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1445 Introductory Astronomy I

Chapter 1

The Night Sky

and Motions of Sun, Earth and Moon

R. S. Rubins Fall, 2010

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The Geocentric Universe

In the ancient idea of a geocentric universe, the Earth was assumed to be at the center of the universe.

Outside the Earth, the Sun and the Moon were the most important celestial objects.

We now know that the importance to us of the tiny Moon, lies only in its proximity, just 240,000 miles from the Earth.

• Behind the Moon were the fixed stars, which appeared to move together around the Earth in a regular motion.

Among the stars were found the planets, following irregular paths, but never straying far from the Sun’s path, which is known as the ecliptic.

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The Planets

The ancient Greeks introduced ingenious, but complicated ideas, to describe planetary motions about the Earth in a manner in keeping with the geocentric model.

Their final model was that of Ptolemy (2nd century), which held sway until the Copernican revolution of the 16th century.

The Earth lies at 93 million miles (or 1 astronomical unit) from the Sun, which is small distance compared to the 3 billion mile of the outermost (major) planet Neptune.

Both these distances are insignificant compared to the distance the nearest star, Proxima Centauri, which is about 25 trillion miles (approximately 4 light-years) away.

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How Many Stars?

• A total of about 6000 stars can be seen by the unaided human eye, although only about half at any one time.

• However, about one half of these stars that we imagine to be single are actually binary pairs; i.e. double stars, which are very close together.

• Thus, without realizing it, we actually see about 9000 stars.

There are estimated to be about 200 billion (2 x 1011) stars in our galaxy, the Milky Way.

Since there are at least 50 billion galaxies in the visible universe, there should be a total of more than 10 billion trillion (1022) stars. although the vast majority cannot be seen, even with the most powerful telescopes.

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Practical Use of Astronomy

• The time to plant seeds was predicted from

i. the positions of the constellations;

ii. the height of the noontime Sun.

• Planning sea travel often depended on the tides, which are influenced by the positions of the Moon and the Sun.

• The positions of the Sun in the day and the constellations at night were used for navigation at sea.

• In particular, the North Star, Polaris, was very important in navigation (in the northern hemisphere), because it closely marks the direction of due north, and its altitude in the sky gives the latitude from which it is observed.

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Constellations• In popular usage, the term constellation is used to denote a

recognizable grouping of stars. • Astronomers have redefined the constellations as 88 regions of

the night sky, while referring to the groupings as asterisms .

The constellation Orion popular usage astronomers usage

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The Big Dipper as a Guide

The two “pointer stars” furthest from the handle of the Big Dipper point to Polaris (the North Star).

The next two stars point in to Regulus, the brightest star in the constellation Leo.

The pattern may appear upside-down because it rotates about Polaris.

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The Winter Triangle

The Winter Triangle connects three bright stars: Betelgeuse (in Orion), Procyon (in Canis Minor) and Sirius (in Canis Major).

This triangle is almost equilateral, but slightly stretched in the direction of Sirius.

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The Summer Triangle

The Summer Triangle connects three bright stars: Vega (in Lyra), Deneb (in Cygnus) and Altair (in Aquila).

This triangle is stretched in the direction of Altair.

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Celestial Sphere 1• The celestial sphere is an imaginary hollow sphere, with the

Earth at its center, to which all the stars seen in the night sky appear to be fixed .

The motion of the stars in the night sky may be visualized as a rotation of the celestial sphere from east to west about a north-south axis.

• The rotation is from east to west because the stars rise in the east and set in the west.

• The fixed stars are actually at widely varying distances, all more than 4 light years (25 trillion miles) away, moving relative to each other with motions that are not apparent to us.

• As a result, changes in appearance of the constellations are not apparent in a human life-span.

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Celestial Sphere 2

Know the following:

North Celestial Pole

South Celestial Pole

Celestial Equator

Declination (latitude)

is measured from

the Celestial Equator.

