I am standing at the first point of Aries.
This is a point on the sky; you can't literally standing on it. Either this means
a) "Imagine you are co-moving with the sky and located at the first point of Aries;" or
b) "At a particular moment in time, the first point of Aries is directly overhead."
I think (b) is more plausible.
The sky is going west to east from my bow.
Again taken literally this doesn't make a lot of sense. Maybe we shouldn't interpret it as motion; it could be simply that if you look out from the bow and then look up your eyes are scanning the sky from west to east, i.e., the boat is heading west. However....
My Navigational Star is directly ahead and beckons me east.
Kind of contradicts my guess from the last clue.
Navigate by my Navigational Star's value
My Navigational Star appears at the North Pole
Hm. I'm guessing "appears at the north pole" means "is visible if you're standing at the north pole", which tells you the star is in the northern hemisphere.
My Navigational Star will appear in 2 hours
Degrees and Hours in equal measure[/quote]
CN doesn't measure anything in hours. Astronomers measure Right Ascension in hours, though. RA increases east from the first point of Aries, and 24 hours is a full circle through the sky. Sidereal hour angle increases west from the first point of Aries, and 360° is a full circle.
One useful thing about RA is it tells you how long until a given star passes overhead. Maybe this can be used in conjunction with the previous clue about the star appearing in two hours. But "appearing" usually means "rising", which is dependent on lots of things. However, maybe we can make some simplifying assumptions and pretend those other factors aren't important, like:
1) Assume the height of your eye above the surface of the ocean is zero, so the visible horizon is the true horizon.
2) Assume your latitude is the same as the star's declination, so the star will rise due east (or is it due west in this fantasy world?)
In that case, if the star will appear over the horizon in two hours, it will be overhead in eight hours, so its right ascension (since at this moment you're at the first point of Aries) is 8h. 8h is 120°, so the sidereal hour angle of the star must be -120° or 240° (it's minus 120° because RA and SHA increase in opposite directions).
Unfortunately no navigational star as a sidereal hour angle
of exactly 240°. The two closest stars are
- Pollux: SHA 243°, declination N 28°
- Avior: SHA 234°, declination S 59°
Of those, obviously only Pollux is visible from the north pole, so I'm guessing that's your navigational star.
Also interesting is that Pollux happens to be visible in the evening at this time of year.
Of course, it's also possible that they're not using one of the standard navigational stars. I'm not really motivated to check other stars.
Anyway, assuming Pollux is the star, your latitude is 28° (we assumed earlier that the star's declination is our latitude). Unfortunately I don't think there's enough information to determine longitude. The clues describe a bunch of observations that would be the same regardless of what longitude you made them from.
However, you said you had a list of U.S. cities. 28°N intersects the U.S. only in southern Texas (just north of Corpus Christi, 97°03'W) and Florida (St. Petersburg/Tampa area in the Gulf side, and Palm Bay on the Atlantic side; 82°48'W and 80°36'W, respectively). So if we're supposed to assume that you are just leaving/arriving at a U.S. city, it could be one of those places, though Palm Bay does not look like a good Atlantic port to be heading due east from.
So if we're heading out from a U.S. port, I'm guessing Corpus Christi, TX, 28°N 97°03'W).
If we're arriving, I'm guessing St. Petersburg, FL, 28°N 82°48'W.
If this was happening yesterday, the time wound be nearly 3pm.