Geog 204  Physical Geography
Spring 2007
Dr. Malamud-Roam

Exercise 3

Due Tuesday, March 20th

  1.     Using the known value of the Solar flux at Earth's orbit, 1370 W/m2, calculate the Solar Flux at Venus and Mars. 

    Given that Mars orbits the Sun at an average distance of 1.52 A.U. and Venus orbits the Sun at an average distance of 0.72 A.U. 

             Inverse-Square Law, S = So (ro/r)2   

    S is the Solar Flux received at the Planet orbiting at r distance from the Sun (radius), and So is the reference Solar Flux at Earth (1370 W/m2), which is at ro distance from the Sun (that is, 1 A.U.).

    How important would you say distance is in determining the solar flux received? 

     

    2.  Stefan-Boltzmann Law says that the TOTAL flux of radiation emitted by a star is directly related to its absolute temperature.  And apparently, the total radiation flux is very sensitive to changes in Temperature (related to 4th power of T), so that

     

                            F = sT4

    Sigma is a constant with value of 5.67 x 10-8 W/m2/K4.

    For our sun, with temperature of 5780K,

             Fsun = s(5780K)4 â 6.3 x 107W/m2

                                                    Note that this is energy flux per unit area

     

    Now, consider a star that is only ½ as hot as our sun.  What will be its total flux?

    3.  Using the answers from Question 1, determine the effective radiating temperatures  (Te) of Mars and Venus. 

    Given that Mars has an albedo (A) of 0.22 and Venus has an albedo of 0.8. 

    Remember that the Planetary Balance equation had the value Te in it,

                                  s Te4 = S/4 (1-A),

    which we rearranged to solve for Te as follows:

                           Te = 4à[(S/4s)*(1-A)]

    S is the solar flux received at each planet (calculated in Question 1), s is a known constant (5.67 x 10-8) and A is the albedo 

    Are these values surprising?

     

    How do you account for the fact that the surface temperature (Ts) on these planets are: 

                      Venus Ts = 730 K                         Mars Ts = 218 K