Geography 140
Introduction to Physical Geography

Lecture: The Earth in Space (continued)

Earth-Sun Relations at Solstices and Equinoces
and Motion of the Solar System Itself

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        7. Earth-sun relations on or about 21 June.
           a. On or about this date (and it can vary from about the 20th to 
              the 23rd, depending on the leap year cycle), the North Pole 
              points towards the sun, which allows the direct ray to strike 
              well north of the equator, at 23½° N, which 
              corresponds to the axial tilt.  This concentrates the lion's 
              share of the solar radiation in the Northern Hemisphere, making 
              for warm or hot weather.  The Southern Hemisphere is cheated of 
              the solar radiation, giving it cold weather.

                   [ June 21 ] 

           b. This latitude is called the Tropic of Cancer (geotrivia: Why 
              not, say, Scorpio or Aries? Because the astrological sign of 
              Cancer is said to begin on this date -- this should make you 
              popular at parties). 
           c. This means the northernmost tangent ray is displaced past the 
              North Pole, 23½° past 90°: 23½° closer 
              to the equator on the other side of the pole.  Subtract 
              23½° from 90° and you get a latitude of 
              66½° N.
           d. This latitude is called the Arctic Circle. On that date, the sun 
              never completely sets there.  This is the midnight sun 
              experience!  Areas within the Arctic Circle are called the "Land 
              of the Midnight Sun."
           e. Places north of there go longer and longer periods without 
              sunset.  At the Arctic Circle, it's only one day, but the period 
              of midnight sun increases until, at the North Pole, you go six 
              whole months without sunset!  Now you know what's behind the 
              story of the North Pole having a six month day:  June 21st could 
              be thought of as the "noon" of the six month day!
           f. Places along the equator, however, get 12 hours of day and 12 
              hours of night.  North of the equator, any place spinning around 
              the earth's axis spends more of its time facing the sun than the 
              night sky.  Now you know why the days are long in summer and the 
              nights are short.  The difference between night and day gets 
              greater and greater as you move north: At high latitudes, you 
              can have something like 20 hours of daytime and only 4 hours of 
              nighttime! 
           g. In the Southern Hemisphere, everything is just the opposite:
                i. The equator has 12 hours of day and 12 hours of night.
               ii. The farther south you go, the less time a location spends 
                   in the daylight and the more time it spends facing the 
                   night sky: Nights are progressively longer and days 
                   shorter.
              iii. Finally, at 66½° S, you reach the Antarctic 
                   Circle, but now it's 24 hours of nighttime and 0 hours of 
                   daytime.
               iv. As you move farther south from the Antarctic Circle, the 
                   time spent in darkness increases from one day to one week 
                   to one month until finally, at the South Pole, you go for 6 
                   months of nighttime (this would be the midnight of the six 
                   month night down there).
           h. In our Northern Hemisphere, this date is called the summer 
              solstice and marks the beginning of our summer; in the Southern 
              Hemisphere, this date is the winter solstice and marks the start 
              of their winter.
           i. So, Earth-Sun relations account for the greater heat in the 
              Northern Hemisphere (direct ray and other high angle rays are 
              concentrated north of the equator), the longer daylength in the 
              Northern Hemisphere, and the midnight sun experience in the 
              Arctic regions. 
           j. Now you can understand why it is that the northern and southern 
              hemispheres have opposite seasons.               
           k. A bit of geotrivia.  This date is called a solstice, which, in 
              Latin, means "the sun stands still."  What this means is, if you 
              were to stand at one particular spot each evening and 
              systematically recorded where exactly the sun set each day all 
              year round, you would find that the sun set in a noticeably 
              different place each night, particularly in September and March.  
              In June and July, however, you would hardly notice any 
              difference in the location of sunset (north of due west).  So, 
              the ancients said "the sun stood still" and this time is still 
              called the solstice.  
        8. Earth-Sun relations on or about 21 September (again, this date 
           changes, depending on the leap-year cycle)
           a. As the earth swings along its orbit around the sun, the constant 
              tilt of its axis means that the North Pole begins to shift away 
              from pointing into the sun.
           b. By September 21st, the North Pole is only tangentially visible 
              from the sun, pointing to the upper left -- and the South Pole 
              has just swung around into being barely tangentially visible to 
              the lower right.  The equator would now appear as a straight 
              line trending from the upper right to the lower left.
           c. Swinging around the planet to a point above the equator, where 
              we can see half of the tangent rays on the planet, we see that 
              both poles are touched by the tangent rays and the circle of 
              illumination forms a straight line crossing the equator at right 
              angles:

