Academic Integrity: tutoring, explanations, and feedback — we don’t complete graded work or submit on a student’s behalf.

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).