Systems in which numbers are used to give the locations of bodies or events




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Astronomy Notes, Page



I. Astronomy and Time


A. Coordinate Systems

- systems in which numbers are used to give the locations of bodies or events


1. Coordinates

- set of numbers used to locate something

- must agree on a Zero Point, the spot from which the coordinates are measured


2. Great Circle

- circle that divides a sphere into two parts (Ex. = the Equator)


3. Terrestrial Coordinate System

- system used to locate places on the Earth

- the Zero Point is located on the equator, directly south of Greenwich, England


a. Longitude

- describes distance east or west from the zero point

- angle, measured east or west, around the equator from the point where the Prime Meridian intersects the equator

- Prime Meridian (at 0° longitude) is the longitude line passing through Greenwich, England; at 180° E and W longitude is the International Dateline


b. Latitude

- angle measured north or south from the equator

- Equator is at 0° latitude; North and South Pole at 90°N and 90°S latitude respectively


B. The Celestial Sphere

- the imaginary sphere surrounding the Earth upon which celestial bodies appear to carry out their motions


1. Angular Measurement

- used to describe the positions and sizes of objects seen in the sky


a. Degrees

- one degree is 1/360 of a circle

- the most commonly used system for measuring angles uses degrees

- at arms length your index finger is about 1° across, your fist about 10° across the knuckles, and your outstretched hand about 18° across from the tip of your thumb to the tip of your little finger


b. Minute of arc

- is 1/60 of a degree

- some planets have angular sizes almost as large as a minute of arc


c. Second of Arc

- 1/60 of a minute

- equals the angular diameter of a penny at a distance of 4 kilometers (2.5 miles)

- angular sizes of stars are all smaller than 1 second of arc


2. The Horizon System

- coordinate system used to locate the positions of objects in the sky, using altitude and azimuth as coordinates


a. Zenith

- point on the celestial sphere directly above your head


b. Celestial Horizon

- the great circle dividing the celestial sphere into an upper (visible) and lower (invisible) half

- the celestial horizon is situated 90° from the Zenith


c. Meridian

- circle on the celestial sphere that passes from the south celestial pole to the north celestial pole and passes through the observer's zenith

- north and south points on the observer's horizon occur where the meridian crosses the horizon

- celestial equator is the circle midway between the north and south celestial poles; it divides the celestial sphere into northern and southern halves


d. Altitude

- angular distance above the celestial horizon

- the horizon has an altitude of 0° and the zenith has an altitude of 90°


e. Azimuth

- angular distance measured eastward from north around the celestial horizon to the point directly below the chosen position on the celestial sphere

- the azimuth of the east point on the celestial horizon is 90°, the south point is 180°, and the west point 270°

- altitude and azimuth of a star depend on the time and the location where the observation is made


C. Diurnal (Daily) Motion

- daily motion of the stars is westward on a circle that is centered on the North Celestial Pole (situated about 3/4° from Polaris, the North Star)

- pattern of diurnal motion makes it look as if the celestial sphere is rotating on an axis passing through the celestial poles

- motion appears to be counterclockwise if facing north and clockwise if facing south


1. Diurnal Circle

- path that a star appears to follow in the sky

- usually you can observe only part of the diurnal circle because the rest is below the horizon (except for stars that lie in the North Circumpolar Region or in the South Circumpolar Region)


2. Equatorial System

- coordinate system used to describe the angular location of astronomical objects

- uses right ascension and declination as coordinates


a. Declination

- north-south coordinate equal to the angular distance of a star from the celestial equator

- declination is measured in degrees, minutes, and seconds of arc


b. Right Ascension

- angular distance measured eastward along the celestial equator from the Vernal Equinox to the point on the celestial equator nearest the star's position

- Vernal Equinox is the location of the Sun on the celestial sphere on the first day of spring

