Earth’s Orbit: Temperature and Sunlight
A planet’s orbit around its Sun determines its weather and climate, its structure
and composition, and even its ability to support life. The primary factor
determining a planet’s average temperature is the irradiance it receives from its
Sun, which is largely determined by the distance from its Sun. Planets closer to
the Sun receive more intense radiation and are hotter. The basic law is the
Inverse Square Law. A planet half the distance from its Sun will receive four
times the irradiance while a planet twice the distance from its Sun will receive
only 1/4th the irradiance.
Earth is the 3rd planet, 150 million km from the Sun. At this distance, every
square meter on Earth receives an average of 342 Watts. This is enough to
melt ice over most of the planet but not so much that the oceans boil. This
makes the average climate ideal as far as we are concerned because life as we
know it depends on liquid water. Thus, blood, which is essentially iron-enriched
sea water, flows through our veins and water circulates through each cell.
The two planets closer to the Sun – Mercury and Venus – are infernos too hot
to support liquid water and life. Little Mars remains alluring to scientists looking
for signs of life because its temperature appears to be just warm enough. But
the outer planets, starting with Jupiter are frigid spheres largely composed of
hydrogen and helium and appear utterly hostile to life as we know it.
Sunshine and Temperature on Earth
Distance to the Sun is the main factor that determines temperature differences between
planets. But temperatures on each planet are driven by variations of sunshine (Solar Irradiance
or Insolation) that differ over latitude and over the seasons. These variations are determined by
three main factors, namely
1. Angle (Height) of the Sun in the Sky
2. Hours of Daylight
3. Distance to the Sun (least important factor!)
These factors are themselves determined by 2 geometrical laws of Solar Irradiance,
1. Inverse Square Law of Distance
2. Zenith Angle Cosine Law
which are linked to Earth’s Orbit. At present, Earth is closest to the Sun (perihelion) on Jan 3 and
furthest (aphelion) on July 4. The noon Sun appears overhead furthest north (23.5° N Lat) on
about June 21 (North Hemisphere Summer Solstice and longest day) and furthest south (-23.5° S
Lat) on about Dec 21 (North Hemisphere Winter Solstice and shortest day).
Latitude and Mean Annual Temperature (T)
Over the year all places on Earth get 50% daylight and 50% night so that mean annual T is
determined by the average height of the Sun in the sky, which is greatest at the Equator and
decreases to a minimum at the Poles. Thus mean annual T decreases from Equator to the Poles.
Summer vs Winter
Since summer occurs in July in the North Hemisphere and January in the South Hemisphere,
Summer occurs when the Sun is highest in the sky and daylight hours are longest.
Definitions
1. Radiation = Propagation of electromagnetic energy through free space.
2. Irradiance = Flow (Flux) Intensity of radiant energy (Units W m-2)
3. Insolation = Solar irradiance striking Earth.
4. Declination = Latitude at which the Sun strikes overhead
5. Terrestrial Radiation = Infrared radiation emitted by the Earth.
6. Albedo = Fraction of radiation that is reflected by an object
7. Zenith Angle = Angle (of Sun, etc.) from top of sky.
8. Equinoxes = Days when day = night = 12 hours over all Earth.
9. Solstices = Days of extreme declination  Dec21 and June 21.
10. Aphelion = Day when Earth is furthest from Sun  July 4.
11. Perihelion = Day when Earth is closest to Sun  Jan 3.
Recall the Scale of Earth’s Orbit and the Sun
When we zoom out to the scale of Earth’s Orbit, the Sun looks like a tiny grain and
Earth is 1/5th the size of the blue dot. From Earth, the Sun appears like a pea viewed
from arm’s length - a circle of blinding light slightly more than ½ degree (0.53) wide.
SUN
EARTH ON JUL 4
.
107 km
EARTH ON JAN 3
Three observations resulting from this picture have important consequences.
1: All points on Earth (Poles and Equator) are almost the same distance from the Sun.
2: Earth is closest to the Sun on January 3 and furthest from it on July 4
3: All sunbeams striking any part of Earth are essentially parallel.
What are the consequences?
1: The height of the Sun in the sky makes the Poles colder than the Equator.
2: The height of the Sun in the sky and the length of the day make the seasons.
3: This will help us understand rainbows and day and night on Earth.
Tilt of Earth’s Orbit with Respect to Earth’s Equator:
Obliquity of the Ecliptic
The plane that slices through Earth’s Equator
is tilted at a 23.5 angle from the plane that
slices through Earth’s Annual Orbit about the
Sun. Because of this tilt, the North Pole is lit
on June 21 and dark on Dec 21, while the
opposite is true for the South Pole.
This tilt is responsible for the seasons
and possibly for life on Earth as well.
Mar 21
June 21
Dec 21
In this figure you only
see the night half of
Earth on Sept 21 and the
day half on March 21.
On June 21 and Dec 21
you see that the half of
Earth facing Sun is lit.
