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2. Knowing the Heavens
• Ancient naked-eye astronomy
• Eighty-eight constellations
• The sky’s ever-changing appearance
• The celestial sphere
• Celestial coordinates
• Seasons: Earth’s axial tilt
• Precession of Earth’s rotational axis
• Position & time in astronomy
• Observations & the modern calendar
Ancient Naked-Eye Astronomy
• Cultural context
– Most people lived in rural areas near few people
– Most people were too poor to afford fuel for light
– Most people had lots of time to observe the sky
• People were extremely familiar with diurnal sky motion
• People were extremely familiar with lunar phases
• People were extremely familiar with planetary motion
– People used their imagination
• Constellation arrangements & names
• Astrology & its presumed impact on human affairs
• Scientific context
– People devised accurate measurement equipment
– People tried to predict future events
• Conjunctions of planets with each other & with stars
• Eclipses of the Sun & Moon
Ancient Positional Astronomy
• Definition
– Study of the location in the sky of celestial objects
• Sky location is inextricably tied to observation time
• Examples
– Moon’s position
Monthly
cycles
– Sun’s
Annual
cycles
position
– Planets’ positions
Synodic period cycles
• Instruments
– Stonehenge
England
– Chichén Itzá
Yucatan Peninsula
– Casa Grande
Arizona
Stonehenge: Wiltshire, England
http://www.seeyourinterest.com/2013/05/stonehenge-wiltshire-england/
Chichén Itzá, Yucatan, Mexico
http://www.journeymart.com/holidays-ideas/festivals/chichenitza-equinox-mexico.aspx
Casa Grande National Monument
http://www.theroamingboomers.com/wp-content/uploads/2010/07/Casa-Grande-Ruins-National-Monument.jpg
Eighty-Eight Constellations
• Constellations
– Names given to irregular areas of the night sky
• Based on recognized patterns
• Similar to
cloud
patterns
– Constellation sizes vary tremendously
• Ursa Major
is a very large constellation
• The Southern Cross is a very small constellation
– Stars in constellations are usually far apart
• Analogous to aligned nearby trees & distant mountains
• Asterisms
– Easily recognized parts of constellations
•
•
•
•
Big Dipper
Pleiades
Orion
Trapezium
The Pleiades Asterism
http://en.es-static.us/upl/2009/07/Pleiades_1000.jpg
A Modern Orion Representation
An Ancient Orion Representation
Sky’s Ever-Changing Appearance
• Diurnal motion
The daily motion of the stars
– Caused by the Earth’s very regular axial rotation
– Observational evidence
• The motion of the Sun across the sky every day
• The motion of the stars across the sky every night
• Monthly motion
– Moon
One cycle per “moonth”
• Annual motion
The yearly motion of the Sun
– Caused by Earth’s slightly irregular orbital revolution
– Observational evidence
• The annual cycle of changing Sun elevation at noon
• The annual cycle of changing constellations at midnight
• Irregular motion
– Planets
One cycle persynodic year
Stars Through the Night
The night sky over Kitt Peak Observatory west of Tucson, Arizona
Circumpolar Stars Through a Night
The South celestial pole over Siding Spring Mountain, Australia
The Celestial Sphere
• Unassisted human vision
– Earth appears to be at the center of a huge sphere
• Diurnal motion requires at least one celestial sphere
• Annual motion requires at least one additional sphere
• Irregular motion requires at least two additional spheres
– Many celestial bodies are beyond closest sphere
• These spheres must be made of transparent crystal
– No compelling evidence for any other model
• Assisted
human vision
– The Moon
• Obvious mountains & craters
– The planets
• Jupiter has
four large moons
• Saturn has
rings
• Venus has phases like the Moon
A Model of the Celestial Sphere
Celestial Coordinates
• Foundations
– Two natural points: The celestial poles
– One natural surface: The celestial equator
• Characteristics
– Spherical coordinate system
• Coordinate lines always intersect at right angles
– North-to-South
• Units:
• Positive:
• Negative:
direction
Angle
– 8°12’06”
Point is north of the celestial equator
Point is south of the celestial equator
– East-to-West direction
• Units:
• Positive:
• Negative:
Declination
Right ascension
Time
5h 14m 32.2s
Point is east of the vernal equinox
Point is west of the vernal equinox
Celestial Sphere Coordinates
Earth’s Axial Tilt Causes Seasons
• Facts
– The Earth is a massive spinning top
• The axis points in nearly the same direction in space
• Precession seen as a very slow wobbling of Earth’s axis
• Cause
– Earth’s rotational axis is tilted to its orbital plane
• ~ 23.5°
• Result:
Sun angle varies ~ 47° summer to winter
