Radiation  Solar radiation drives the atmosphere.  The amount of radiation the Earth’s surface and atmosphere receives is dependent on: l The angle at which the sun’s rays strike the Earth’s surface at various latitudes. –Latitude — Time of year –Elevation-Zenith angle— Refraction of radiation –Declination angle— Altitude of site above sea level The time of day& year. Length of day. l Depleting effects of the atmosphere. l 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. l Most have nearly circular orbits.

 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 =

 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 equal to the ratio of the cubes of their semi-major axes.  If period is given in Earth years and distance in Astronomical units, AU, then: and, If period is given in Earth days and distance in gigameters, Gm, then:

  So, the time for one orbit is given by: where, Y = period of planet in years, a = days/Gm -3/2 R = Distance planet is from Sun in Gm A Gigameter = 10 6 km = 10 9 meters

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Earth Satellites  Also move in elliptical orbits which are nearly circular.  Consider a satellite moving in a circular orbit.

 Acceleration is:  In diagram,  v points toward the orbit center, so acceleration also points toward orbit center. Called centripital “center seeking” acceleration, a c.  The vectors, v, v o, and  v form a triangle geometrically similar to triangle ABC.  The angle  is equal to the angle between CA and CB.  Then,

 Or,  Then,   Since,  Then, satellites moving in a circular orbit are moving with an acceleration: 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).  The force of gravity is given by:  Then, since F=ma,  G = Gravitational Constant

 Let t orbit be the time to complete one orbit of the earth. The distance that satellite travels in one orbit is 2  r.  Since,  Then, and,  Substituting into the force equation gives:

 Rearranging gives:  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: l Angle at which sun’s rays strike the Earth. l Time of day l Depleting effects of atmosphere. l Length of day.

Determining Elevation angle of Sun at noon.  Must know solar declination angle. d = Julian date of year. d r = 173  r = o d y = 365 or 366 C = 360 or 2 

 Graphically:  Equation:  = latitude, e = longitude, t UTC = Universal Coordinated Time, t d = 24 hours,  = elevation angle,  s = solar declination angle.

 Azimuth angle: Angle of Sun’s position relative to north is: where,  = azimuth angle,  s = solar declination angle,  = latitude,  = zenith angle = (C/4)-  C = 360 or 2 

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 o.  Civil twilight: Sun center no lower than -6 o.  Military twilight: Sun center no lower than - 12 o.  Astronomical twilight: Sun center no lower than -18 o.

 Corresponding times: where, t d = 24 hours (length of day) e = longitude  = latitude,  s = solar declination angle,  = elevation angle C = 360 or 2 

Flux  Flux density: Rate of transfer of a quantity across a unit area (perpendicular to the flow) per unit time. l Mass flux: kg/m 2 s l Heat flux: J/m 2 s or W/m 2

 Kinematics: The branch of mechanics dealing with the description of the motion of bodies or fluids without reference to the forces producing the motion.

Propagation of radiation  Speed of light varies with the medium through which it passes.  In a vacuum: c o = 299, 792, 458m/s  Wavelength:, in units meters/cycle or  m, where, v = frequency, in units of Hz = cycles/s, and  m = 1 x m.  Wavenumber: , number of waves per meter, = 1/ cycles/m.  Circular (angular) frequency =  radians/s = 2  v

Emission  Any object with temperature above absolute zero emits energy.  Blackbody: a perfect emitter. Emits the maximum possible radiation for its temperature.