23.5
Plane of Earth’s Orbit
Sept 21
This drawing is not to scale: Both Sun and
Earth are too large compared to the orbit.
Sep 21
Earth’s Orbit and
the Seasons
The plane of Earth’s
Equator passes
through the Sun only
on the Equinoxes
Dec 21
Jun 21
Mar 21
December 21
Summer Solstice at
the South Pole. North
Pole lies in darkness.
Sep 21
March 21 or Sept 21 Jun 21
Equinoxes: Sun
strikes directly
overhead at the
Equator and is on the
Kepler’s
horizon at the Poles.
Mar 21
Law
Sep 21
June 21
Summer Solstice at
the North Pole. South
Pole lies in darkness.
Jun 21
Dec 21
Mar 21
Dec 21
23.45
Earth’s Orbit and The Seasons: Declination June
d
The Sun appears to
move north and
south
with
the
seasons. On about
June 21, the Sun
reaches its northernmost
latitude,
23.45o.
The latitude where the Sun is overhead is called the declination, d = D.
Yellow and blue dotted lines mark the hours. All along the dividing line between
day and night the Sun rises in the NE. All latitudes in the North Hemisphere
receive more hours of day than night while night is longer in the South
Hemisphere
Earth’s Orbit and The Seasons: Declination Dec
d
Declination
On about Dec 21, the Sun reaches its southernmost latitude, -23.45o. This is
the first day of winter in the North Hemisphere. The North Pole lies in
darkness, the South Pole in light.
In December, all latitudes in the North Hemisphere receive fewer hours of day
than night while day is longer in the South Hemisphere
Declination Angle, d: Annual Cycle
d  23.5cos(# Days from June 21)
Summary of the latitude that the Sun is Overhead on Earth over the year.
Click to Animate
15
10
Sep 21
June 21
20
Dec 21
25
5
0
-5
d = Declination
-10
-15
-20
-25
0M
1A
2M
3J
4J
5
A
S6
7
O
8
N
9
D
J10
11
F
12
M
How to Draw Sunlight on Earth
Click to Animate
1. Draw a Ball
2. Draw Parallel Light Beams
3. Brighten half of ball facing light – this is day
Overhead Point
24 h day
d=D
Day
Night
24 h night
4. Put a dot at point where light strikes directly.
5. Choose day of year (i. e., value of declination, d).
6. Draw Equator (d from overhead point)
7. Draw Poles 90 from Equator
8. Draw regions of 24 hours of day and night around Poles
The Sun’s Path Across the Sky: View from Earth
The previous slides showed the Sun and Earth from space. Now we view the
Sun’s path across the sky from Earth. The link between the two views is the
small celestial hemisphere shown in the slide after next.
Long before anyone suspected that Earth revolves about the Sun, people
traced the Sun's path across the sky. Using the sun paths they built sundials to
tell time. If we know how to make the sun path, we can orient ourselves no
matter where we are on Earth. We can also tell how high the Sun gets in the
sky and how many hours of sunlight a place gets each day.
The Sun burns an imaginary path on the celestial hemisphere, our view of the
heavens. It rises in the eastern part of the sky and sets in the western part. But
it only rises due east and sets due west on the two equinoxes. For the half
year after March 21, the Sun rises in the northeast and sets in the northwest.
For the six months after September 23 it rises in the SE and sets in the SW.
Outside the tropics, the Sun crosses the sky from left to right in the North
Hemisphere and from right to left in the South Hemisphere. In the Tropics the
Sun rises almost straight up, stands near the zenith at noon and then sinks
almost straight down so that it gets dark quite soon after sunset.
Hourly positions of the Sun above Bursa, Turkey from winter solstice in December (bottom track) to equinox
(middle track) to summer solstice in June (top track). In December, the Sun stayed low in the sky and day
was short. This lack of Sun caused winter. In June, the high Sun and long day caused summer.
Note that the three sun path
are parallel
Noon
40.19 N Lat
Finding Z at Noon
f = L = Latitude
d = D = Declination
Finding Z at Noon on any day.
Sun paths are needed to find Z
at other times of the day.
Recipe for Constructing Sun Paths
Start with the Equinox Sun Path because…
Choose Latitude, L
= f = 53 (N>0)
f
Z=0
Z=-30
Warning:
South
Latitude
RUN SUN PATH
Z=-60
(S<0)
53
W
These are
zenith angles,
not latitudes
N Z = -90
Z = 90 S
E
…on the Equinoxes
1. Sun rises due East and sets due West [Draw (red) circles]
2. Noon Sun is at angle Z = Latitude from the Zenith on the N-S
line that goes through the Zenith [Draw (yellow) circle]
3. Draw the Equinox Sun Path by Connecting the Dots.
Then Construct the Sun Path For Any Other Day.
