While contemplating the Universe on a solo boat trip, you lose track of your loc
ID: 158029 • Letter: W
Question
While contemplating the Universe on a solo boat trip, you lose track of your location. Fortunately, you have some astronomical tables and instruments, as well as a UT clock. Suppose, at a given time, you are able to establish the following: • Today is the summer solstice. • The Sun is at your meridian at an altitude of 75 above the southern horizon. • The UT clock reads 2:00.
(a) What is your latitude? How do you know?
(b) What is your longitude? How do you know?
(c) Consult a map (for example, type “40 N 88 W” in Google Maps), and determine where the nearest land is. Which way should you sail to reach it?
Explanation / Answer
The observer's latitude is defined by the declination going through the observer's zenith.
If it is the equinox, then the Sun is on the celestial equator (declination = 0).
If the altitude at local noon (meridian transit) is 75 south, then you are in the northern hemisphere.
The angle between the Sun and your zenith is 90-75 = 15.
Therefore, the declination going through your zenith is 15 N.
That is your latitude.
b. Now for Longitude, Ignoring the time equation
the sun crosses the meridian at 12:00 local time.
If your UT clock shows 2:00, then you are 2 hours west of longitude 0.
360 degrees = 24 hours
therefore 2 hours = 30 degrees.
You are at 15 N 30 W.
c. in google , 378 nautical miles Southeast of the Big Island (Hawaii).
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