                   [ September or March 21 ] 

           d. Looking at the situation, we see that the direct ray is now 
              directly (sorry) on the equator on this date.
           e. Looking at any location, we can see that it will spend half of 
              one rotation facing the sun and half facing away from the sun.
           f. This means that all places on Earth experience 12 hours of 
              daylight and 12 hours of night.
                i. The equator always has 12 hours each, all year round.
               ii. But so does Long Beach at 34°N
              iii. And Buenos Aires, Argentina, roughly 35° S
               iv. And at the North Pole, the first 12 hours of this date are 
                   the last 12 hours (technically, given the twilight effect) 
                   of the six month day and the last 12 hours of the date are 
                   the first 12 hours of the six month night:  This is sunset 
                   at the North Pole.
                v. Similarly, the first 12 hours of the date at the South Pole 
                   are the last 12 hours of the six month night and the last 
                   12 hours of the day are the first 12 hours of the six month 
                   day (with caveats for the twilight quality).
               vi. So, everywhere on Earth, night is (technically) equal to 
                   day on this date:  Everywhere on Earth has the same amount 
                   of nighttime today. This is, therefore, an equinox, which, 
                   in Latin, means "equal night."
           g. We call this date the fall equinox in the Northern Hemisphere or 
              the autumnal equinox, and it marks the beginning of fall (or 
              autumn) for our hemiphere; in the Southern Hemisphere, this is 
              the spring equinox or the vernal (green) equinox, and it marks 
              the start of spring there, when greenery pops out all over.               
        9. Earth-Sun relations around 21 December (again, remembering that the 
           date changes from one year to the next)
           a. The earth continues along its orbit, all the while maintaining 
              the constant tilt of its rotational axis.  This means that the 
              North Pole begins to point away from the sun, while the South 
              Pole now points toward the sun.  The equator would look like a 
              curve bent upwards.

                   [ December 21 ] 

           b. This produces exactly the opposite situation we analyzed for the 
              21st of June.
           c. The direct ray is now positioned well into the Southern 
              Hemisphere.  How well? 23½° S.  Want to guess the 
              name of this latitude?  Yup -- it's the Tropic of Capricorn, 
              because astrology buffs tell you it's the beginning of the "sun 
              sign" Capricorn (even though, because of the precession of the 
              equinoces, the sun no longer rises in the constellation 
              Capricorn on this date).  This concentrates the most direct rays 
              of the sun in the Southern Hemisphere, together with the heat 
              they produce.  The Southern Hemisphere is now hotter than the 
              Northern.
           d. The northernmost tangent ray again strikes at the Arctic Circle, 
              but this time in such a way as to shade the North Pole and the 
              Arctic regions.  The Arctic Circle now gets 24 hours in which 
              the sun technically fails to rise.  The farther north you go, 
              the longer the time the sun fails to rise, until, at the North 
              Pole, you are now in the middle of the six month night.  This 
              date is the "midnight" of the six month night.
           e. The southernmost tangent ray again strikes at 66½° S, 
              along the Antarctic Circle, but this time so that the South Pole 
              and the Antarctic regions are now bathed in constant sunshine:  
              24 hours at the Antarctic Circle and progressively longer and 
              longer periods of constant sunshine until, at the South Pole, we 
              experience the "noon" of the six month day there.  It's now the 
              Antarctic regions (those bounded by the Antarctic Circle) that 
              are the "Lands of the Midnight Sun."
           f. The equator still spends half a rotation in the daytime and half 
              in the nighttime (hence, the constant equality of night 
              at day at the equator.
           g. All places north of the equator spend a greater and greater 
              proportion of their rotational periods in nighttime and a 
              smaller and smaller period facing the sun:  It's now the 
              Northern Hemisphere that has short days and long nights.  This 
              gets progressively more extreme, until at the Arctic Circle, 
              we're talking 24 hours of nighttime and 0 hours of daytime.
           h. All places south of the equator not only enjoy the warmer 
              temperatures that the concentrated sunlight in their hemisphere 
              brings, but the longer and longer days of summer and shorter 
              nights of winter. At the Antarctic Circle, this disparity 
              between day and night finally hits the 24:0 ratio.
           i. This date, then, is the winter solstice in the Northern 
              Hemisphere, which marks the start of our winter, and the summer 
              solstice in the Southern Hemisphere, marking the beginning of 
              the Austral summer.
       10. Earth-Sun relations on or about 21 March (don't forget the 
           changeability of this date).
           a. The earth continues along its orbit, maintaining its constant 
              axial tilt, and this means that the South Pole no longer points 
              toward the sun.

