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 ]](https://home.csulb.edu/~rodrigue/geog140/21june.jpg)
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 ]](https://home.csulb.edu/~rodrigue/geog140/21sept.jpg)
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 ]](https://home.csulb.edu/~rodrigue/geog140/21dec.jpg)
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.
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 ]](https://home.csulb.edu/~rodrigue/geog140/declination.gif)
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.
Document and © maintained by Dr.
Rodrigue
First placed on web: 09/04/00
Last revised: 06/04/07