of the observer. When the
Sun is below the celestial equator during the seasons of autumn and winter, you
will have less than 12 hours of daylight. The Sun will rise in the southeast, follow
a short, low arc south of the celestial equator, and set in the southwest. The exact
path it follows depends on the date and the observer's latitude.
Drawn for northern latitudes, these are the paths the sun takes across the sky on
the equinoxes and solstices. Can you see that the summer path is longer (and
therefore that the summer sun stays in the sky longer)?
Slide 29
Solstices
Slide 30
Since the ecliptic is tilted 23.5 degrees with respect to the celestial equator,
the Sun's maximum angular distance from the celestial equator is 23.5
degrees. This happens at the solstices. For observers in the northern
hemisphere, the farthest northern point above the celestial equator is the
summer solstice, and the farthest southern point is the winter solstice. The
word ``solstice'' means ``sun standing still'' because the Sun stops moving
northward or southward at those points on the ecliptic.
The Sun reaches winter solstice around December 21 and you see the least
part of its diurnal path all year---this is the day of the least amount of daylight
and marks the beginning of the season of winter for the northern
hemisphere. On that day the Sun rises at its furthest south position in the
southeast, follows its lowest arc south of the celestial equator, and sets at its
furthest south position in the southwest.
The Sun reaches the summer solstice around June 21 and you see the
greatest part of its diurnal path above the horizon all year---this is the day of
the most amount of daylight and marks the beginning of the season of
summer for the northern hemisphere. On that day the Sun rises at its furthest
north position in the northeast, follows its highest arc north of the celestial
equator, and sets at its furthest north position in the northwest.
Slide 31
The axis tilt causes the seasons!!
Slide 32
Slide 33
p. 22
Slide 34
Longer day
p. 23
Slide 35
Shorter day
p. 23
Slide 36
p. 23
• There are no seasons on the equator
(except for the changes related to
weather)
• In reality the seasons “lag”: for example,
maximum summer temperatures occur ~ 1
month later than the summer solstice.
Blame oceans that act as storages of heat!
Slide 37
Seasons - summary
1.
Seasons are NOT caused by varying distances from the Earth to the Sun
2. The primary cause of seasons is the 23.5 degree tilt of the
Earth's rotation axis with respect to the plane of the ecliptic.
The Seasons in the Northern Hemisphere
Note: the Earth is actually closest to the Sun in January 4!
Perihelion: 147.09 × 106 km; Aphelion: 152.10 × 106 km
Slide 38
Thus, we experience Summer in the Northern Hemisphere when the
Earth is on that part of its orbit where the N. Hemisphere is
oriented more toward the Sun and therefore:
1. the Sun rises higher in the sky and is above the horizon longer,
2. The rays of the Sun strike the ground more directly.
Likewise, in the N. Hemisphere Winter the hemisphere is oriented
away from the Sun, the Sun only rises low in the sky, is above the
horizon for a shorter period, and the rays of the Sun strike the
ground more obliquely.
Slide 39
Keeping track of time …
Slide 40
Slide 41
Solar and Sidereal Day
The fact that our clocks are based on the solar day (24 hours) and the Sun appears
to drift eastward with respect to the stars (or lag behind the stars) by about 1 degree
per day means that if you look closely at the positions of the stars over a period of
several days, you will notice that according to our clocks, the stars rise and set 4
minutes earlier each day. Our clocks say that the day is 24 hours long, so the stars
move around the Earth in 23 hours 56 minutes. This time period is called the
sidereal day because it is measured with respect to the stars. This is the true
rotation rate of the Earth and stays the same no matter where the Earth is in its
orbit---the sidereal day = 23 hours 56 minutes on every day of the year. One month
later (30 days) a given star will rise 2 hours earlier than it did before (30 days × 4
minutes/day = 120 minutes). A year later that star will rise at the same time as it did
today.
Slide 42
Precession of the rotation axis
Slide 43
Precession causes the north celestial pole to drift
among the stars, completing a circle in 26,000 years.
Slide 44
Sidereal and tropical year
The precession of the Earth's rotation axis introduces another difference
between sidereal time and solar time. This is seen in how the year is measured.
A year is defined as the orbital period of the Earth. However, if you use the Sun's
position as a guide, you come up with a time interval about 20 minutes shorter
than if you use the stars as a guide. The time required for the constellations to
complete one 360° cycle around the sky and to return to their original point on
our sky is called a sidereal year. This is the time it takes the Earth to complete
exactly one orbit around the Sun and equals 365.2564 solar days.