                   [ September or March 21 ] 

           b. By the time the March equinox rolls around, the North Pole and 
              the South Pole are again just tangentially visible from the sun, 
              the North Pole now pointing to the upper right and the South 
              Pole to the lower left.
           c. Again, the equator would form a straight line, this time 
              trending from the upper left to the lower right.
           d. Other than that, the geometry of direct rays and of tangent rays 
              is exactly as it was for the 21st of September or thereabouts. 
                i. The equator again gets a boring 12:12 ratio of day to 
                   night.
               ii. So does every other place on Earth, including the North 
                   Pole (coming out of its six month night: sunrise) and the 
                   South Pole (coming out of its six month day: sunset).
           e. This date, too, is an equinox ("equal night"):  the spring or 
              vernal equinox here in the Northern Hemisphere and the fall or 
              autumnal equinox for those in the Southern Hemisphere.
       11. To view an animation illustrating Earth-Sun relations at equinoces 
           and solstices, click here.   
       12. Quick review of the cartographic terms associated with revolution, 
           the tilt of the earth's axis, and seasonality.
           a. The tropics are the outer limits of the noon overhead sun, of 
              the direct ray of the sun.
                i. The Tropic of Cancer is the one in the Northern Hemisphere, 
                   at 23½° N, and the direct ray of the sun is 
                   experienced there on one day of the year, on or about the 
                   21st of June.
               ii. The Tropic of Capricorn is the one in the Southern 
                   Hemisphere, at 23½° S, and it experiences the 
                   noon overhead sun one day each year, too, but on or around 
                   the 21st of December.
              iii. All places in between the tropics experience the direct ray 
                   of the sun two days a year, once when the direct ray is 
                   migrating north to Cancer and again when the direct ray is 
                   migrating south to Capricorn (for instance, the equator, 
                   halfway between the two tropics, receives the direct ray of 
                   the sun on or about the 21st of September and again on or 
                   about the 21st of March).
           b. Declination of the sun refers to that latitude experiencing the 
              noon overhead sun on a given day.
                i. The declination of the sun is 23½° N on or about 
                   the 21st of June.
               ii. It's 23½° S on or around the 21st of December.
              iii. It's 0° around the 21st of September and again around 
                   the 21st of March.
               iv. You can learn the precise declination of the sun for any 
                   date by plugging in the following formula:
                   d = 23.44 * sin [360/365 * (284 + N)]  where:
                       d = declination
                       N = the number of a day in the year (so, 1 January 
                           would be 1, 25 February would be 56, you get the 
                           idea).
                   You would add N to 284 and divide 360 by 365.  Then, you 
                   would multiply those two answers and take the sine 
                   (you can try this convenient online scientific 
                   calculator, which has a sine button).  
                   After doing that, you'd multiply that answer by 22.44 
                   (which is 23°26'28" expressed as a decimal to make the 
                   math easy).  Voilà! -- declination for a given day. 
                v. You can also learn the declination for a given day by 
                   simply consulting a declination chart, such as this one:

