Download L2-January 10/08

SCI238 W08
Lecture 2:The Sky
The Origins ofAstronomy
Sun pillar atTahoe
L2-Jan10/08
Early Astronomy
Today’s Lecture
 this week’s events
 Moon
 naked-eye astronomy
 seasons, time and the calendar, precession
 origins of astronomy: prehistory (Stone Age)
 origins: Greek (beginnings of “science”?)
 Pythagoras
 Aristotle
 Hipparchus
 Ptolemy
 Eratosthenes
 origins: Chinese, Hindu, Arabic contributions to
astronomy
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The Sky/Origins of Astronomy
This week’s events:
the Moon: First Quarter Jan 15
Venus: visible low in east before sunrise; brightest
“morning” star
Mars: is visible all night, rises at sunset
Jupiter: not visible
Saturn: rises at 10pm
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Ecliptic = Sun’s path through the Sky (actually the “reflex”
or negative or opposite of the Earth’s motion around the
Sun); it is not in the same plane as the equator – which is set
by the rotation of the Earth. These two planes (ecliptic and
equator) are inclined to each other by 23 ½ degrees Why?
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it is this inclination of Earth’s rotation axis to
its orbital plane that is the primary cause of
our seasons
Why?
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Sunlight: direct/indirect
total hours above the horizon
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Time of day and the seasons: Dec 22
North Pole
Arctic Circle
Tropics
noon
Equator
3 pm
Antarctic Circle
6 pm
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Time of day and the seasons: Mar. 22
North Pole
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Time Measurement
 one second is now defined by a
“hyperfine transition of cesium”… it has a
frequency of 9,192.631,779 per second
(ATOMIC TIME)
one solar second
 1  1.8 10 8 t ( years )
one atomic second
 one day was originally defined by the
Sun’s position (e.g. noon to the next noon)
and this defined the second:
24x60x60=86400 seconds = one synodic
or solar day
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Earth travels ~1o/day around its orbit
So…one solar day requires ~361o of rotation
solar day
vs.
sidereal day
…and a solar
day is ~4 min
longer than a
sidereal day
it’s all in
the orbit!
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many kinds of day, year…
• measuring by the stars: one sidereal day = 23 hours,
56 min., 4.091 sec. which is 86164.091 seconds
• Apparent Solar Time = time measured by Sun’s
position in the sky (a local time)
• Mean Solar Time = average length of Solar day
• Standard Time is the system where all places on the
Earth in a 15 degree wide (in longitude) Time Zone
use the same Mean Solar Time
• Sidereal Year (time for Earth to complete one orbit
against the stars) is 365.6366 Mean Solar Days
• Tropical Year (time from one spring equinox to the
next – i.e. against the Sun) is 365.242199 Mean
Solar Days
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Twenty full Moons: May 05-Dec06
a month?
full Moon to full...
differences in?
•angular diameter
•“aspect”
caused by?
more on scale and
distance later…
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The Calendar




