What is the relationship between solar radiation intensity and lunar phases?

[charlie05]

Homework Statement

What is the intensity of solar radiation in a place where is the full moon ?

I know luminosity of the Sun and Earth's distance from the Sun R_E and Moon´s distance from the Earth R_M. Trajectory of Earth and Moon are circular.

Homework Equations

distance of the site from the sun is d = R_E + R_M

The Attempt at a Solution

Radiation intensity decreases with the square of the distance.
Intensity of radiation is amount of radiant power per unit area

 

[berkeman]

Homework Statement

What is the intensity of solar radiation in a place where is the full moon ?

I know luminosity of the Sun and Earth's distance from the Sun R_E and Moon´s distance from the Earth R_M. Trajectory of Earth and Moon are circular.

Homework Equations

distance of the site from the sun is d = R_E + R_M

The Attempt at a Solution

Radiation intensity decreases with the square of the distance.
Intensity of radiation is amount of radiant power per unit area

Sorry, your problem statement didn't translate very well. Is there a diagram associated with this question? Are they asking what is the intensity of sunlight at the combined distance Re + Rm? As if you were on the Moon and the Earth was nearly between the Moon and the Sun?

 

[charlie05]

sorry for my bad English :-(
I think - full Moon - position is Sun - Earth - Moon
in full Moon - Earth is between the Sun and Moon ...and distance between the Sun and the Moon is the sum of Earth's distance from the Sun R_E and Moon´s distance from the Earth R_M. At this distance I have to calculate solar radiation intensity.

 

[berkeman]

sorry for my bad English :-(
I think - full Moon - position is Sun - Earth - Moon
in full Moon - Earth is between the Sun and Moon ...and distance between the Sun and the Moon is the sum of Earth's distance from the Sun R_E and Moon´s distance from the Earth R_M. At this distance I have to calculate solar radiation intensity.

Okay, makes sense.

So it sounds like you have all the information you need to do the calculation. You said you have the radiant intensity at the Earth's surface, right? And you know the intensity decreases with the square of the distance. So can you show us how you would calculate the lower intensity when you add in the extra distance to the Moon?

 

[charlie05]

I know only luminosity of Sun...3,827.10 ²⁶ W...but maybe I do not to calculate from this information...
but I think, I can find the radiant intensity at the Earth's surface in some tables... I_E = 1360 W/m²

I_E/I_M = R_E² / ( R_E + R_M )²

 

[berkeman]

IE = 1360 W/m2

That looks about right -- I always remember that it's about 1kW/m^2 at the Earth.

IE/IM = RE2 / ( RE + RM )2

That doesn't look quite right to me. Remember that the intensity is proportional to the inverse of the square of the distance. Intensity gets lower the farther away you get...

 

[charlie05]

conversely... :-)
I_M/I_E = R_E² / ( R_E + R_M )²

 

[berkeman]

conversely... :-)
I_M/I_E = R_E² / ( R_E + R_M )²

Yeah, that looks better. What answer do you get? Can you show your work?

 

[charlie05]

R_E = 150.10⁶ km
R_M = 384.10³ km
I_E = 1360 W/m²

I_M = 1353 W/m² ?

 

[berkeman]

R_E = 150.10⁶ km
R_M = 384.10³ km
I_E = 1360 W/m²

I_M = 1353 W/m² ?

Looks good to me. Do you have a way to check the answer? Is the value of the intensity at the Earth a standard value that you got from your class or textbook?

 

[charlie05]

value on Earth I found my physical tables..solar irradiance

 

[charlie05]

thank you very much for your help :-)