In this lab, you will investigate the geometry between the sun and the earth.
You will find links to 3 images taken from various strategic places on Earth.

Scientific objective:

To understand how the solar zenith angle changes throughout the year at different locations.

Matlab objective:

To gain experience in writing and incorporating your own functions into your assignments.

About Matlab Functions:

Functions allow you to expand the capabilities of Matlab by streamlining your programming. Take Planck's function, for example. How many times have you used (typed) that particular function? What if you had written a function two homework assignments ago that computed planck's spectral radiance for you, like this one: planck_wl.m?
In this lab, you will be using several of the relations in class notes. Some you will have to write, and a couple I have written for you:

• s_zen_ang.m which calculates solar zenith angle
• julian.m which converts gregorian dates to julian days.

To find out more about functions in matlab, type "help function" in your matlab session.

Some functions you might find it useful to write include:

• declin.m:the declination angle in radians.
• ws.m: the sunrise hour angle in radians.

Matlab notes:

The first (unbroken) comment lines in a function are accessible by typing "help function_name" in matlab.

The internal Matlab trigonometric functions use radians by default. If you want answers in degrees, use the Matlab function rad2deg.m, or remember to convert in your own programs.

Image 1

This picture was taken in Australia.

• What time of day was it taken?
• Estimate the day of the year that it was taken.

Image 2

This picture was taken at the equator (in Ecuador) at noon. The photographer was facing west.

• Estimate the day of the year that it was taken.
• Calculate the solar zenith angle.

Image 3

This is a multiple exposure taken at South Pole.

• What time of year was it taken?
• What was the length of this day?

Question 2 Planetaary Energy Balance

Radiation objective:

To become familiar with the equilibrium temperatures of the planets in our solar system, based on the principles of energy balance given in class.

MATLAB objective:

To learn the educational value of simple mathematical models.

The following web address is a Java Applet that runs a simple equilibrium model Equation 1.31 in the notes. It plots the planet's distance from the sun versus its equilibrium temperature.  Go to this page and answer the four questions listed there. The most important question deal with what planetary characteristic causes the bump in the curve?

Below is some data that may, or may not help you answer the qeustion. Pay close attention to units!
 

                Mean            Mean distance 
     Planet     Radius (km)     from Sun (10^6 km)      Albedo

     Mercury    2439            58                      0.058
     Venus      6049            108                     0.71
     Earth      6371            150                     0.30
     Mars       3390            228                     0.16
     Jupiter    69,500          778                     0.34
     Saturn     58,100          1430                    0.34
     Uranus     24,500          2870                    0.34
     Neptune    25,100          4500                    0.29
     Pluto      1500            5900                    0.4