- right ascension is measured in hours, minutes and seconds (one hour equals 15 degrees)


c. Locating a Star using the Equatorial System

- right ascension (or hour angle) and declination are used to locate stars in the equatorial system, which resembles the terrestrial system of longitude and latitude

- use Star Catalogues to find a particular star to observe

- you need to know where on the celestial sphere the vernal equinox is located; use Sidereal Clocks to keep track of the local hour angle of the vernal equinox; sidereal clocks read 0h (zero hours) when the vernal equinox crosses the meridian and 24h when the vernal equinox returns to the meridian; once the vernal equinox is located, the right ascension and declination of a star can be used to find the star


D. Motions of the Planets


1. Prograde versus Retrograde Motion


a. Prograde (Direct) Motion

- when a planet moves eastward with respect to the stars


b. Retrograde Motion

- when a planet appears to reverse its direction of motion and move westward with respect to the stars

- Synodic Period of a Planet is the interval of time in which episodes of retrograde motion occur


2. Conjuction and Opposition


a. Conjunction

- time when a planet is nearly aligned with the Sun

- for Mercury and Venus, retrograde motion can only take place when the planet appears to pass near the Sun in the sky (near every other conjunction)


b. Opposition

- when the planet is opposite the Sun in the sky

- retrograde motion for all planets (except Mercury and Venus) happens when planets are at opposition


E. Keeping Time


- time keeping is based primarily on celestial events


1. The Ecliptic

- the path that the Sun appears to follow among the stars


a. Zodiacal Constellations

- the constellations through which the Sun appears to move during a year

- includes Virgo, Libra, Scorpius, Sagittarius, Capricornus, Aquarius, Pisces, Aries, Taurus, Gemini, Cancer and Leo


b. Year

- time it takes the Sun to move through the zodiacal constellations and return to the same spot on the celestial sphere (complete one circle around the Zodiac)

- the year is 365.242199 days or 365 days, 5 hours, 48 minutes and 46 seconds long


2. The Seasons


a. Sun Declination

- angle between the equator and the ecliptic is 23.5°, so the Sun's declination varies from +23.5° (north of the celestial equator) to -23.5° (south of the celestial equator) during the year

- Tropic of Cancer is at 23.5° north latitude and Tropic of Capricorn is at 23.5° south latitude


b. Summer Solstice

- the point on the ecliptic where the Sun's declination is most northerly (directly overhead at 23.5° north latitude)

- marks the beginning of Summer, around June 22


c. Winter Solstice

- the point on the ecliptic where the Sun's declination is most southerly

- marks the beginning of Winter, around December 22


d. Autumnal Equinox

- the point in the sky where the Sun appears to cross the celestial equator moving from north to south

- marks the beginning of Autumn, around September 22


e. Vernal Equinox

- the point in the sky where the Sun appears to cross the celestial equator moving from south to north

- marks the beginning of Spring, around March 21

- is the zero point from which right ascension is measured in the equatorial coordinate system

- Tropical Year is the length of time it takes the Sun to return to the vernal equinox; this is the unit of time associated with the annual cycle of the seasons


3. The Month

- the interval from New Moon to New Moon

- therefore there are about 12 lunar cycles per year and 12 months

- Julian Calendar made months 30 or 31 days long; Roman politics resulted in the formulation of our current Calendar

- Religious Calendars (Muslim, Jewish) are often based primarily on lunar cycles


a. Sidereal Month

- the length of time it takes for the Moon to return to the same place among the stars (about 27.3 days)


b. Synodic Month

- the length of time required for the Moon to return to the same position relative to the Sun (about 29.5 days)

- because the Sun moves eastward among the stars, it takes more than a Sidereal Month for the Moon to return to the same position in the sky relative to the Sun


4. Days of the Week

- seven days probably due to 7 visible objects in sky seen by ancient peoples that move with respect to stars (Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn)

- weekdays are named primarily for astronomical objects or ancient gods


5. The Day

- the time from sunrise to sunrise


a. Day Length

- approximately 24 hours (Mean Solar Day)

