Astronomy questioncan someone please help me answer these as

Astronomy question--can someone please help me answer these astronomy questions and show the work/steps for the answers? (Picture below)

Note: I am located in New York City (for the longitude part of the question)

a. You observe Polaris at an altitude of 70 in the North, a quarter moon just rising, and your watch says its 6 AM EST in NYC. What time is it locally? What\'s your latitude and approximate longitude? How do you know? Where are you? (Hint: what\'s the longitude of NYC? How many degrees of longitude per timezone? You can use an online Atlas to see where you are). b. Suppose instead, from the position of the Southern Cross, you estimate that the South Celestial Pole is at an altitude of 25° in the South. You see a full moon halfway between the zenith and the western horizon, and your watch tells you its 7 PM EST in NYC. Where are you?

Solution

a) It has been an ancient knowledge that the altitude of Polaris above the horizon is the same as one\'s latitude on Earth. Since you are observing Polaris at 70^oN it is approximately your latitude.

For any lat long data I usually use latlong(.net) as the online atlas. You can refer to the same.

Since the quarter moon is just rising, the time at your location must be around 12 PM since the full moon rises at sunset and the new moon rises at the sunset.

Therefore, there is a six-hour gap from NYC and since NYC longitude is 74^oW. Since every hour represents approximately 15^o longitude we can say that you are at approximately 164^oW.

Therefore your coordinates would be approximate, 70^oN and 164^oW. Looks like you are at coastal Alaska, be warm.

b) Follow the same steps. Use pole star position for latitude and moon time for longitude.