Right Ascension (longitude)

is measured from the

Vernal Equinox (see below).

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Australian View of the South Celestial Pole In the Celestial Sphere picture, the stars all rotate from east to

west about the line through the celestial poles.

Thus, in Australia, near the Earth’s south pole, the stars all appear to rotate about the South Celestial Pole.

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The Apparent Motion of the Night Sky

• The stars appear to move from east to west as follows:

i. vertically downwards at the equator (if facing West);

ii. downwards and to the right in the USA (if facing West);

iii. from left to right at the north Pole;

iv. from right to left at the South Pole.

Equator USA North Pole

West West

Celestial Sphere and Ecliptic 3

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Geocentric view • Since the Earth is considered to be at rest at the center of the

Universe, the ecliptic is defined as the annual path of the Sun around the celestial sphere.

Sun moves on the ecliptic.

23½ o is the angle between the ecliptic and the celestial equator.

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Celestial Sphere and Ecliptic 2• In the geocentric view, the plane of the ecliptic makes an

angle of 23½o, with the celestial equator.

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The Ecliptic: Heliocentric View• In the heliocentric view, the ecliptic is defined as the path

of the Earth’s orbit around the Sun.• The Earth rotates from east to west, about an axis tilted by

23½o from the normal to the ecliptic plane.•

Normal tothe ecliptic.

North-southrotationalaxis.

23½o

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Equinoxes• Equinoxes (Latin “equal nights”) are those times of the year

in which day and night are of roughly equal length, which occur when the Sun’s position on the ecliptic crosses the celestial equator.

• The vernal equinox occurs on about March 21, when the Sun crosses the celestial equator heading north.

• The autumnal equinox occurs on about September 22, when the Sun crosses the celestial equator heading south.

• Between the vernal and autumnal equinoxes, the days are longer in the northern hemisphere, and the Sun is higher in the sky at mid-day.

• The reverse is true for the time between the autumnal and vernal equinoxes.

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Solstices and the Seasons

• The summer solstice occurs on about June 21, when the Sun reaches the point on the ecliptic furthest north from the celestial equator.

• In summer, the Sun rises in the NE and sets in the NW.

• The winter solstice occurs on about December 21, when the Sun reaches the point on the ecliptic furthest south from the celestial equator.

• In winter, the Sun rises in the SE and sets in the SW.

• If the Earth’s rotation axis were not tilted, seasons (as we know them) would not exist, and every night would last roughly 12 hours.

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Equinoxes, Solstices and the Seasons 3

Summer Winter

The Sun’sdaily path

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The Seasons and the Earth’s Axis• The seasons result from both the 23½o tilt of the Earth’s

rotation axis and its orbit about the Sun.

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Effect of the Changing Distance of the Sun

• While the Sun’s distance from the Earth varies slightly throughout the year, becoming closest on about January 3, it has no noticeable effect on the climate.

• The effect of the Sun being closer in the northern winter is reduced by the fact that the southern hemisphere has a higher percentage of oceans, which reflect heat and light back into space more efficiently than do forested land masses.

• If the Earth’s orbit were very elliptical (like Mercury), then this effect would be more pronounced, and if, in addition, the Earth’s axis were not tilted, then the seasons would be produced only by the varying distance of the Sun.

However, in the latter case, the seasons so produced, would occur at the same time for both hemispheres.

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The Earth’s Precessional Motion 1

• The precessional motion of the Earth’s axis is a very slow conical motion caused by the combined gravitational pulls of the Sun and the Moon.

• The motion is analogous to that of a spinning top.• Calculations have shown that without the presence of the

Moon, the 23½o tilt of the Earth’s rotation axis would not be maintained, with wild swings in the tilt angle being the rule.

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The Earth’s Precessional Motion 2

• During the precessional period of about 26,000 years, the Earth’s north-south axis traces out a circle in the sky.

• Presently, the celestial North Pole points to within a degree of Polaris, but in the year 14,000, it will point roughly towards Vega.

