Social Science 101

Dr. Christine M. Rodrigue

EARTH-SUN RELATIONS LECTURE

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THE EARTH IN SPACE (the Final Frontier)

Shape of the earth
     During the Dark Ages, most Europeans believed that the earth was flat
     To this day, there is a "Flat Earth Society" http://www.flat-earth.org
     Today, we've gone back to the ancient Greek and mediaeval Arab idea 
          that the earth is round
          It's not perfectly round, though
               The earth's rotation creates a bulge along the equator and a 
                    flattening along the poles:  The shape, then, is a 
                    flattened oval
               The shape is called an "oblate ellipsoid" = "flattened oval"
          It's not quite a perfect oblate ellipsoid, either
               There's a slight constriction in the Northern Hemisphere
               This may reflect the concentration of the land masses there 
               The effect is a slight tendency to a pear-like shape
               This pear-like oblate ellipsoid is called a "geoid"

Size of the earth
     Circumference:  ~40,000 km (39,840 km) or ~25,000 mi. (24,900 mi.)
     Diameters 
          ~13,000 km or ~8,000 mi.
          Very slightly different diameters depending on the direction of 
               measure because of the oblateness of the earth):
               Equatorial:  12,757 km (7,927 mi.)
               Polar:  12,715 km (7,900 mi.)

