For vacation, you decide to take a solo boat trip. While contemplating the universe, you lose track of your location. Fortunately, you have some astronomical tables and instruments, as well as a UT clock

Question

You thereby put together the following description of your situation: ? It is the day of the summer solstice. ? The Sun is on your meridian at an altitude of 83.5° in the south. ? The UT clock reads 22:00. a. What is your latitude? How do you know? b. What is your longitude? How do you know?

Answer 1

a. Your latitude is 30°N. Because it is the summer solstice, the Sun follows a path 23.5° north of the celestial equator through the sky. Thus, the Sun's meridian altitude of 83.5°S tells you that the celestial equator crosses the meridian at 60°S. Because we know that the celestial equator crosses the meridian at 90° - (your latitude), your latitude is 90° - 60° = 30°; it is north latitude because the celestial equator is in your southern sky.
b. Your longitude is 150°W. The Sun is on your meridian, so it is noon for you. The UT clock reads 22:00, or 10 P.M., so Greenwich is 10 hours ahead of you. Each hour represents 15° of longitude, so 10 hours means 150°; you are west of Greenwich because your time is behind.