Astronomy Assignment, In need of assistance. Can anyone help? ?

[jmensche22]

Mariners in the 1700's had an enormous problem: as soon as they were out of sight of land, they were lost. This limited exploration of the seven seas, and led the government of England to offer a 20,000 prize (over $1,000,000 in today's money) to anyone who could develop a method by which sailors could locate their position at sea to within 30 miles. This was won in 1762 by an English inventor, John Harrison.

Imagine now that you have just crashed on a deserted island, located somewhere in the pacific. Pulling yourself out of the wreckage, you discover that your entire stock of Civilized Goods amounts to the following:

a) One Timex watch set to Cobleskill Time
b) One axe
c) One protractor (used to complete Astronomy Labs when travelling)
d) One globe of the World
e) 500 pounds of crunchy granola bars
f) 100 pounds of nails
g) One copy of Navigation For Dummies
h) One (now seemingly worthless plane ticket good for March 21, 2006

You sit down, eat the first of many Granola bars, and consider your circumstances. If you can figure out where you are on the map, you can build a boat and head towards civilization. But how do you figure out where you are?

You open the worn copy of Navigation For Dummies, and are greeted with the following cheery thoughts:

Navigation is easy

a) Latitude lines lie parallel to the Equator. Lines of Longitude run North-South.
b) The Earth takes 24 hours to swing through 360 degrees of Longitude. This is equal to 15 degrees/hour
c) The axis of Earthly Rotation is tilted 23 1/2 degrees from the Ecliptic. As a result, the height of the sun at noon varies with the season. The amount of variation over a year is given by the Analemma (the figure 8 on the side of the globe)

The rest of the book is mutilated beyond recognition.

So, there you have it, Figure out where you are (your latitude and longitude), or die from overeating granola bars. How do you do it?