There are two questions for this, that is why I have made it worth the max point

Question

There are two questions for this, that is why I have made it worth the max points. Please answer all for best response.

Note: If it appears that necessary information is missing from a problem, make a reasonable assumption and state the assumption. Moon reflects about 10% of the incident solar radiation. The Moon is a Lambertian surface. A Lambertian Moon would appear uniformly bright across its disk, i.e., its brightness will be uniform in all directions (theta, phi). Assume no losses in the Sun-Moon-Earth paths Given a solar constant (power density of Sun) of S s = 1370 W/m 2 at the Moon, and the Earth-Moon distance of r = 3.8 times 10 8 m. Assume that the Moon subtends an angle of 0.5 degree at the Earth, and the Sun-Moon-Earth geometry and the Moon is a flat disk normal to the Sun-Moon line, as shown: What is the total solar power reflected by the lunar disk reaching the Earth (in Watts)? What is the Moon's brightness at the Earth for theta = 30 degree (in W m -2 sr -1)? When the Sun's spectrum is photographed, using rockets to range above the Earth's atmosphere, it is found to have a peak in its spectral exitance at roughly 465 nm. Compute the Sun's surface temperature, assuming it to be a blackbody.

Explanation / Answer

1. a) Diameter of moons face can be calculated assuming the distance to be r and the angle substanded be 0.5 (Given)

So, for radius, angle substended = 0.25 ,

radius, x = r tan(0.25) = 1.658*10^6 m

Area = 8.637*10^12 m2 ;

Energy received = Area * Power = 1.183*10^16 W

This reflected energy is distributed in the semispherical layers with base as the moon.

So, Density at earth's surface = Energy/(4*pi*r*r) = 65.2 W/m2

2. From Wein's displacement law,

Lambda max * T = b ; where b is constant = b = 2897768.5 nm

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