Download m02a02

Module 2: Star Gazing
Activity 2:
Earth’s Seasons
Summary:
In this Activity, we will investigate:
(a) the Earth’s orbit around the Sun,
(b) the origin of the seasons on Earth, and
(c) the Earth’s precession.
The Ecliptic
At the end of the last Activity we introduced the ecliptic,
which is the apparent path of the Sun across the sky.
Remember that the plane of
the ecliptic is an imaginary
surface in space containing
the Earth’s orbit around the
Sun.
The Earth takes one year to make a complete orbit
around the Sun.
What else do you know about the Earth’s orbit around
the Sun besides how long it takes?
(a) The Earth’s orbit around the Sun
You might think that the Earth
travels around the Sun in a
circular orbit ...
… but actually the shape of
the Earth’s orbit is an ellipse.
You can think of an ellipse as a “squashed” circle
(but note that this one is quite exaggerated!).
Elliptic orbits can have various shapes,
from:
“squashed”, or more
technically, orbits of high
eccentricity
to:
nearly or completely circular,
or more technically,
orbits of low or zero eccentricity.
A circle is in fact a special case of an ellipse.
Ellipses are characterised by their eccentricity e,
which varies from:
e=0
e  0.8
Circles are ellipses with zero eccentricity.
e = 0.99999...
The Earth’s orbit is nearly circular, with e = 0.0167.
Its average distance from the Sun is 149,597,900 km.
We write large numbers like this in a mathematical shorthand
called scientific notation, where
149,597,900 km = 1.49597900 x 108 km
where the 108 is 1 followed by 8 zeros. This is the same as
multiplying 1.49597900 by 10 eight times.
In astronomy, however, we have more convenient way
of representing the average distance from the Earth
to the Sun:
it’s defined as one Astronomical Unit,
where 1 AU = 1.495979 x 108 km
1 AU
We’ll find Astronomical Units (AU) convenient when
we compare distances between the Sun and other
planets in our Solar System.
The small eccentricity of the Earth’s orbit (0.0167) means
that its distance from the Sun varies by
0.0167 x 2 *x 1.495979 x 108 km,
or about 5.00 x 106 km during the course of a year.
This is a variation of
only about 3% in the
overall orbital radius,
but represents a
distance of about
400 times the Earth’s
diameter.
For more information about
elliptic orbits, click here.
* The factor of 2 is here is because the eccentric orbit
can take the Earth to a distance of 1AU  0.0167AU
(b) The origin of the seasons on Earth
As we saw in the last Activity, one (Earth) year is the
time it takes for Earth to make a complete orbit around
the Sun.
The Sun
The Earth
However, we can’t really feel that the Earth is orbiting
the Sun (even though the Earth is travelling 30 km/s!),
and these days not many people take notice of the
Earth’s orbital position (that is, people don’t take much
notice of the changing of the constellations in the night
sky).
We primarily notice the passing of a year by the cycle
of the seasons.
Other planets have seasons too. Investigating the
reasons for Earth’s seasons will help us understand the
conditions on other planets also.
So what is the cause of the seasons?
Clearly the seasons have something to do with the
Earth’s orbit around the Sun. Yet many people are
confused about why the Earth has seasons.
Before going on to the next slide,
have a think about it yourself:
what is the cause of the seasons?
“The seasons are caused by the changing distance between
the Earth and the Sun, and it is warmer in summer because
the Earth is closer to the Sun at summer time.”
This is a very common response - and it is true that the
Earth-Sun distance does charge. As we just saw, the Earth’s
distance from the Sun varies by about 3% during its orbit.
So could summer occur when the Earth is closest to the Sun?
The problem with this idea is that when it’s summer in the
northern hemisphere, it’s winter in the southern hemisphere,
and vice versa. So if this were the correct answer, it would
be the same season in both hemispheres at the same time which is not the case.
The Earth’s rotational axis is tilted by 23.5° with respect to
a line drawn perpendicular to the plane of the ecliptic.
23.5°
Earth’s rotation axis
The seasons result from
this tilt of the Earth’s axis
of rotation.
This is true not only of the
Earth, but all other planets
plane of the ecliptic with tilted rotation axes, as
we shall see.
The direction of the rotational axis stays (nearly) fixed in
space while the Earth orbits the Sun and the hemisphere
that seems to “lean into” the Sun experiences summer,
while the hemisphere that “leans away” from the Sun
experiences winter.
northern hemisphere
summer in NH
(leans into Sun)
winter in SH
(leans away from Sun)
And six months later the opposite is true:
“leans away” from Sun
 winter in NH
southern hemisphere
“leans into” Sun
 summer in SH
Thus the tilt of the Earth’s rotation axis naturally explains
why the seasons are opposite in the northern and
southern hemispheres.
In December, when the southern hemisphere is tilted
towards the Sun, the southern part of the Earth receives
more sunlight and experiences long summer days.
At the same time, the northern hemisphere is tilted away
