2a) Venus and Mars orbit the Sun at average distance of 0.72AU and 1.52 AU, resp

Question

2a) Venus and Mars orbit the Sun at average distance of 0.72AU and 1.52 AU, respectively. what is the solar flux at each planet? ( 1 astronomical unit is defined as the average distance from Earth to the Sun, approximately 93 million miles)

b) how does the solar flux of Venus compare to that of Earth (larger, smaller. by what factor)?

c) Venus has an 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.

d) how do the effective radiating temperatures determined in part (c) compare with the value for earth? what about the trend in effective temperature with distance from the sun is surprising?

e) the mean surface temperatures of Venus and Mars are 730K and 218 K. using the answer to part (C), determine the magnitude of the greenhouse effect on each planet

f) how do the results of e compare with the magnitude of the greenhouse effect on Earth?

Explanation / Answer

Inverse square law: S = S0 (r0 /r)

S Earth = 1370 W/m 2

r Earth = 1 AU

r Venus = 0.72 AU

r Mars = 1.52 AU

S Venus = S Earth ( r Earth / r Venus ) 2

S Venus = 1370 W/m 2 (1 AU/ 0.72 AU) 2

S Venus = 2642.8 W/m 2

S Mars = S Earth ( r Earth / r Mars ) 2

S Venus = 1370 W/m 2 (1 AU/ 1.52 AU) 2

S Venus = 593.0 W/m 2 b.

C) 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.

T e 4 = S(1-A)/4

A Venus = 0.8

A Mars = 0.22

T e =[(S Venus /4 )(1-A Venus )] 1/4 T e =[(2642.8 W/m 2 /4 (5.67 10 –8 W/m 2 /K 4 )(1-0.8)] 1/4 Venus T e = 219.7 K

For Mars:

T e =[(S Mars /4 )(1-A Mars )] 1/4 T e =[(593.0 W/m 2 /4 (5.67 10 –8 W/m 2 /K 4 )(1-0.22)] 1/4 Mars T e = 212.5 K 18


D) How do the effective radiating temperatures determined in part (b) compare with the value for Earth, and why is this result surprising?

The values of T e for both Venus and Mars are 219.7 K and 212.5 K respectively, which is less than the T e value for earth (255 K).

This is surprising as one thought that as Venus is closer to the Sun than both the Earth and Mars, si intercepts greater solar flux and its T e value would be greater than Earth, and greater than Mars.

But, this is not the case. The high albedo of Venus causes much of the Sun’s radiation to be reflected, and that causes the effective temperature less than expected.

E) The mean surface temperatures of Venus and Mars are 730 K and 218 K, respectively. Using the answer to part (b), determine the magnitude of the greenhouse effect on each planet.

Greenhouse Effect: T g = T s-T e

T s (Venus) = 730 K T s (Mars) = 218 K

For Venus: T g (Venus) = T s(Venus)-T e(Venus) T g (Venus) = 730 K – 219.7 K T g (Venus) = 510.3 K

For Mars: T g (Mars) = T s(Mars)-T e(Mars) T g (Mars) = 218 K – 212.5 K T g (Mars) = 5.5 K

F) How do the results of (d) compare with the magnitude of the greenhouse effect on Earth?

As venus atmosphere contains 90 bar of CO 2 , and has more of a greenhouse effect than Earth that causes a temperature increase of 510.3 K as compared to 33 K (more than 15 times the magnitude).

And mars has smaller a greenhouse effect than Earth, that only raises its temperature by 5.5 K. Mars greenhouse effect is less as its atmosphere is thin (6 mbar) the cold temperature which means that there is very little H 2 O in its atmosphere. This shows the composition and size of the atmospheres of Venus and Mars.

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