Question

Explore the dependence of sunlight on earth-sun distance. The solar constant, S_0 is the solar radiation at zero zenith angle at the mean earth-sun distance, R_m. As we learned in class the intensity of solar radiation decreases with the square of the distance. Use matlab to devise a function that calculates the daily averaged solar radiation as it depends on earth-sun distance (ignore seasonal changes in the sun's angle) through the course of one year. Use for the eccentricity the present day value of about 0.017.

In polar coordinates the distance from the ellipse to a focal point is given by: r = a*(1-e^2)/(1+e*cos(theta)) where a is the semi-major axis (R_m), e is the eccentricity and theta is the angle measured from the semi-major axis. Compare the range of radiation with that when the orbit has a large eccentricity (ecc= 0.06).

To summarize: Step 1. Replace the solar constant with a value that represents the daily average. The solar constant is the flux at distance R_m, so the R_m factors out. Hint: consider how sunlight varies over a 24-hour period. Do this part with paper and pen.

Step 2. Determine how solar radiation varies through the course of 1 year. Plot with eccentricity = 0.017 and 0.06. Do this part with matlab.

Answer 1