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2. Motions on the sky: The celestial sphere

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Star trails

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The diurnal motion

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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.

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We can define a useful coordinate system for locating objects on the celestial sphere by projecting onto the sky the latitude-longitude coordinate system that we use on the surface of the earth.

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.

The celestial sphere

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Latitude

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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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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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Star trails around South Celestial Pole (Gemini Observatory, Chile)

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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.

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This angle = 90o – Latitude!

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Measuring distances on the sphere

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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

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The "Road of the Sun" on the Celestial Sphere

1. Diurnal motion from east to west due to the earth’s spinning around its axis, with ~ 24 h period

2. Drift eastward with respect to the stars ~ 1 degree per day with the period of ~ 365.25 days

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Ecliptic and Zodiac

Sun travels 360o/365.25 days ~ 1o/day

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axis

As a result, planes of the ecliptic and celestial equator make an angle 23.5o

Celestialequator

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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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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.

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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)?

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Solstices

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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.

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The axis tilt causes the seasons!!

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Longer day

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• 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!

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Seasons - summary1. 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.

Note: the Earth is actually closest to the Sun in January 4!

The Seasons in the Northern Hemisphere

Perihelion: 147.09 × 106 km; Aphelion: 152.10 × 106 km

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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.

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Keeping track of time …

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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.

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Precession of the rotation axis

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Precession causes the north celestial pole to drift among the stars, completing a circle in 26,000 years.

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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.

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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.

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Actual motion of the sun and fictitious uniformly moving mean sun

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Myr ago

Puzzle: Ice Ages!

• 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!

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Last Glacial Maximum: 18,000 yr ago32% of land covered with iceSea level 120 m lower than now

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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

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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

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• 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

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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).

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26,000 yr cycle

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As a result, the flux of solar radiation received by the Earth oscillates with different periodicities and amplitudes

This triggers changes in climate

Our Earth makes a complicated motion through space , like a crazy spaceship

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2 4 6 8 10

-1

-0.5

0.5

1

2 4 6 8 10

-1

-0.5

0.5

1

2 4 6 8 10

-1

-0.5

0.5

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f1

f2

f3

2 4 6 8 10

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-1

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f1+f2

2 4 6 8 10

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-1

1

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f1+f2+f3

Adding oscillations with different phases and incommensurate frequencies

f1 = sin[2 t + 1]f2 = 0.7 sin[3.1 t + 2.4] f3 = 1.3 sin[4.5 t + 0.3]

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Adding Milankovitch cycles of solar irradiation for 65 degree North latitude

(Berger 1991)

Note the last peak 9,000 years ago when the last large ice sheet melted

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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.

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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 atmosphereInstant ice age?

Meteorite impacts; Mass extinctions

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• 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?

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