We often try to come up with scenarios where staid, sober celestial navigation might save the day at sea. Here's a story for you where you can use your celestial analysis skills to save some drunken comrades. And we'll try to do it by using the same "latitude by two stars" that we were discussing in the thread about that photo taken from a seaside cave in Maine.
The Party Begins:
It is late January, 2018. You are sailing from New York City to Bermuda for an epic bachelor party aboard S/V Blue Moon, a luxurious mega-yacht. Your foolish friends have decided they can be crew on this voyage. How hard can it be? That's fine... until the party begins, and they all get stinking drunk. There is mayhem on the boat.
You awake one late afternoon and discover that everyone else aboard is delirious --someone has spiked the rum with unknown chemistry, and your bumbling friends are babbling about sailing to Las Vegas. Woo-hoo! Vegas... here we come! Unfortunately, the electronics would not fulfill their drunken fantasies, so they applied a hammer to the problem. The electronics have been trashed, the radio and all cell phones have been thrown overboard.
All normal forms of navigation have been disabled, but there is a sextant (well, of course there is). Can you navigate to Bermuda? You know that it is late January 2018. You left NYC Friday night. Maybe today is Tuesday, maybe Wednesday. The sky is clear, and not long after sunset the stars come out. The Moon appears full, low in the east. It's nautical twilight, and Orion is in the southeast, off the bow. You're sailing at 3 knots... but we probably don't have to worry about that. Other details: height of eye is 17 feet. You have zeroed out IC. It's chilly. You guess the temperature is in the uppers 30s (°F), and the weather is fine and clear, suggesting high pressure.
You take the following sights at approximate one-minute intervals, timed by a cheap watch pulled off the wrist of a guest from Wisconsin. When was it last set? You have no idea...
watch time: body, raw sextant altitude
4:10:05: Procyon, 16° 03'
4:11:01: Moon UL, 17° 14'
4:12:08: Sirius, 13° 25'
4:13:04: Moon UL, 17° 37'
4:14:14: Procyon, 16° 51'
Ignore the Moon sights for now. You probably don't need them, right? The sights before and after Sirius are paired so that we can easily average. What would the altitude of Procyon be if made simultaneous with the Sirius sight?
Now work out your latitude. How can you do that? We discussed options in the thread related to the ice cave. They all apply here, too. It's just two simultaneous star altitudes, and they should yield one specific latitude. Or are there two latitudes? This is a calculation with many options. For example, could you estimate your latitude using only the two Procyon altitudes and the time between them? But that's not particularly accurate, is it? What is the most accurate procedure for calculating your latitude?
What do you find? Are you north or south of Bermuda's latitude?
Next, for the expert dying for an even trickier challenge: can you estimate your longitude well enough to be useful? For this, you can try to use the Moon's observed position. First, even without calculation, can you decide the date? Note that the Moon usually looks full for three days in a row, so the phase alone is not quite sufficient. But there's enough info here. Next, can you estimate GMT/UT based on the Moon's altitude?? This is similar to a lunar, but it's not as accurate. Nevertheless, you should be able to get a longitude to go along with your latitude. Can you trust it? What should you do? What course should you set to get your drunken friends to their date with debauched destiny?!?
Hmm... "Date with Debauched Destiny"... straight to Netflix, or should we try for theatrical release? Imagine the musical theme to accompany the spherical trigonometry work.
Clockwork Mapping / ReedNavigation.com
Conanicut Island USA
Note: the image here illustrates the general appearance of the sky at about the right time (nautical twilight) and on the correct date, but it is intentionally the wrong ocean and a somewhat different latitude so that you can't just pattern-match against a view in Stellarium.