Homework #5:   Sunset -> Size of Earth

Download this image file...

	https://vanderbei.princeton.edu/FRS_131/python/Sunset.png

As done in previous assignments, open up the StackImages app.
Note:
    If you don't remember how that's done, click on 
        https://orfe.io/stackimg.html
        (or on https://vanderbei.princeton.edu/stackimg.html)
    and look for the section that starts "Each time you wish to work with and run StackImages" and follow the instructions there.

Click on "Select Images", navigate to the folder on your computer containing Sunset.png and "Open" that image file.

Next, click on the "Show" button on the second line in the app. 
A second window called "Figure 2" will pop up showing the sunset.
As usual, you will see four slider bars.  Feel free to tinker with them if you like.  Or not.   It's up to you.
Somewhere in the Figure 2 window you will see a menu bar with some clickable buttons.
On some computers they appear at the top of the window and on some others they appear at the bottom.
The leftmost one looks like a house.
Click on the one that looks like a magnifying glass and then click and drag a little square over the sunset in the image.
That will give a very zoomed in view of the sunset.
If you aren't happy with how you clicked and dragged, you can click on the leftmost button, which looks like a house.   
It will return you to the full image and you can again do the click-and-drag to get a nice zoomed-in view of the sunset.

Now move your cursor over the Sun.
The x and y "pixel" coordinates of the cursor will be displayed to the right of the clickable icons in the menu bar.

(a) Write down the x and y coordinates of the "top" of the Sun.
(b) Write down the x and y coordinates of the "bottom" of the Sun's reflection.
(c) Write down the x and y coordinates of the point on the "horizon" between the above pair of points.

Compute the size of the angles alpha and beta in "pixel" coordinates.

Estimate the "pixel diameter" of the Sun (you'll just need to eyeball this).

Using the fact that the Sun is about 1/2 degrees in diameter, compute alpha and beta in degrees or radians (whichever you prefer).

Using a standing height, h, of 6 feet, use the formula that's derived in 

        https://vanderbei.princeton.edu/FRS_131/lectures/lec3.pdf

to compute the radius of the Earth.  

Compare your answer to the known size of the Earth.