                   [ September or March 21 ] 

               vi. Alternatively, you can consult an analemma, 
                   which provides day by day information on the sun's 
                   declination and information on whether the sun is fast or 
                   slow (that is, whether the apparent motion of the sun takes 
                   less than 24 hours or more than 24 hours, because of the 
                   difference in tropical time and sidereal time and where we 
                   are in our orbit -- more on that in a bit).  
           c. The Arctic and Antarctic circles are the outer 
              limits of the midnight sun phenomenon.
                i. They are the farthest latitudes from each pole that ever 
                   experience the midnight sun or the sunless noon.
               ii. This happens only one day at the Arctic or Antarctic 
                   circles and for progressively more and more days as you 
                   move closer to the poles, until at the poles we're talking 
                   six months of constant sunshine and six months of constant 
                   nighttime.
              iii. Their latitudes, 66½° N or S, reflect the axial 
                   tilt of 23½° from the vertical of the plane of 
                   ecliptic:  You get them by subtracting the axial tilt from 
                   90° N or S, the latitude of each pole.
       13. Mentioning the analemma reminds me about the sun-fast/sun-slow 
           thing.  
           a. Because the earth's orbit is elliptical, that means its speed 
              varies over the course of the year:  It moves fastest around 
              perihelion and slowest around aphelion.
           b. This is predicted by Johannes Kepler's laws.  Kepler, who lived 
              from 1571 to 1630, is one of the folk heroes of many sciences.  
              He formulated three laws for the understanding of planets' 
              motions:
                i. Each planet travels in an elliptical orbit, with the sun at 
                   one of the two foci of that orbit.
               ii. Most relevant here: The imaginary line connecting a planet 
                   with the sun sweeps out equal areas in equal times.  That 
                   is, let's say we drew a line from Earth to the sun at one 
                   point in time (oh, July 1st) and then did it again some 
                   time later (oh, how about ten days later, July 11th?).  
                   We'd figure out the area in the wedge between the sun and 
                   the earth at those two points in its orbit.  Then, we'd 
                   repeat the experiment half a year later, drawing a line 
                   from the earth to the sun on, let's say, January 1st and 
                   then again ten days after that, January 11th.  Again, we'd 
                   calculate the area.  What we'd find is the longer wedge at 
                   aphelion (July) would have to be skinnier so that it 
                   included the same area as the shorter wedge at perihelion 
                   (January).  This means the earth wouldn't have travelled 
                   along its orbit as far in July as it would in January.  
                   Thus, the earth speeds up in January and slows down in July 
                   to preserve Kepler's Second Law.
              iii. For the sake of completeness, Kepler's Third Law states 
                   that the square of the period of a planet (its year) is 
                   proportional to the cube of its mean distance from the sun.  
                   The farther it is out there, the longer its year. That's 
                   why, when astronomers figure out how long an extrasolar 
                   planet's revolution takes, they can infer how far it is 
                   from its star.       
           c. This variation in speed means that, at the end of a 24 hour 
              rotation of 360°, the planet has moved farther along its 
              orbit than it would have in 24 hours on a perfectly circular 
              orbit -- or not so far along (depending on the time of year).  
              So, rotating 360° means you return to the 0° point, 
              which would be obvious if you were looking at a far distant star 
              outside the solar system (assuming you could in broad 
              daylight!).  But the sun will be relatively little or somewhat 
              more to your left 24 hours later, because you've moved along the 
              orbit while you were rotating.  It won't be in the same relative 
              position with respect to some other distant star.  To see the 
              sun in the same relative position in a circular orbit, you need 
              to rotate a shade under 361°.  If the orbit is elliptical, 
              though, 361° will overcompensate at some times (aphelion) 
              and undercompensate at others (perihelion) because of the 
              different rates of speed and distance covered in the orbit at 
              different times of year.  So the sun would be seen as farther 
              east or west than you expected it to be when your watch reads 
              noon.  This is also why sunrise and sunset are not perfectly 
