2. a. Venus and Mars orbit the Sun at average distances of 0.72 and 1.52 AU, res
ID: 285655 • Letter: 2
Question
2. a. Venus and Mars orbit the Sun at average distances of 0.72 and 1.52 AU, respectively. What is the solar flux at each planet? b. Venus has a planetary albedo of 0.8, and Mars has an albedo of 0.22. Using the answer to part (a), determine the effective radiating temperatures of these planets. c. How do the effective radiating temperatures determined in part (b) compare with the value for Earth, and why is this result surprising? d. The mean surface temperatures of Venus and Mars are 730 and 218 K, respectively. Using the answer to part (b), determine the magnitude of the greenhouse effect on each planet. e. How do the results of (d) compare with the magnitude of the greenhouse effect on Earth?Explanation / Answer
a) Given,
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.
Solution:
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),
So is the reference Solar Flux at Earth (1370 W/m2),
ro distance from the Sun (that is, 1 A.U.).
Then, For venus S = 1370 * (1/0.72)2 = 2642.75 W/m2
For Mars S = 1370 * (1/1.52)2 = 592.97 W/m2
b) Given
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 = [(S/4s)*(1-A)] 1/4
S is the solar flux received at each planet (calculated in Question a),
s is a known constant (5.67 x 10-8)
A is the albedo
For Venus Te = [2642.75 *(1-0.8) / (4*5.67*10^-8) ] (1/4) = 219.72 K
For Mars Te = [592.97 *(1-0.22) / (4*5.67*10^-8) ] (1/4) = 212.51 K
c) On Venus it should be 4X larger, or S=2644W/m2, which gives nearly TE=220 K. The effective radiating temperature of Venus is colder than Earth's because the albedo of Venus is so high. With either value for S, TE is much colder than the actual temperature of 753 K.
Even though Venus receives more solar energy than the Earth is, its effective temperature is colder. This is due to the high albedo on Venus (0.8): 80% of solar radiation is reflected to space and only 20% is absorbed by the surface.
d) Magnitude of green house effect for venus = 730-220 = 510 K
For Mars = 218-212 = 6 K
The actual temperature at the suface of Venus is much warmer: 730 K ! The enormous greenhouse effect of 510 K (=730-220) on Venus is due to high levels of CO2 in its thick atmosphere. Mars has a much weaker greenhouse effect because it's atmosphere is much thinner than that of the Earth.
The effective radiating temperature of Mars is thus 212 K. The observed temperature on Mars is 218 K, so it's atmosphere has a small greenhouse effect of 218-212 = 6 K.
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