- Mean Solar Time is the time kept according to the average length of the Solar Day (24 hours)


b. Apparent Solar Day

- the amount of time that passes between successive appearances of the Sun on the meridian

- Apparent Solar Time is time kept according to the actual position of the Sun on the meridian (that is, the difference between the apparent and mean solar time)

- the Solar Day is longer when the Earth is near the Sun and shorter when farther away


c. Sidereal Day

- the length of day it takes for a star to return to the meridian

- the length of a Sidereal Day is 23h 56m 4 s (23 hours, 56 minutes, 4 seconds)


6. Time Zones

- regions of the Earth, roughly 15° wide in longitude, where everyone keeps the same standard time

- the Earth has 24 time zones of one hour each


a. U.S. with Eastern, Central, Mountain, and Pacific Standard Time Zones

- when you move West to East across a time zone add an hour; East to West subtract


b. Daylight Savings Time

- set clocks ahead of Standard time during summer; this provides more recreation hours and saves energy

c. International Date Line

- at 180 degrees longitude where the day shifts


d. Universal Time (UT)

- time kept in the time zone containing longitude 0 (through Greenwich, U.K.)

- provides a "standard" World time


2. Daylight Length

- due to Earth's tilted rotational axis


a. Northern Hemisphere with sunshine more direct in Summer than Winter; therefore longer day


b. Equinoxes

- with Northern and Southern Hemispheres equally lit and day/night of equal length everywhere on Earth


4. A.M. and P.M.

- noon sun lies overhead (at the meridian) at noon

a. Antemeridian (A. M.) - sun lies before (ante) the meridian


b. Postmeridian (P. M.) - sun lies past (post) the meridian


5. Calendars


a. In order for seasons not to get out of sequence with the calendar add one day every fourth year (Leap Year)


b. Gregorian Calendar

- because the Tropical Year is shorter than 365 1/4 days, Century Years are not leap years unless they can be evenly divided by 400 (1900 was not a leap year, but 2000 was)


c. B. C. and A. D.

B. C. - before Christ


A. D. - anno Domini, "in the year of our Lord"

- another system uses BCE (Before the Common Era) and CE (Common Era)


II. Early Cosmological Models


A. Prehistoric Astronomy


Ethnoastronomy – anthropological study of skywatching in contemporary cultures


Archeoastronomy/Archaeoastronomy – how ancient cultures interpreted and utilized sky phenomena


- the religion of many prehistoric peoples included cosmological elements


- humans have kept track of the Moon's phases for possibly 30,000 years

- many prehistoric cultures have kept track of the equinoxes and solstices, probably for religious and/or economic (Ex. = agricultural) purposes


- famous proposed examples include solar alignments in the Neolithic (New Stone Age) tombs at Newgrange (3200 BC) and Knowth (2500-2000 BC) in the Republic of Ireland and at Maeshowe (2800 BC) on the Mainland of Orkney, Northern Scotland

- both solar and lunar alignments have been proposed for Stonehenge (3100-1600 BC) and other prehistoric sites in southern England, and Anasazi/Pueblo sites (900-1150 AD) within Chaco Canyon, northwestern New Mexico


B. Mesopotamian Astronomy

- the Mesopotamians, situated in the region of the Tigris and Euphrates Rivers of modern Iraq, were the first astronomers to make long-term written records of their observations


1. Ziggurats

- pyramid-like towers with seven terraces, each representing one of the wandering celestial bodies visible to the naked eye (Sun, Moon, Mercury, Venus, Mars, Jupiter, Saturn)

- represent the first "observatories", first built about 6,000 years ago

- the Babylonians' ability to predict celestial events marked the beginning of astronomy in the scientific sense (by about 2700 years ago they were able to predict some lunar eclipses)