Earth motions
     Rotation:  Earth's spinning movement around its own axis each day
          24 hours
          Angular speed of motion:  15 degrees an hour
          Linear speed, therefore, is about 1,600 km/hr or 1,000 mph at the 
               equator (only)
          Major effects:
               Night and day
               Apparent motion of the heavenly bodies from east to west, as 
                    the earth rotates from west to east
     Revolution:  Earth's movement around the sun each year
          365.24219 days
          Rotation and revolution are not in synchrony, therefore
          Calendar fixes are needed to keep them aligned
               See:  http://www.ast.cam.ac.uk/RGO/leaflets/leapyear/
                    leapyear.html
               Leap year -- every year evenly divisible by 4 gets a Feb 29
               Except for the turns of the century
               Unless the century can be divided by 400
               So millenial changes are leap years
          Orbital distance from the sun
               Orbit is elliptical, with variations in speed to conserve 
                    angular momentum 
                    Planets, including Earth, sweep out equal areas in 
                         equal amounts of time
                    So, when the earth is closer to the sun, it has to 
                         travel faster, and, when farther from the sun, it 
                         has to slow down 
                    See http://www.astro.virginia.edu/~eww6n/physics/
                         Kepler'sLaws.html
               Average distance from the earth to the sun
                    ~150,000,000 km (~93,000,000 mi.)
                    This distance is called an astronomical unit (AU) for 
                         measuring the orbits of other planets in our solar 
                         system (Saturn, for example, is about 10 AU from 
                         the sun) or other objects in the neighborhood of 
                         the solar system
               Minimum distance 
                    ~147,250,000 km (~91,500,000 mi.)
                    This happens at perihelion (~3 January)
               Maximum distance
                    ~152,100,000 km (~94,500,000 mi.)
                    This happens at aphelion (~4 July)
          The major effect of revolution is the seasons, but revolution 
               cannot produce seasonality all by itself:  it has to work 
               with a second factor to produce this effect
               This second factor is the tilt of the earth's axis
               The plane of reference for our little dirtball spinning 
                    through space is the plane of ecliptic
                    This is an imaginary flat surface, or plane, resting on 
                         the earth's orbital path
                    The earth's axis is tilted 23 1/2 degrees from the 
                         vertical of the plane of ecliptic
               This axial tilt is constant through time
                    The axis points the same direction at the same angle 
                         all year round (that is, the North Pole always 
                         points to Polaris, the North Star)
                    There is a very long scale (e.g., ~24,000 years) wobble 
                         in the earth's axis, which makes the North Pole 
                         point at different "north" stars over the 
                         millenia, but we can disregard this at the scale 
                         of human lifespans
               The constancy of the axial tilt throughout the earth's 
                    revolution means that, at one part of the year (around 
                    June), the North Pole is pointed toward the sun, while, 
                    at the opposite time of year (around December), the 
                    South Pole points toward the sun
                    So, in June, the Northern Hemisphere gets most of the 
                         insolation (INcoming SOLar radiATION) and warmth, 
                         while the Southern Hemisphere gets little; in 
                         December, the situations are reversed
               Looking at the geometry of the Earth-Sun relationship in 
                    more detail at particular points in the earth's orbit
                    June 21 or so  
                         Solstice (Latin for the sun stands still)
                              Summer solstice in the Northern Hemisphere
                              Winter solstice in the Southern Hemisphere
                         Direct ray strikes well north of the equator
                              23 1/2 degrees north
                              The Tropic of Cancer
                              This is the latitude experiencing the noon 
                                   overhead sun
                              In other words, the declination is 23 1/2 
                                   degrees north
                         Northernmost tangent ray (the one that just barely 
                              brushes the planet and continues on into 
                              space)
                              Strikes beyond the North Pole
                              66 1/2 degrees north
                              The Arctic Circle
                         Southernmost tangent ray
                              Doesn't quite make it to the South Pole
                              66 1/2 degrees south
                              The Antarctic Circle
                         The Circle of Illumination
                              If you drew a line connecting all places 
                                   touched by the tangent rays of the sun
                              Defines the line between night and day
                              The Circle of Illumination is a great circle 
                                   dividing Earth into a night half and a 
                                   day half
                         How this geometry affects the seasonal temperature
                              The wedge of insolation between the Arctic 
                                   Circle and the Equator is larger than 
                                   that between the Antarctic Circle and 
                                   the Equator
                              The sun rays striking the Northern Hemisphere 
                                   are more direct and concentrated than 
                                   those hitting the Southern Hemisphere
                              Together, these factors account for the 
                                   heating of the Northern Hemisphere in 
                                   its summer and the chilling of the 
                                   Southern Hemisphere in its winter
                         How this geometry affects the length of day
                              Follow any place on the Equator over the 
                                   course of the day's rotation:  half of 
                                   the rotation faces the sun and half 
                                   faces away from the sun
                              Follow any place from 1 degree north to 66 
                                   degrees north, and you'll find that it 
                                   spends more time during the rotation in 
                                   the sunny part of the planet and less 
                                   time facing the night sky
                              The days become relatively longer and the 
                                   nights shorter the farther you are from 
                                   the Equator
                              At 66 1/2 degrees north, night disappears:  
                                   someone along the Arctic Circle spends 
                                   24 hours in technical daytime, and you 
                                   have reached the "Land of the Midnight 
                                   Sun"
                              As you travel north from the Arctic Circle, 
                                   the length of time without sunset gets 
                                   longer and longer until, at the North 
                                   Pole, you experience six months of 
                                   daylight:  the June solstice is the 
                                   "noon" of the North Pole's six month  
                                   day!  
                    December 21 or so  
                         Solstice (Latin for the sun stands still)
                              Winter solstice in the Northern Hemisphere
                              Summer solstice in the Southern Hemisphere
                         Direct ray (or declination) strikes well south of 
                              the equator
                              23 1/2 degrees south
                              The Tropic of Capricorn
                         Northernmost tangent ray 
                              Strikes short of the North Pole
                              66 1/2 degrees north
                              The Arctic Circle
                         Southernmost tangent ray
                              Overshoots the South Pole
                              66 1/2 degrees south
                              The Antarctic Circle
                         The Circle of Illumination and the geometry of 
                              Earth's rotation at this point in the 
                              revolutionary round
                              The wedge of insolation between the Antarctic 
                                   Circle and the Equator is now larger 
                                   than that between the Arctic Circle and 
                                   the Equator
                              The sun rays striking the Southern Hemisphere 
                                   are now the ones that are more direct 
                                   and concentrated than those hitting the 
                                   Northern Hemisphere
                              So, now, the Northern Hemisphere is chilled 
                                   and the Southern Hemisphere is toasty 
                                   warm:  it's winter in the north and 
                                   summer in the south
                         How this geometry affects the length of day
                              The days become relatively longer and the 
                                   nights shorter the farther south you are 
                                   from the Equator
                              At 66 1/2 degrees south, night disappears
                              As you travel south from the Antarctic 
                                   Circle, the length of time without 
                                   sunset gets longer and longer until, at 
                                   the South Pole now, you experience six 
                                   months of daylight:  
                                   The December solstice is the "noon" of 
                                        the South Pole's six month  day 
                                   It's also the "midnight" of the North 
                                        Pole's six month night)!  
                    March 21 and September 21 (or thereabouts)
                         These are the equinoces (from equal nights)
                              The March equinox is the spring or vernal 
                                   equinox in the Northern Hemisphere and 
                                   the fall or autumnal equinox in the 
                                   Southern Hemisphere
                              The September equinox is the fall or autumnal 
                                   equinox in the Northern Hemisphere and 
                                   the spring or vernal equinox in the 
                                   Southern Hemisphere
                         At this point in the earth's orbit, both poles are 
                              just tangentially visible from the sun:  the 
                              tangent rays hit the poles
                         The Circle of Illumination passes through the 
                              poles
                         This puts the declination squarely on the Equator
                         Insolation is now evenly split between the two 
                              hemispheres
                         Day and night are everywhere the same length
                              Obviously, as usual, at the Equator
                              Also for all the places from 1 degrees north 
                                   or south to 66 degrees north or south
                              Ditto for the Arctic and Antarctic circles
                              This is true even at the poles!
                                   The first twelve hours of 21 March are 
                                        the last twelve hours of the six 
                                        month night in the Northern 
                                        Hemisphere and the last twelve 
                                        hours are the first twelve hours of 
                                        the new six month day there
                                   The first twelve hours of 21 March are 
                                        the last twelve hours of the six 
                                        month day in the Southern 
                                        Hemisphere and the last twelve 
                                        hours are the first twelve hours of  
                                        the new six month night there
                                   The opposite is true on or about 21 
                                        September
          Those cartographic coordinates, again
               The Arctic and Antarctic circles are the outer limits of the 
                    "midnight sun" phenomenon
               The tropics of Cancer and Capricorn are the outer limits of 
                    the noon overhead sun (or direct ray) phenomenon
                    These two tropics experience the noon overhead sun on 
                         one day each year:
                         Cancer experiences it around 21 June
                         Capricorn around 21 December
                    All places between the two tropics experience the noon 
                         overhead sun two days each year (for the Equator, 
                         those two dates are the equinoces)

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last revised: 06/08/98