synodic month: 29.53 days (12x29.53=354 days)
sidereal month: 27.32 days
Roman calendar: 13th month every 3rd year
Julian calendar: 12 months,30 or 31 days/month
 leap year every 4th year (year is then 365 ¼ days)
 started 1 January 45 BC
 added 3 extra months to 46 BC
 actual year = 11 min, 14 sec <365.25 days
 by 1582 the calendar was 10 days “short”
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The Calendar
 Solution???
 the Gregorian calendar:
 4 October 1582 was followed by 15 October 1582 (in
Catholic countries)
 century years were not leap years unless divisible by
400
 in England and North America 11 days were added in
1752
 when is Washington’s birthday??
 Napoleon’s victory at Austerlitz in 1805
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Precession
 the Earth spins on its rotation axis, which is
set off at some random angle relative to its
orbital motion
 the other planets, especially Jupiter, exert a
“sideways” force on the spinning Earth
 any spinning object that is pushed sideways
responds by moving at right angles to the
“expected” direction
 the Earth (its rotation axis) changes
direction of spin because of the forces on it
from other bodies
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→ Precession
The Sky/Origins of Astronomy
Precession affects the orientation of a
spinning object’s axis, but not its tilt
Axial rotation period = 24hr; precession period ~26,000yr
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Earth’s rotational axis is always inclined 23.5o to
its orbital plane – but slowly precession changes the
direction in the sky that marks north…
Currently NCP ~ Polaris; in ~13,000yr ~ Vega
Currently NCP ~ Polaris
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Eclipses
 Lunar Eclipse: when the moon passes
through the Earth’s shadow (the
Moon disappears, or “is eclipsed”)
can happen only at Full Moon
 Solar Eclipse: when the Earth passes
through the Moon’s shadow (the Sun
disappears)
can happen only at New Moon
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•Earth is between
the Sun and Moon
• blocks sunlight
from illuminating
the Moon
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Lunar Eclipse
The Sky/Origins of Astronomy
sunlight completely blocked in umbra,
partially blocked in penumbra
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Types of
Solar Eclipses
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Eclipse “Seasons”
• in order for an eclipse to happen, the Earth, Sun,
and Moon must all line up.
• but, while the Sun follows the ecliptic, the Moon
follows a different path around the sky; because
the Earth/Moon orbital plane is inclined ~5o to
the ecliptic
• these planes cross only twice each year => two
eclipse seasons/year
• orientation of Moon’s orbit constantly changes:
the “line of nodes” (where lunar path crosses the
ecliptic) makes a complete circuit every 18.6
years!
• eclipse seasons occur ~20 days earlier each year.
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eclipse seasons illustrated
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orbital planes…ecliptic and lunar
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paths of total solar eclipses 2006-2030
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one total eclipse in 2008;The
one
annular
Lunar eclipses: 2002-2010
viewable in NA
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“Stone-Age” Astronomy
Primarily to mark seasons, special
times of year … the world’s
largest calendars…
 Stonehenge “stone circles”, and
standing stones
 pyramids
 Mayan, Peru
 Medicine Wheels
 also: sundials to give time of day
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Sunrise over Stonehenge: June 21, 2005
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sun dagger at summer solstice:
noon in Chaco Canyon, NM
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Giant “sundial”
in St. Peter’s
Square
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Crescent Moon “predicts” rainfall in
central Nigeria
cause? -> variation in relative positions of Sun and
Moon along the ecliptic throughout the year
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Ancient Greek Astronomy
 planet = “wanderer” – there were 7
planets (Sun, Moon, Mercury, Venus,
Mars, Jupiter, and Saturn)
 Pythagoras (~560-480BC)
 Aristotle (384 - 322BC)
 Aristarchus of Samos (310-230BC)
 Eratosthenes (276-195BC)
 Hipparchus (~190-120BC)
 Ptolemy (~140AD)
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Ancient Greek Astronomy
 Philolaus: non-geocentric cosmology: Earth moves
around central fire (not the Sun!) & “counter
Earth” on opposite side of this fire
 Pythagoras: the “heavenly bodies” are
spherical
 Aristotle
 How can the Earth move? → Geocentric Universe
 Correct explanations of phases of Moon and of
eclipses
 Sun much more distant than the Moon
 Earth spherical
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Ancient Greek Astronomy
 Aristarchus of Samos
Measured the relative distances of the
Moon and Sun and found the Sun was
18-20 times further away then the
Moon
Determined relative sizes of Earth,
Moon, and Sun from lunar eclipse data
(Moon diameter= 1/3 × Earth, Sun
diameter = 7 × Earth)
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Aristarchus’s method of
distances
Determine the
length of time from
third quarter (at
bottom) to first
quarter (at top) = t
1 t
 angle(Moon  Earth  Sun)
2 month
Earth - Moon distance
 cos(angle )
Earth - Sun distance
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Aristarchus’s method for
determining sizes
•Moon and Sun are the same (angular) size in the sky
(1/2 deg.) => they must fit within the same (1/2 deg)
pair of lines: so their relative distances are known.
•From eclipse timing it was known that the Earth’s
shadow is 8/3 the size of the moon. Combine these to
get relative sizes of Earth, Moon, Sun
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angular scale, distance, and diameter
And so…

diameter


360
2  distance
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Eratosthenes
measured the
size of the
Earth from
“shadows”:
sun angles
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Eratosthenes measured Earth’s diameter
d Alexandria Syene
7


360
circumferenceEarth
if dA-S=5000stadia
=> circumference of
Earth = 250,000stadia
or… ~42,000km
(true ~40,000km)
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Ancient Greek Astronomy
 Hipparchus
invented trigonometry
measured positions and brightnesses of 850
stars – high precision, valuable today
celestial coordinate system, magnitude
system, discovered precession
estimated Moon’s size and distance
measured length of year (to within 6
minutes of correct value!)
explained eclipses
“invented” epicycles
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Retrograde Motion
 tracking planetary positions had shown
that some – most notably Mars – did not
follow simple paths across the sky
 superior planets make a loop in the sky
once every year
 the part of their path when a planet is
moving “backward” in the sky is called
“retrograde motion”
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Retrograde Motion
normally planets
appear to move
from west to
east in the sky
but, at times,
superior planets
reverse direction
briefly before
resuming EW
motion
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retrograde motion:
is easily explained in a
Sun-centred SS
•planets more distant
from the Sun orbit
more slowly
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Mars’ retrograde motion
Feb 2006
July 2005
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epicycles “invented” to explain retrograde
motion in a geocentric SS
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Ancient Greek Astronomy
 Ptolemy (140BC)
circles are perfect
→ Epicyclic Theory of Solar System
Needed epicycles on epicycles
→ complicated model
Used parallax to measure distance to
Moon
Published a 13 volume summary of all
astronomical knowledge: the “Almagest”
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Greek Model: Earth is at the centre of the SS/universe;
all objects, including the stars, have their own spheres
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Parallax: Hipparchus and Ptolemy
First, measure the angle to the centre of the Moon from two
positions on the Earth at the same time. Here the Moon is overhead
at one place and at angle α from another place.
In the triangle formed with centres of both Moon and Earth and the
position of the “other place” we know all of the angles (we know
where we are on the Earth – therefore know β), and the length of
one side is the radius of the Earth…
This is enough to get the distance to the Moon! True value =60!
Solar distance was too small by ~10
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Pre-scientific Astronomy in
“the rest of the World”
 Hindus
measurements of Moon
systems of numbers
 Islamic
algebra
records of positions of planets
eclipse records
 Babylonians, Assyrians, Egyptians: calendar,
time-keeping, surveying
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Pre-scientific Astronomy in
“the rest of the World”
 Chinese
Oldest records: 2159BC - two astronomers
executed for calendar errors
good records of comets, meteorites and
supernova (“new stars”)
350BC: Shih Shen makes first star catalogue with
800 entries
Old astronomical records are invaluable!
Normally things change in the sky so slowly that the
timescale is >> than a person’s lifetime
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