Note: All Sun Paths are Parallel to the Equinox Path
Z=0
Choose Jul 21
d = 20.4
Z=-30
d
These are
zenith angles,
not latitudes
Z=-60
W
N Z = -90
Z = 90 S
E
On All Other Days
4. Draw noon Sun displaced by –d from equinox so that Z = L – d.
5. Draw Sun path (Solid Curve) parallel to (dashed) Equinox Sun path.
Maximizing Solar Power
Solar voltaic panels are made of
materials such as silicon and cadmium
telluride, which convert sunlight directly
to electricity. Parabolic reflectors aim all
the sunlight at the focus, where heat is
so intense that it produces steam, which
drives turbines that generate electricity.
Solar panels and parabolic reflectors
produce the most energy when they face
the Sun directly. Therefore, many are
mounted on Sun-facing devices that turn
as the sun moves around the sky and
therefore act much like sun dials and
astronomical observatories.
Power is greatest when the Sun is near
the zenith because that is when the path
through the thin atmosphere and the
losses due to scattering and absorption
of light are smallest.
Some solar power plants cover hundreds
of acres and generate megawatts.
Geometric Laws of Irradiance
Irradiance is the rate that energy flows across a screen divided by the screen’s
area. Its units are Watts per square meter or W m-2. The irradiance of direct
sunshine 1367 W m-2 when Earth is at its mean distance from the Sun.
A light such as the Sun may emit energy at a constant rate, but a screen will
intercept more or less of that energy depending on its distance to the light and
its orientation relative to the light. The screen will intercept the most energy
(irradiance on the screen will be greatest) when it is closest to the light and
faces it directly (at a 90 angle). This gives birth to two geometrical laws of
irradiance discussed and illustrated on the next slides.
1: The inverse square law (relates irradiance to distance from the light).
2: The cosine law (relates irradiance to angle between the light and screen).
Sunshine and Temperature
on Earth: Distance to Sun
 d0 
I = I0  
d 
2
For Earth - Sun
d0 = 149.5(10)6 km
I0 = 1370 W m-2
Because Earth’s orbit is an ellipse
distance to sun varies over the year
d = 149.5  2.5 cos(dd )

dd = # of days from July 4
Sunshine and Temperature on Earth: Zenith Angle
Width of Sunbeam striking
a specified area of ground
Sunlight varies over the
Earth producing
variations of temperature,
density and pressure
Cosine Law of Sunshine Intensity
When the Sun is overhead, 100% of a beam of
Click to Begin Animation
width, I0 strikes a piece of ground of width, I0.
I0
As the Sun goes down and
Zenith Angle, Z increases,
progressively less of the
sunbeam of width I0, strikes
the piece of ground. More
of the sunbeam misses that
piece of ground and is lost.
Z
The fraction of the sunbeam that
strikes the ground = IZ/I0, which
trigonometry shows is equal to
cos(Z). Hence the Cosine Law
I Z = I 0  cos(Z )
COSINE LAW
h Z
I0
I0
h
Z
Z
GROUND
Measuring the Sun’s Zenith Angle and Irradiance
r
Zenith Z = cos1  
c
Angle
Compass
N
W
Z
Long Ruler
r
E
c
S
r
Ruler with length, r
r = 20  30 cm is good
Shadow
Azimuth or Compass Angle
Instructions
1. Align the long ruler and the short ruler with the Sun and its shadow.
2. Tilt the short ruler until it produces the longest shadow.
3. Sun’s relative Irradiance = r/C (100%), where C is the maximum shadow length.
4. Sun’s zenith angle, Z = cos-1(r/C) = angle whose cosine = r/C
5. For next 5 Saturdays or Sundays measure Shadow, C at 1200 EST or 1300 EDT (during
Daylight Savings Time) and calculate both r/C and Z.
Date
Time (EST or EDT)
C
POWER = r/C
Z=cos-1(r/C)
Reading the Chart
Example 1: On Sept
21 at 60º N Latitude,
Iavg = 250 W m-2.
550
500
450
400
350
300
W m-2
250
200
150
100
50
0
Example 2: On Nov
21 at 30º S Latitude,
Iavg = 535 W m-2.
Global Radiation, Temperature, Snow Cover: Annual Cycle
The following slides display annual cycles of measured Global
Solar Radiation
2: Surface Temperature
3. Precipitation
4: Snow Cover.
1:
As the belt of most intense radiation moves north from December to
June and then back south from June to December, the patterns of
temperature, precipitation and snow cover follow, but with smaller
excursions and a lag of about 1-2 months (since it takes time to heat
and cool the Land, Ocean and Atmosphere).
All these world maps and more concerning global energetics come from
the web site, http://geography.uoregon.edu/envchange/clim_animations/
All data for these maps is based on the NCEP (National Center for
Environmental Prediction) Reanalysis.
Annual March of Absorbed Solar Radiation
Annual March of Global Temperatures
Annual March of Global Precipitation
Annual Cycle of Global Snow Cover