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The Zodiac

• On its apparent eastward journey around the ecliptic, the Sun appears to pass through the twelve Constellations of the Zodiac.

• In 1930, astronomers added a thirteenth constellation – Ophiuchus – which the Sun passes through between December 1 and December 19 each year.

• Over 2000 years ago when the pseudoscience of astrology was introduced by the famous mathematician Euclid, a person’s astrological sign was determined by where the Sun was in the Zodiac on his/her birthday.

• Because of the Earth’s precessional motion, our birthdays are now one sign later than they were 2000 years ago.

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Traveling on Spaceship Earth

• Although we imagine ourselves to be at rest, the Earth takes part in the motions outlined below.

• The Earth spins about its N-S axis, with a period of 1 day, and a rotational speed varies from 1650 km/hr (1030 mi/hr) at the equator to zero at the poles.

• The Earth orbits the Sun with a 1 year period, and a speed of above 100,000 km/hr (60,000 mi/hr).

• Our solar system orbits the center of our galaxy with a 230 million year period, and a speed slightly of about 800,000 km/h (500,000 mi/hr).

• Our galaxy orbits the mass-center of the Local Groupr of galaxies, which in turn orbits the center of the Local (or Virgo) Supercluster.

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Siderial and Synodic Periods

• A siderial period is a period measured with respect to the distant stars.

• A synodic period is the period measured from a planet (or moon).

• The solar day is the synodic day measured from Earth, which is longer than the siderial day by about 4 min.

• The lunar month is the synodic month measured from Earth, which is longer than the siderial month by approximately 2.2 days.

• The tropical year is the synodic year, measured between successive vernal equinoxes, which is shorter than the siderial year by about 20 minutes.

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Solar and Sidereal Days• The solar day is the average time (24 hours) between

successive noon-times, as measured at 0o longitude in Greenwich, England (the prime meridian).

• The sidereal day is the time (23 hours 56 min.) taken for a planet to make one complete revolution.

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Lunar and Sidereal Months• The synodic or lunar month is the time (approximately 29½

days) between identical phases of the moon; e.g. from full moon to full moon.

• The sidereal month is the time (approximately 27.3 days) it takes the Moon to make one full orbit (360o) around the Earth.

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The Year and the Calendar• Ancient astronomers realized that the year was roughly 365¼

days long.• In 47 BCE, Julius Caesar added an extra day every 4 years,

thus creating leap years of 366 days.• Pope Gregory XIII reformed the Julian calendar in 1582, leaving

out 10 days to get the seasons back on schedule, and decreeing that only those century years divisible by 400 were to be leap years.

• The average Gregorian year differs by only one day in 3300 years from the tropical year.

• With the modification that the years 4000, 8000, 12,000 and 16,000 are not to be leap years, the Gregorian system will not have to be revised for 20,000 years.

• An extra second was added between Dec. 31, 2008 and Jan.1, 2009 to allow for irregularities in the Earth’s rotation.

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Lunar Calendars• Lunar calendars follow the Moon’s cycle, which averages 29½

days per month.

• Since the year would contain only 12 x 29.5 = 354 days, an additional month was added usually every 3 years.

• The Jewish calendar (now in the year 5767) is lunar, and is synchronized with the solar calendar by following the 19 year cycle, introduced by the Greek astronomer Meton in 432 BCE.

• Easter has a partially lunar basis, being scheduled as the first Sunday following the first full moon on or after March 21.

• The Islamic calendar is purely lunar, so that 12 months contain about 11 days fewer than a solar year.

• That is why, for example, Islamic festivals, such as Ramadan begin about 11 days earlier on each subsequent year.

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Phases of the Moon 1

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Sky at Sunset The Moon’s position at sunset is shown for 14 evenings,

beginning at the new moon and ending at the full moon.

• Note that west is to your right, which occurs if you are facing to the south, so that the Sun sets to your right.