Sun intensity varies ~ 30% summer to winter
• Patterns
– Opposite in northern & southern hemispheres
– Repeated every year
• Summer Sun high at noon & days longest of the year
• Winter
Sun low at noon & days shortest of the year
Changes in Sunlight Intensity
Earth’s Axial Tilt: Constant In Space
Hallmarks on the Celestial Sphere
• The ecliptic
One circle around the sky
– The apparent path of the Sun
– The projection of the Earth’s orbit
• The equinoxes
through the sky
onto the sky
Two points on the ecliptic
– Derivation:
Equal night & day hours
– Intersection points of ecliptic & celestial equator
• Vernal
March
• Autumnal
September
equinox:
equinox
equinox:
equinox
• The solstices
First day of northern spring
First day of southern spring
Two points on the ecliptic
– Derivation:
North–south Sun motion ceases
– Points halfway between the two equinoxes
• Summer solstice:
• Winter solstice:
First day of northern summer
First day of southern summer
A Model of Solstices & Equinoxes
The Tropics & Circles
• The celestial tropics
– The farthest pole-ward the Sun is directly overhead
• Tropic of Cancer
~ 23.5° North of the celestial equator
• Tropic of Capricorn ~ 23.5° South of the celestial equator
• The celestial circles
– The farthest equator-ward daylight lasts 24 hours
• Arctic
circle ~ 23.5° South of North celestial
~ 66.5° North of
celestial equator
• Antarctic circle ~ 23.5° North of South celestial
~ 66.5° South of
pole
pole
celestial equator
Earth at Northern Winter Solstice
This is also known as the Southern Summer Solstice
Earth at Southern Winter Solstice
This is also known as the Northern Summer Solstice
Earth’s Rotational Axis Precession
• All spinning tops
– Abundant angular momentum
– Unbalanced forces cause rotation axis to wobble
• Directly proportional to angular momentum
• Circular motion of the axis projected into space
• Earth as a spinning top
– RPMs are low but mass is high
– Sun & Moon
cause rotation axis to wobble
• Circular motion of the axis projected into space
– ~ 26,000 years for one complete
precession
cycle
• Changing orientation of the celestial equator
– Precession of the equinoxes
– ~ 26,000 years for one complete first-day-of-season cycle
Precession: Earth A Spinning Top
Ever-Changing Celestial North Pole
Position & Time in Astronomy
• Apparent solar time
– Time based on the Sun’s position in the sky
• Earth’s orbital revolution varies due to its elliptical orbit
– Earth orbits the Sun slowest when distance is greatest
– Earth orbits the Sun fastest when distance is least
• Earth’s axial rotation does not vary
– Local solar noon occurs at Sun’s meridian transit
• The Sun is at its highest point in the sky
• This is the basis for sundial time
• Mean
solar time
– Apparent solar time averaged over an entire year
• This does not vary
• This is the basis for clock time
The Prime Meridian at Greenwich
Earth’s Variable Orbital Speed
Angelic Sundial: Chartres, France
Sidereal & Synodic Time
• Definitions
– Sidereal time
“siderus” =
“star”
• Time based on relationship to the stars
– Synodic time
“synod”
= “meeting”
• Time based on relationship to the Sun
• Causes
– Earth rotates one
time relative to the stars
• 360° of rotation
• Astronomers use sidereal time
Sidereal day
Telescope time
– Earth revolves one degree around the Sun
• ~ 361° of rotation
• Everyone else uses synodic time
Synodic day
Clock time
Visualizing Sidereal Time
Observations & the Modern Calendar
• Observations
– 1.0000 sidereal year = 365.2564 mean solar days
– Julian calendar
Leap years every four years
• Complicated because of precession of the equinoxes
– 1.0000 tropical year = 365.2422 mean solar days
• Julian calendar in error by 11 min 14 sec per year
• The modern calendar
– Gregorian calendar
Pope Gregory XIII intervenes
• Concern about the progressive shift of the date of Easter
• He arbitrarily dropped 10 days (October 5 to 14, 1582)
• He modified the system of leap years
– Only century years divisible by 400 are leap years
– The year 2000 was therefore a leap year
– The year 2100 will not be a leap year
Important Concepts
• Positional astronomy
• Patterns in the sky
– Constellations
– Asterisms
• Movements in the sky
–
–
–
–
Diurnal…
Monthly…
Annual…
Irregular…
Stars
Moon
Sun
Planets
• The celestial sphere
– The celestial poles & equator
– The celestial grid
• Right ascension [time]
• Declination
[angle]
– Earth’s axial tilt
• The ecliptic
• Vernal & autumnal equinoxes
• Winter & summer solstices
• Tropics of Cancer & Capricorn
• Arctic & Antarctic circles
• Precession of the equinoxes
• Time in astronomy
– Apparent & mean solar time
– Sidereal & synodic time
• The calendar & astronomy
– Julian & Gregorian calendars