Precision sunrise shrines.
(some lost in space back story here, will get chatbot to generate)
(data is newly generated at each refresh.)
Your crew follows an ancient alien map and come into orbit of the planet COSINUS. A scan shows that the
planet has been long abandoned, but you detect a few shrines on the surface. Suddenly, you and your crew
are transported to the surface of the planet and you find yourselves in front of one of the shrines.
Upon examining the shrine, your crew is able to translate the inscriptions and learn that COSINUS was once
home to an ancient civilization that built a series of shrines along the equator of the planet. These shrines
are precisely spaced at equal intervals, and the distance between two adjacent shrines is called a "Metron."
Each shrine on the planet COSINUS is some kind of sunrise detector. The shrines are able to detect the presence
of sunlight and transmit a signal just as the sun rises above the horizon.
The planet COSINUS is a perfect sphere that rotates at a constant speed and has an equatorial plane that is
perpendicular to its axis of rotation. The sun is sufficiently far away that the rays of sunlight that reach
the planet are essentially parallel, and the sun rises from the west.
The fact that the equator of the shrines is along the great circle perpendicular to the planet's axis of rotation
suggests that the shrines may have some connection to the planet's rotation or the movement of the sun across the sky.
Unfortunately, at the decline of the civilization, many of these shrines were destroyed. However, two consecutive
shrines along the equator still stand: one of them is where you and your team are currently located (the blue shrine),
and another one Metron directly east of your current location (the purple shrine).
In addition to these surviving shrines, the ancient aliens also built some backup shrines. If you go one Metron
directly north, you will find a backup shrine (the red shrine). And one Metron directly east of that backup shrine
is another backup shrine (the orange shrine). These backup shrines will also emit a signal the moment they
detect sunrise.
Your crew decide to camp for the night, and a while after the next day you receieve four signals from the four shrines
with the following time differences:
How many shrines were originally placed along the equator of the planet?
Enter your answer below.
(part 1)
* * * part 2 * * *
You start to wonder why this civilization was so obsessed with sunrises. Reading some more writings on the shrine,
you have learned that the rotation of the planet decayed to the point where it eventually forced the inhabitants to
abandon the planet, likely due to the extreme days and nights that resulted from the decay.
You wonder how lucky you were to catch the sunrise on COSINUS.
How long is a day on COSINUS?
Round your answer to the nearest minutes below.
(part 2)