Phobos is the larger and closer of Mars’s two moons. It has no atmosphere, a mean radius of 11 km, an albedo of 0.07, and an emissivity of 1.0.
(i) Assuming that the radiative temperature of Phobos is 222 K and that it is spherical, what is its mean distance from the sun?
(ii) Mars is much cooler than the Sun (210 K) but much closer to Phobos (9.38*10^6 m). Its radius is 3.4*10^6 m. Does the radiation from Mars have a significant effect on the temperature of Phobos?
PHYSICS- SCIENCE - drwls, Saturday, January 23, 2010 at 5:31pm
(i) Perform an energy balance using the irradiance of the sun at the Mars location (Hsun) and the thermal emission of Mars:
0.93* pi* R^2 * Hsun =
1.0 * sigma* T^4* 4*pi R^2
+ 0.07* pi* R^2 * Hsun
The R^2 terms cancel out. You know that T = 222 K. Solve for R, the mean distance from the sun.
Note that the intercepted solar flux area is pi R^2 but the areas that is doing the infrared emitting is 4 pi R^2.
"Sigma" is the Stefan-Boltzmann constant. Look it up if you don't know it.
ii) Compare the absorbed energy from the sun,
alphap* pi* Rp^2 * Hsun
with the absorbed infrared energy from Mars,
pi*Rm^2*sigma*Tm^4*(1/pi)*(pi*Rp^2/X^2)
Rm = Mars radius
Rp = Phobos radius
X = Mars-Phobos separation
Tm = Mars temperature
alphap = Phobos albedo (assume 0.5) They should have given you a value for alphap
The (1/pi) term in the last equation is necessary to convert total Mars emission per projected area to radiation per area per steradian.
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