2. Geometry/Mathematics

- the Mesopotamians originated the idea of dividing the circle into 360° and further dividing each degree into 60 minutes and each minute into 60 seconds


3. Zodiacal Constellations

- the 12 Mesopotamian zodiacal constellations are essentially those we use today to mark the annual passage of the Sun with respect to the stars


4. Astrology

- Mesopotamians invented the pseudoscience of astrology in the belief that the positions of the celestial objects influenced events on Earth


C. Egyptian Astronomy

- Egyptians used astronomy to develop a calendar, for predicting the Nile flood, and in the design of temples and monuments


D. Greek Astronomy

- the Greeks were the first people to raise astronomy from the level of prediction to that of explanation and understanding


1. Eratosthenes (c. 276-195 BC)

- used the relationship between the latitude and altitude of the midday Sun to find the difference in latitude between Syene and Alexandria

- found that the circumference of the Earth is 50 times as large as the distance between Syene and Alexandria, which differed from the true value (about 25,000 miles) by only 15%


2. Hipparchus (ca. 190-120 BC)

- often said to be the greatest astronomer of antiquity; refined earlier methods of finding the distances to the Sun and Moon, improved the determination of the length of the year, made extensive observations and proposed theories concerning the motions of the Sun and Moon

- when comparing his measurements of the positions of stars versus those of earlier Greek astronomers, Hipparchus discovered that there is a slow movement of the celestial poles with respect to the stars (Precession); this causes the coordinates of stars to change with time


3. Ptolemy (ca. 90-168 AD)

- wrote important works on astronomy, optics, geography and music

- invented terrestrial latitude and longitude and was the first to orient maps with north at the top and east to the right

- his method of describing the brightness of stars (the Magnitude System) is still in use

- the Epicyclic Model perfected by Ptolemy used combinations of circular motions to reproduce the motions of planets; it was considered that the Earth is stationary at the center of the solar system (Geocentric Model); according to the model a planet moved in a circle on an Epicycle, which itself moved on a Deferent; the model could predict the positions of celestial objects with such accuracy that it was used for 1500 years


E. Chinese Astronomy

- at least by 1300 BC Chinese began recording eclipses, meteor showers, novas, and comets

- the Chinese accurately determined the length of the year, discovered precession, and used eclipse cycles to predict when eclipses would occur


F. Mesoamerican Astronomy

- the Olmec Culture (ca. 1250 - 400 BC), situated on the Isthmus of Tehuantepec, Mexico, developed the 52 year-cycle "Calendar Round" system with a 260 day "Almanac Year" and a 365 day "Solar Year" (this was the standard calendar for all later Mesoamerican cultures)

- the Maya of Guatemala and Mexico (ca. 1000 BC - 1225 AD) aligned many of their buildings and monuments with the position of sunrise and sunset at the equinoxes and solstices and the position of Venus; built observatories, prepared extensive tables of the movements of astronomical objects, and perfected the Mesoamerican calendar to keep track of the movements of the Sun, Moon and Venus


III. The Birth of Scientific Astronomy


- during the Renaissance, the assumptions of the ancient astronomers was challenged and an entirely new view of the solar system was formulated


A. Arabic Astronomy

- from the seventh to the fifteenth centuries AD, the center of astronomical studies was in the Islamic world; the Arabs translated and preserved the works of the ancient astronomers

- Arabs were the first to build observatories that were "modern" in organization

- many of the Arabic names for the stars (often containing the prefix "al") are in use today


B. European Astronomy

- by the 15th century AD, the astronomy of the ancients was rediscovered by Europeans

- astronomers began to observe again and test hypotheses against observations

- although the geocentric model of Ptolemy was accepted by almost all astronomers, some had growing doubts about the ancient theories of motion and arguments that the Earth was motionless


1. Nicholas Copernicus (AD 1473-1543)

- Polish astronomer who first fully developed the heliocentric ("Sun-centered") model of the solar system

- published
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