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Sky at Sunrise

The Moon’s position at sunrise is shown for 14 evenings, beginning at the full moon and ending at the new moon.

• Note that west is to your right, which occurs if you are facing to the south, so that the Sun sets to your right.

PHASES OF THE MOON

PHASE SHAPE MOONRISE WHEN VISIBLE AT NIGHT

New moon - dawn -

Waxing crescent late morning evening

1st quarter noon before midnight

Waxing gibbous afternoon until early morning

Full moon dusk All night

Waning gibbous evening from evening

3rd quarter midnight after midnight

Waning crescent early morning early morning

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Solar and Lunar Eclipses 1• The plane in which the Moon orbits the Earth makes an

angle of 5.2o with plane of the ecliptic.• For an eclipse to occur, the Moon must be full or new at the

same time as its path crosses the ecliptic.

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Solar and Lunar Eclipses 2

• The line of nodes is a hypothetical line joining the two points at which the Moon’s orbit crosses the ecliptic.

• Eclipses occur when the line of nodes points towards the Sun.

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The Eclipse Seasons

• Eclipses are relatively rare, because for eclipses to occur, the Moon must be full or new, just as it crosses the ecliptic plane.

• There are just two short periods in a year, known as the eclipse seasons, when eclipses can occur, although there is no guarantee of eclipses occurring during a particular season.

• Between 2 and 5 solar eclipses can occur in a year, and a similar number of lunar eclipses. However, the total number of eclipses in a year cannot exceed 7.

• It was known to ancient astronomers that the basic pattern of eclipses repeats every 18 years 11.3 days. This repetition pattern is known as the Saros cycle.

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Solar Eclipses 1• A solar eclipse occurs when the Moon blocks some or all of

the Sun’s light, so that the Moon’s shadow falls on the Earth.

• The umbra, the central region of the Moon’s shadow, is surrounded by the penumbra .

• Only in the umbra is the sunlight totally blocked, so that a total solar eclipse or an annular solar eclipse occurs.

• A total solar eclipse occurs when the Moon is relatively close to the Earth, so that it appears large enough to totally blot out the Sun, thus allowing the faint solar corona to be seen.

• An annular solar eclipse appears as a thin ring encircling the Moon’s disk when the Moon is too far from the Earth for it to totally block out the Sun.

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Solar Eclipses 2

The umbra forms a dark spot, which is the region of the total or annular eclipse.

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Solar Eclipses 3

• A total eclipse occurs when the Moon is close enough to block out the Sun’s surface, allowing its outermost layer – the corona – to be seen.

• A partial eclipse is seen from the shadow given by the Sun’s penumbra.

• An annular eclipse occurs when the Moon is far enough away, so that it cannot hide the Sun’s surface completely.

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Total Solar Eclipse Only during a total solar eclipse is the solar corona visible.

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Annular Eclipse

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Solar Eclipse Tracks 2000-2020 The width of the track depends both on the Earth’s latitude and

the distance of the Moon from the Earth during the eclipse.

Saros cycle

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Lunar Eclipses 1

A lunar eclipse occurs when the Moon enters the Earth’s shadow.

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Lunar Eclipses 3

The Moon looks red during a total lunar eclipse for the same reason that the Sun appears reddish at sunrise and sunset, and the sky appear blue.

Sunlight is composed of all the colors of the rainbow (red, orange, yellow, green, blue, violet), and the Earth’s atmosphere preferentially scatters the blue end of this spectrum of colors.

The scattered blue light gives the sky its color, while the missing blue end of the spectrum makes the Sun appear yellow during the day and red at sunrise and sunset, when the Sun’s rays take a longer path through the atmosphere to reach us.

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Lunar Eclipses 2• The Moon appears red in a total lunar eclipse because of the

preferential scattering by the Earth’s atmosphere of the blue end of the spectrum of colors in sunlight.

• As a result, more of the Sun’s red light reaches the Moon.

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Lunar Eclipse Over Dallas