              symmetrical, the same time before and ahead of noon on your 
              clock.
           d. So, what does this have to do with the analemma? The analemma 
              gives you the declination of the sun (its N/S latitude) for a 
              given day, and it also gives you the "equation of time," the 
              amount of time by which sun time is off in comparison with a 
              perfectly 24 hour clock.
           e. You can create a really cool analemma of your own, if you have a 
              lot of time and self-discipline (only about a half dozen people 
              on Earth have had the time and obsessiveness!).  What you do is 
              set up a camera to take really fast exposures of the sun on the 
              same exact frame at exactly noon (according to your clock) on a 
              regular basis throughout the year (every ten days or every 
              month).  When, after a year's labor, you develop that one frame, 
              you'll see the analemma in your own sky.  It'll come out looking 
              kind of like here.
     G. Well, this lengthy section (F) takes care of revolution as one of the 
        kinds of motions carried out by Earth (the other major one being 
        rotation, discussed in section E).  There are some other motions, 
        though, in which the earth is involved.
        1. The axis wobbles.  
           a. Right now, the axis is about 23½° from the 
              perpendicular of the plane of ecliptic, but, because of a wobble 
              in the axis, that tilt has varied through time from 21°39' 
              to 24°36'.
           b. The periodicity of this wobble is 40,600 years.
           c. Because of this wobble, the North Pole points to different "pole 
              stars" through time.
                i. Right now, it's Polaris (the North Star)
               ii. In about 12,000 years, the North Star will be pointing to 
                   Vega, the brightest star in the constellation Lyra (the 
                   Harp), which is in our summer skies.
           d. The wobble means that our Northern Hemisphere summer, which now 
              takes place around aphelion, will in 10,000-11,000 years 
              coïncide with perihelion, making our summers a bit hotter 
              (the more so since the Northern Hemisphere heats up more than 
              the Southern Hemisphere in summer anyhow, because of the greater 
              preponderance of landmasses in the Northern Hemisphere).
        2. The eccentricity of the orbit also varies.
           a. Right now, the semimajor axis is 149,597,870.7 km from the sun 
              and the semiminor axis is 149,576,880.8 km, which is not really 
              very different:  The earth's orbital eccentricity, then, is only 
              0.017 (I got that by squaring both the semimajor and semiminor 
              axes, subtracting the smaller from the larger and raising the 
              answer to the 0.5 power and then dividing that answer by the 
              semimajor axis)
           b. The earth's orbital eccentricity varies over time from a minimum 
              of 0.01 to a maximum of 0.07, kind of bouncing from a more 
              perfectly circular shape to a more oval one over complex cycles 
              of 95,000 years and 413,000 years.  We're pretty close to a 
              minimum now (orbit almost circular).  When we attain maximum 
              eccentricity, perihelion will be about 5 percent closer, which 
              will exaggerate our seasons:  Summers will be hotter and winters 
              will be colder.  These changes in seasonality may have something 
              to do with the timing of the great ice ages, so it's not a 
              trivial difference in the long run.
        3. The earth is part of the solar system, which itself revolves about 
           the core of the Milky Way galaxy, to the suburbs of which we 
           belong, moseying along at some 225 km/sec (around 140 mps)!!!  A 
           complete revolution of the galactic center takes about 250 million 
           years.  We're out about two thirds of the way from the core, about 
           30,000 light years out in the disk part of the galaxy, in one of 
           its spiral arms (the Orion-Cygnus arm).  There are some 400 billion 
           stars in this galaxy alone!
        4. The Milky Way is itself moving within the Local Group of galaxies 
           (which includes Andromeda and the Magellanic Clouds) some 300 
           km/sec (185 mps).
        5. With respect to the microwave background radiation, the echo of the 
           Big Bang, we're moving about 380 km/sec (around 235 mps) towards 
           the constellation Leo -- this is our absolute velocity with respect 
           to the structure of space itself.

Well, that's it for the size and shape of the planet and its complicated 
motions in space.  In the next lecture, I'll introduce the geographic grid 
(latitude and longitude) and how to navigate with the stars, sun, a peculiar 
watch, and an analemma.


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Document and © maintained by Dr. Rodrigue
First placed on web: 09/04/00
Last revised: 06/04/07

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