from the Sun and receives less sunlight, experiencing
short winter days.
N
If you live near the
Equator, there is not
much difference between
the seasons all year
round.
Sun
S
If we take the case when the northern hemisphere
is in summer ...
rotation axis
sunlight
equator
not only does the northern hemisphere receive more
sunlight, but it receives more direct sunlight because the
Sun is higher in the daytime sky. This helps heat the
atmosphere in summer.
When the Sun is higher in the
summer sky, the sunlight is
more concentrated ….
Concentrated beam
of Summer sunlight
… than in winter, when the
Sun is lower in the sky, and
the sunlight is more diffuse.
Diffuse, “spread-out”
beam of Winter sunlight
… so for the hemisphere experiencing Summer, sunlight
striking the Earth is more concentrated and this helps to
raise the average temperature.
The reverse is true for the hemisphere experiencing
Winter.
During spring and autumn, the two hemispheres receive
approximately equal amounts of sunlight.
Let’s have a look how it works during the course of a year:
northern spring
northern summer
northern hemisphere
winter
southern
northern autumn
winter
southern spring
southern autumn
southern hemisphere
summer
As we’ve already mentioned, if you live near the Equator,
you don’t really notice the changing seasons during the
course of a year. Generally you just have two seasons:
“dry” and “wet”!
If you are at the North or South Pole, then also experience
two very long seasons: in summer, the South Pole is
leaning towards the Sun and there is “daylight” for nearly
six months. In winter, the South Pole is leaning away from
the Sun and it is “nighttime” for nearly six months.
If we take the case when the northern hemisphere
is in midsummer ...
then the north pole has continuous daylight
and locations in the northern hemisphere
have long periods of daylight,
equator
sunlight
whereas locations in the
southern hemisphere have long nights.
the south pole is in continuous darkness
So in summary, the cause of the seasons is the tilt of the
Earth’s rotational axis, and as a consequence of this tilt:
23.5°
the Sun is higher in the sky for longer
during summer days (and lower in the
sky for a shorter number of hours on
winter days);
and because the Sun in higher in
the summer sky, the heating of the
Earth’s surface is more direct
plane of the ecliptic
(whereas the low winter Sun‘s
heating is more diffuse).
As we will see, whether the rotational axis is tilted or not
determines whether other planets experience seasons
too.
(c) The Earth’s precession
During its yearly orbit around the Sun, the Earth’s
rotation axis is fixed in space.
23.5°
However, if we could watch
the orientation of the Earth’s
rotation axis over a very
long period of time (about
26,000 years!), we would
see that it in fact
plane of the ecliptic
precesses.
The precession of the Earth is due to the gravitational
“tug of war” on the Earth by the Sun and the Moon.
Not to scale!
The Earth’s rotation creates an
“equatorial bulge” (meaning
the Earth is fatter at the
equator than at the poles).
The Earth’s tilt means the Sun and Moon are not aligned with
the equator, and both the Sun and Moon try to pulls the
Earth’s equatorial bulge closer to it.
The combined pull of the Sun and Moon, along with the
Earth’s own rotation, result in the observed precession.
Over a period of 26,000 years, the Earth’s rotational
axis “precesses” through a complete cycle.
Click here to see an animation of precession.
It is this precession which has gradually shifted the
positions of the constellations* in the sky, and, in
particular, the periods of the year which correspond
to each zodiacal constellation.
*
See the previous Activity, Star Patterns
Precession also changes the locations at which
seasons occur in the Earth’s orbit.
The Earth is currently closest to the Sun during southern
summers, but in about 13,000 years it will occur during
northern summers. This may cause southern summers
to become more mild, and northern winters to become
more severe.
Image Credits
NASA: View of the Mid-Pacific Ocean
http://nssdc.gsfc.nasa.gov/image/planetary/earth/gal_mid-pacific.jpg
Now return to the Module home page, and read
more about the Earth’s seasons and precession in
the Textbook Readings.
Hit the Esc key (escape)
to return to the Module 2 Home Page
Elliptic Orbits
y
The Cartesian (i.e (x,y) coordinates)
equation for an ellipse is given by:
b
x
a
where a is the semi-major axis
and b is the semi-minor axis.
If a = b, then the ellipse becomes a circle. The larger a is
than b, the more “squashed” the ellipse is.
We can also write the equation for an
ellipse in polar coordinates (i.e (r,)
coordinates):
y
r

x
where r is the radius and  is the
angle (from the x-axis).
r and  are measured from the focus of the ellipse.
The eccentricity e, which is given by:
describes how “squashed” the ellipse
is, with circles having e = 0.
If we use polar coordinates to plot the
ellipse, we need to run from  = 0 to
 = 2 (or  = 0 to 360°).
y
For a circle, the radius remains constant
with angle, and hence our Cartesian plot:
will look pretty boring r
in polar coordinates:
x

An ellipse, however, will look like a sine wave:
y
r
x
Cartesian

Polar
Return to Activity