Download Radiation

Radiation
Solar radiation drives the atmosphere.
The amount of radiation the Earth’s surface and
atmosphere receives is dependent on:

The angle at which the sun’s rays strike the Earth’s
surface at various latitudes.
– Latitude
– Elevation-Zenith angle
– Declination angle



— Time of year
— Refraction of radiation
— Altitude of site above sea level
The time of day& year.  Length of day.
Depleting effects of the atmosphere.
Depletion by particles between Sun and Earth.
The planets
Planets orbits
Kepler’s Laws
1. The orbits of the planets are ellipses with
the Sun at one focus of the ellipse.

Most have nearly circular orbits.
d1  d2  constant
a = 1/2 longest axis = semi-major axis
b = 1/2 shortest axis = semi-minor axis
c = distance of foci from center
Eccentricity, e = c/a
Always less than 1. Earth: e = 0.0167
2. The line joining the planet to the Sun
sweeps out equal areas in equal times as the
planet travels around the ellipse.
3. The ratio of the squares of the
revolutionary periods for two planets is
2
3
P1
R1
equal to the ratio of the

2
3
cubes of their semi-major axes. P
R2
2
If period is given in Earth years and
distance in Astronomical units, AU, then:
2
3
P1
R1
2
3
and,
P

R
2 
3
1
1
1year 1AU
If period is given in Earth days and distance
in gigameters, Gm, then:
2
3
P1
R1
2 
3
365.25463days  149.59787Gm
 P12  133410.9447R1
3
3347928.929
3
12
P1 .1996216379R
3
 So, the time for one orbit is given by:
where,
Y  aR 2
Y = period of planet in years,
a = 0.1996days/Gm-3/2
R = Distance planet is from Sun in Gm
A Gigameter = 106 km = 109 meters

v  M  0.0333988 sin(M)  0.0003486 sin (2  M)
0.0000050 sin(3  M)
Earth Satellites
Also move in elliptical orbits which are
nearly circular.
Consider a satellite moving in a circular
orbit.
Dv dv
Acceleration is: a  lim

D t 0 Dt
dt
 In diagram, Dv points toward the orbit
center, so acceleration also points toward
orbit center. Called centripital “center
seeking” acceleration, ac.
The vectors, v, vo, and Dv form a triangle
geometrically similar to triangle ABC.
The angle Dq is equal to the angle between
CA and CB.
Then, Dv  DL
v
r
v
Or, Dv  DL
r Dv
v DL
Then, a  lim
 lim
D t 0 Dt
Dt 0 r Dt

DL
v
Since, Dlim
t 0 Dt
Then, satellites moving in a circular orbit v 2
are moving with an acceleration:
ac 
r
which is directed toward the
center of their orbit.
The force giving the satellite the
acceleration it has (directed toward the
center of its orbit is gravity).
mme
The force of gravity is given by: Fg  G 2
r 2
msatell iteme
v
Then, since F=ma,
G
 msatell ite
2
r
r
11
2
2
6.672x10
N

m
kg
G = Gravitational Constant
11
6.672x10
m s kg
3
2
Let torbit be the time to complete one orbit
of the earth. The distance that satellite
travels in one orbit is 2pr.
Since, distance  rate  time
2 pr
Then, 2 pr  v t orbit and, v 
t orbi t
Substituting into the force equation
gives:
m
m
4p 2 r 2
G
satell ite e
2
r
 msatell ite
r  (torbit )
2
2
m
4
p
r
Rearranging gives: G e 
2
2
r
(torbi t)
torbi t 
2
4p r

Gme
2 3
3
2
torbit
2 pr

Gme
For a satellite moving in a circular orbit.
Season Effects
Amount of incoming solar radiation
(insolation) received at the Earth’s surface
is dependent on:




Angle at which sun’s rays strike the Earth.
Time of day
Depleting effects of atmosphere.
Length of day.
Determining Elevation angle of Sun at noon.
Must know solar declination angle.
C (d  d )  d = Julian date of year.
r 
 s  r  cos


dy

 dr = 173
fr = 23.45o
dy = 365 or 366
C = 360 or 2p
Graphically:
Equation: sin y   sin f sin  s  
C t

cosf  cos s  cos  UTC  l e 


 td

f = latitude,
le = longitude,
tUTC = Universal Coordinated Time,
td = 24 hours,
y = elevation angle,
s = solar declination angle.
Azimuth angle: Angle of Sun’s position
relative to north is: cosa   sin  s   sin f  cosz 
cosf  sin z 
where,
a = azimuth angle,
s = solar declination angle,
f = latitude,
z = zenith angle = (C/4)-y
C = 360 or 2p
Sunrise, Sunset & Twilight
Geometric sunrise/sunset: Center of sun has
zero elevation angle.
Apparent sunrise/sunset: Top of sun crosses
horizon as viewed by observer. Center at
elevation angle of -0.833o.
Civil twilight: Sun center no lower than -6o.
Military twilight: Sun center no lower than
12o.
Astronomical twilight: Sun center no lower
than -18o.
-
Corresponding times:
tUTC
sin f sin   sin y 


t d 
s

 l e  arccos


C 
 cos f  cos  s



where,
td = 24 hours (length of day)
le = longitude
f = latitude,
s = solar declination angle,
y = elevation angle
C = 360 or 2p
Flux
Flux density: Rate of transfer of a quantity
across a unit area (perpendicular to the
flow) per unit time.


Mass flux: kg/m2 s
Heat flux: J/m2 s or W/m2
Kinematics: The branch of mechanics
dealing with the description of the motion
of bodies or fluids without reference to the
forces producing the motion.
kg
Kinematic mass flux

F
 air
2
m
m
s
 wind speed = kg 
s
m3
J
o
2
F
K m
m s
Kinematic heat flux 
=

 air C p  kg   J 
s

 3  

o
m  kg K 

= temperature  wind speed
Propagation of radiation
Speed of light varies with the medium through
which it passes.
In a vacuum: co = 299, 792, 458m/s
co
Wavelength: l  v, in units meters/cycle or mm,
where, v = frequency, in units of Hz = cycles/s, and
mm = 1 x 10-6 m.
Wavenumber: , number of waves per meter,
=
1/l cycles/m.
Circular (angular) frequency = w radians/s = 2pv
Emission
Any object with temperature above
absolute zero emits energy.
Blackbody: a perfect emitter. Emits the
maximum possible radiation for its
temperature.