The slow shift of the star coordinates from precession means that the Sun will
not be at exactly the same position with respect to the celestial equator after one
sidereal year. The tropical year is the time interval between two successive
vernal equinoxes. It equals 365.2422 solar days and is the year our calendars
are based on. After several thousand years the 20 minute difference between
sidereal and tropical years would have made our summers occur several months
earlier if we used a calendar based on the sidereal year.
Slide 45
There is a further complication in that the actual
Sun's drift against the stars is not uniform.
Apparent solar time is based on the component of the Sun's motion parallel to
the celestial equator. This effect alone would account for as much as 9 minutes
difference between the actual Sun and a fictional mean Sun moving uniformily
along the celestial equator.
Slide 46
Slide 47
Actual motion of the sun and fictitious
uniformly moving mean sun
Slide 48
Puzzle: Ice Ages!
Myr ago
• Occur with a period of ~ 250 million yr
• Cycles of glaciation within the ice age occur with a period of 40,000 yr
• Most recent ice age began ~ 3 million yr ago and is still going on!
Slide 49
Last Glacial Maximum: 18,000 yr ago
32% of land covered with ice
Sea level 120 m lower than now
Slide 50
Slide 51
Ice Ages - cause
• Atmospheric composition, especially greenhouse
gases and dust;
• Changes in the Earth’s orbit and inclination;
• The motion of tectonic plates resulting in
changes in the landmass distribution;
• Variations in the solar output;
• The impact of large meteorites;
• Eruptions of supervolcanoes
Slide 52
Cycles of glaciation - cause
• Theory: cyclic climate
changes due to variations in
the Earth’s orbital parameters
– Precession (26,000 yr cycle)
– Eccentricity (varies from 0.00 to
0.06 with 100,000 and 400,000
yr cycles)
– Axis tilt (varies from 24.5o to
22.1o with 41,000 yr cycle
Milutin Milankovitch 1920
Slide 53
Slide 54
• Varies from 0.00 to 0.06 (currently 0.017)
• Periodicity 100,000 and 400,000 yr
• Eccentricity cycle modulates the amplitude of the precession cycle
Slide 55
Slide 56
An effect called precession causes the Sun's vernal equinox point to slowly
shift westward over time, so a star's RA and dec will slowly change by about
1.4 degrees every century (a fact ignored by astrologers), or about 1 minute
increase in a star's RA every twenty years. This is caused by the gravitational
pulls of the Sun and Moon on the Earth's equatorial bulge (from the Earth's
rapid rotation) in an effort to reduce the tilt of the Earth's axis with respect to
the ecliptic and the plane of the Moon's orbit around the Earth (that is itself
slightly tipped with respect to the ecliptic).
Slide 57
26,000 yr cycle
Slide 58
Our Earth makes a complicated motion through
space , like a crazy spaceship
As a result, the flux of solar radiation received by
the Earth oscillates with different periodicities and
amplitudes
This triggers changes in climate
Slide 59
f1 =
sin[2 t + 1]
f2 = 0.7 sin[3.1 t + 2.4]
f3 = 1.3 sin[4.5 t + 0.3]
Adding oscillations with different
phases and incommensurate
frequencies
1
f1
f1+f2
0.5
2
2
4
6
8
10
1
-0.5
-1
2
1
f2
4
6
8
10
8
10
-1
0.5
-2
2
4
6
8
10
f1+f2+f3
-0.5
f3
-1
2
1
1
0.5
2
-1
2
-0.5
Slide 60
-1
4
6
8
10
-2
4
6
Adding Milankovitch cycles of solar irradiation for
65 degree North latitude
Note the last peak 9,000 years ago when the last large ice sheet melted
(Berger 1991)
Slide 61
Very good agreement in general, but some findings are
still contradictory
Myr ago
The response of the climate system to external variations is highly
nonlinear: small external variations can trigger large changes in
climate. Example: ice-albedo positive feedback loop.
Slide 62
Are these effects enough to explain
the Ice Ages???
Other factors? Volcanic winters, impacts, …
71,000 yr ago: eruption of Mount Toba (Sumatra)
2,800 km3 of material thrown in the atmosphere
Instant ice age?
Meteorite impacts; Mass extinctions
Slide 63
• Meteorite impacts
– Mass extinctions and abrupt climate changes
– Meteorite hypothesis
– KT boundary 65 million yr ago (Cretacious-Tertiary
mass extinction):
• 200-km impact crater near Yukatan, Mexico
– PT boundary 251 million yr ago: largest extinction
• 90% of marine and 70% of land species extinct
• 200 km diameter impact crater just found offshore the northwestern
Australia
• Role of climate changes in the development of
hominids?
Slide 64
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