Waldo is lost and needs your help finding his location. Waldo has a sextant (a big protractor ... a device for measuring angles in the sky) and an accurate watch set to Greenwich time. In this exercise, you don't need to worry about clock adjustments such as "the equation of time" or daylight saving time.
Part 1 (easiest) - The date is March 20th and the sun is crossing the meridian when Waldo notices that his clock reads 12 noon and the sun is directly overhead (at the zenith point). Where's Waldo?
Set up information: On March 20th, the sun is directly over the celestial equator. The diagram above is a generic image good for any observer in the northern hemisphere. The key is to measure angle B. Once that is known, you simply subtract it from 90 to get your latitude (angles A and B are complimentary ... meaning their sum is 90).
Latitude: If the sun is directly overhead, angle B is 90 ... so angle A is zero. You are on the equator.
Longitude: Since your sun is in sync with a clock set to Greenwich time, you are on the Prime Meridian .... your longitude is 0 degrees.
Part 2 (a bit harder) - The date is March 20th and the sun is crossing the meridian when Waldo notices that his clock reads 12 noon and the sun is 38 degrees from the southern horizon. Where's Waldo?
Latitude: Now angle B measures 38 degrees so angle A is 90-38 = 52. Your latitude is 52 degrees north.
Longitude: Since your sun is in sync with a clock set to Greenwich time, you are on the Prime Meridian .... your longitude is 0 degrees.
You are close to Cambridge England.
Part 3 (harder yet) - The date is December 21st and the sun is crossing the meridian when Waldo notices that his clock reads 6 pm and the sun is 23½ degrees from the southern horizon. Where's Waldo?
Now the sun is 23 ½ degrees below the celestial equator so things get a bit trickier. You need to modify the image to reflect this (see angle shown in red). You should see that angle B is the sum of two angles (both equal to 23½).
Latitude: Now angle B measures 47degrees so angle A is 90-47 = 43. Your latitude is 43 degrees north. You are on the same latitude as Milwaukee.
Longitude: Your sun is 6 hours away from the sun in Greenwich. Since each hour represents 15 degrees, you are 6 x 15= 90 degrees west of Greenwich.
You are very close to Dodgeville Wisconsin!!!
Part 4 (the hardest) - The date is May 1st and the sun is crossing the meridian when Waldo notices that his clock reads 3:12 am and the sun is 35 degrees from the northern horizon. Where's Waldo?
Wow ... this one is very hard so I will be very lenient. You are in the southern hemisphere so you need to reverse the diagram. Your (southern) latitude is now equal to the angle between the south celestial pole and the southern horizon (shown in black). You need to find the angle shown in green and then subtract that from 90 degrees. In addition, the sun is 15 degrees above the celestial equator so that, too, must be taken into account.
Latitude: The angle shown in green is 35 + 15 = 50 degrees. That makes your southern latitude 90 - 50 = 40 degrees (south)
Longitude: Your sun is earlier than a sun set to Greenwich. This means you are east of Greenwich but by how much? Time wise, your sun is 8 hours 48 minutes prior to the Greenwich sun. 48 minutes = 48/60 = .8 hours so the total time is 8.8 hours. 8.8 x 15 = 132 degrees East of Greenwich.
You are floating in the ocean just south of Australia.
Hint: Use the watch to obtains Waldo's longitude. Use this graphic as an aid to obtain Waldo's latitude.
