The Perfect Sunset

Recently, I showed a student of mine a Flash applet from the Astronomy Department at the University of Nebraska-Lincoln. It very generally demonstrates how the sunset changes its North-South location on the horizon during the course of the year (due largely to the tilt in the Earth's axis).

In talking about the sunset's movement, my student expressed to me a lifelong desire: to see the sun setting over the Golden Gate Bridge. It takes a little figuring out, since not only does the sunset move during the year but where it happens depends on where on Earth you are (eg If you are far North of the Equator during the summer, then sunset will appear to happen much farther North than if you were standing at the Equator)!

After thinking about different locations in the East Bay to view the Golden Gate Bridge from, I've determined that Cesar Chavez Park is the optimal place (or possibly the nearby Berkeley Pier).


Latitude is a measure of how far North or South a place on the Earth is from the Equator, so knowing the latitudes of both Cesar Chavez Park and the Golden Gate Bridge will help us to find the date of our particular sunset. Latitude is given in degrees, like the way you measured angles in Geometry.

The Flash applet below gives you control over the Time of Day, Date, and Latitude of the observer. Given that

Latitude of Chavez Park: 37.87^oN
Latitude of Golden Gate Bridge: 37.82^oN

can you use the Flash applet below to find the date of the perfect sunset?

[There are some hints below the applet that may help you.]



Key (for 3-D Observation Simulator)

• Yellow Line: Sun's Declination (Daily Path)
• White Line: Sun's Ecliptic (Annual Path)
• Blue Line (E-W): Celestial Equator
• Blue Line (N-S): Prime Hour Circle

Hint 1

If you're feeling stuck, play around with the Date and Latitude. See what happens in different places at different times of year. What patterns can you find?

Hint 2

Pay close attention to the Sun's Declination. Go ahead and read about it on Wikipedia. There's a continuous measure of declination in the box in the lower left of the applet.

Hint 3

The latitudes of Cesar Chavez Park and the Golden Gate Bridge are just 0.05^o apart. How significant is that in our calculations, considering that our accuracy is limited by that of the applet?

Planetary Orbits

From the Astronomy Department at the University of Nebraska-Lincoln:

Playing with Functions

Comparing graphs of linear equations can be really helpful in trying to understand them, but just trying to graph them takes a really long time. Fortunately for us, someone out there wrote a Java applet (a simple program) just for us, called Slope Slider. The whole concept is that you can push the colored sliders left and right to easily change the slope and y-intercept.

The big questions to think about are:

• What happens to the slope when it's greater than 1 and getting bigger?
• What about the slope between 0 and 1?
• How different are the lines with slopes +10 and -10? What about +100 and -100?

[Note: When you're done with the "Slope Slider" check out this other applet that graphs functions for you. Typing in the function can be a little bit funky, since you have to use an asterisk (*) to do multiplication and a caret (^) to show that what follows is an exponent, but it can graph almost any function you want.]

Internet Resources on the Housing/Finanacial Crisis

• This American Life (radio show) episodes:
  
  1. 5/9/08: The Giant Pool of Money
     
     • Through that link, you can read a summary of the episode, download a transcript of it as a PDF or stream the audio to your computer -- or pay a dollar to download the audio, but who wants to do that?
  2. 10/3/08: Another Frightening Show About the Economy
     
     • For this episode, there's a summary, but you can only stream the audio or buy it-- no transcript to read available yet
  
  
• New York Times (newspaper) multimedia presentation:
  • The Debt Trap; videos, interactive charts, and newspaper articles about all the different people who are affected by debt and how they fall into it in the first place
  
  
• Washington Post (newspaper) slide show:
  • Anatomy of a Crisis; the slides are narrated, describing how the "Housing" crisis turned into the "Financial" crisis
  • Note: the narrator goes a little too fast if you're not already familiar with the events and the vocabulary he throws around