More
to the point, how should I proceed? I
think perhaps here that an explanation of the seasons should make a good a
starting point as any, given that it really isn’t a difficult scientific
problem and that someone so dear to me proved a classical type B in refusing to
listen to the solution. You can judge as
well at this point: do I make a clear,
coherent theory of the seasons such that a school child could understand it, or
do I leave you still scratching your head?
Let
us begin. I know that somewhere in your
primary education you learned that Earth moves by a double motion: it revolves
around the sun, in a time period known as a year,
and it also rotates on its own axis (an imaginary line connecting the north and
south geographical poles), in a time period we call a day. Abstract knowledge is
not enough here, remember; an act of reasonable, logical imagination is
needed. Thus, I’ve provided a picture of
this double motion, as seen from some vantagepoint way out in space:
Here
the sun is at the center of the picture, and Earth is the blue spheres
revolving about her (of course, there’s only one Earth; the six in the picture
simply show it at different points in its orbit). Although it doesn’t demonstrate Earth’s
rotation about its own axis, it does show the axis, as the faint blue lines
drawn through the various Earths, tilting from bottom left up toward the
right. Earth spins on that axis, which,
you’ll notice, doesn’t change direction as the planet orbits the sun – hint,
this is the key to the explanation. Oh:
The terms periapsis and apoapsis refer to the points in Earth’s orbit
when it is closest and when it is furthest from the sun; for the orbit is not a
perfect circle, but is actually, as Johannes Kepler realized in the 16’th
century, an ellipse in which the sun is at one focus (of two foci) of the
ellipse.
[I
should not assume anything. You can make
an ellipse yourself by using the following directions: place a piece of paper on a table; stick two
pins some distance apart from each other (not too far from each other or too
far from the center of the paper, or the ellipse will fall off the paper and
the experiment won’t work); take a piece of string with the two ends tied
together (making it a loop) and place the loop around the two pins and a pencil
that is in contact with the paper (it should yield a triangular shape for the
string); with the pencil inside the fully stretched out string (remember, the
string is stretched about only the pencil and the two pins), draw the naturally
closed shape on the paper, keeping it taut as you draw all the way around. This shape is an ellipse and the two pins the
foci of the ellipse. It looks, as you
can see in the Earth/sun picture, like a squashed circle; and that’s a good way
describe it.]
All
planetary orbits, including Earth’s, are ellipses with the sun at one focus;
that, recall, is one of (the three of) Kepler’s Laws of planetary motion. Now, you might think at once that this
explains the seasons; for when Earth is closest to the sun it will be summer,
and when it furthest, winter will grip the planet.
You
might be tempted towards such an hypothesis.
Instead, what should immediately smack you on the head is something
you’ve known for a very long time:
Earth’s seasons aren’t neatly divided into summer and winter. When it is summer in the northern hemisphere
it is winter in the southern, and vice-versa.
Indeed, if you look at the picture of Earth’s orbit, you’ll see that the
northern winter solstice (the first
day of winter) occurs just two weeks before periapsis, or the closest approach
to the sun. The same is true of the
northern summer solstice and apoapsis.
So
this hypothesis won’t wash (though I have seen it seriously proposed). What hypothesis will pass muster, as in being
consistent with observable facts? I
hinted before that it lay with Earth’s axis, and indeed in here the solution
presents itself. Go back and look at the
Earth/sun picture yet again, especially at the different Earths’ axes, and
observe something I haven’t pointed yet.
Do you see it? Don’t worry if you
don’t because the significance isn’t all that obvious until you think about it.
If
you haven’t spotted it yet, here it is.
The axes are not straight up and down with respect to Earth’s orbital
plane (the imaginary flat and infinite surface the orbit naturally fits
inside), but are tilted with respect to that plane; and furthermore, as said,
they retain the same tilt all the way through Earth’s orbit – um, at the risk
of getting ahead of myself, this is an example of Conservation of Angular
Momentum, one of the great conservation laws of physics (and is truly what
makes the world go round!).
The
axis tilt in this case is about 23° (degrees), in the system where 90° or a
right angle is just two connecting lines perpendicular to each other (└)
– you should have picked this up from high school geometry, but may have
forgotten so I repeat it here.
Look
at the periapsis Earth point, near the upper right corner of the diagram. The whole explanation for the seasons can be
made here, because what I am about to say will apply to all the Earth
points. This is almost the particular
point (it is really at the winter solstice, the first day of winter, December
21) where in the northern hemisphere the axis tilts furthest away from the sun,
and, conversely, in the southern hemisphere tilts furthest towards the sun. This is the
key to the seasons.
Look
at this particular point I’ve chosen carefully.
Northern Earth appears to be, in fact is, leaning away from the sun,
while the southern part of the planet is leaning toward it. For observers standing on both hemispheres,
the northern one not only sees fewer sunlit hours during a winter’s day (which
is why we say winter has shorter hours, though this is not really true; all
days are 24 hours long, nighttime and daytime parts combined), but also the
angle of the sun is lower in the sky, spreading the portion of sunlight per
ground area (space on Earth’s surface) thin. For the southern
observer, it is high summer for the precise same reasons: more sunlit hours during the day, and a high
sun in the sky, concentrating its rays on a minimum area. Can you see this? I hope that, maybe with some effort, you can.
No
wonder it is cold in winter and warm in summer, and that the two hemispheres
have opposing seasons! The small
difference in overall sunlight received from Earth’s orbit being an ellipse (it
is, in fact, only very slightly elliptical, nowhere near as much as implied in
the picture) makes only a small perturbation (change) to the effects of Earth’s
tilted axis.
In the interests of not over-simplifying things
and so “dumbing science down” (all
attempts will be made to avoid doing so in this book, or at least keep it on
the shortest leash possible), I need to be a little more forthcoming – although
you can skip the following if you feel the need to do so, a need which I’ll
just hope you will resist. I have pretty
much stated flat out that Earth’s orbital axis is about 23° and always points
in the same direction, and that is due to the so-called immutable Law of
Conservation of Angular Momentum. In
fact, looked at from year to year, or even century to century, this is
basically true, which is why my explanation of the seasons can stay
afloat. But, as always, the real picture
is more complicated than this. There are
other motions of the Earth. First, the
angle is not always 23° but “wobbles” about somewhat over hundreds of thousands
of years. Also, the direction of the
tilt also moves, in a circular fashion, over a period of about 25,000
years. This means that 12-13,000 years
from now the northern and southern seasons will have switched and we’ll be
celebrating the winter holidays (Christmas, Chanukah, Kwanza, Festivus, etc.)
during the beginning of summer, just as those in Australia and South America do
today. Easter too will come in the fall,
not spring. (This all assumes any of us
humans will still be here to celebrate them, by no means an automatically true
proposition.) These relatively minor
movements can also be perturbed into larger ones, at least in theory, by the
gravitational influences of the other planets, or by passing stars or other
large objects as they come and go near the solar system over periods lasting
millions of years. If you are interested
by the way, our large moon largely, and fortunately I hasten to add, shields us
from most of the more extreme perturbations; I say fortunately, because it is
unclear whether life, or at least complex life, could exist if Earth were that
unstable in its motions. Interesting are
the whims and wills of the universe!
