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Suppose I wake up from a coma on a desert island in the 19th century (i.e. we already use the Gregorian calendar but have no satellites yet). I have a clear view of the sky and a couple of days to make observations and calculations. Can I determine the current day of the week? Also, can I find the answer instantly?

On a related note, is it possible to define days of the week in a purely astronomical (e.g. planet-agnostic) manner such that for the Earth we get the traditional meaning?

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2 Answers 2

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It is possible to determine the day of the year using the distance of the sun from the vernal equinox (you have to account for the equation of time etc, but it is possible). It is also possible to determine the year if your measurements are precise enough, using the current position of the vernal equinox (which changes due to precession). The ambiguity of the factor of 26000 years can be removed by noting the positions of other stars (for example, Barnard's star). Knowing these two, you should be able to find the day of the week.

About your second question, Astronomers like to deal with Julian date, which is a continuous day counting system, and you can determine the day of the week from the Julian date, though only if given a reference, for example Jan 1, 2000, was a Saturday. As such, a week and days of a week are man made (https://en.wikipedia.org/wiki/Week).

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Also, for the year, you have to account for nutation. I forgot to add that. –  Takku Jul 4 at 11:45
    
Ok, the first part is clear now, thank you, but I still don't get the second one. Perhaps I wasn't clear in the question. I accept that the days of the week are man-made, but that doesn't mean that they can't be absolute. For instance, the metre is an ad-hoc man-made unit of measurement, but today we define it as “the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second”. I wonder if there exists a similar definition for, say, Sunday. –  questionguy Jul 4 at 17:39
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Given no other information, no. The method described relies heavily on knowledge of local bodies from which to derive the number of days since a point of index. This is very easy on Earth due to the abundance of information available to us. On a hypothetical planet in which this information isn't available, we have no way to derive days passed. –  Mitch Goshorn Jul 5 at 3:30
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I agree with Mitch. We have defined references to an exact earth day & an exact earth year and we know about the precession & nutation periods in terms of earth years, from which we can get the date. Also, weeks are defined for earth days, so if we do go to other planets, we'll still have to work with earth days. We don't know the constants as accurately for other planets (and definitely not for hypothetical planets, but I don't think we're dealing with those here). And it is nearly impossible to calculate such relations in a time frame as small as a couple of days as was mentioned in the OP. –  Takku Jul 5 at 7:46
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I've been thinking a bit, and yes, you're right. Suppose we have a star far enough from the others with a single planet orbiting around it and no other spatial bodies nearby. Then the planet has a perfect elliptical orbit. Now assume that a "year" consists of precisely 100 "days". If I drop you off on the planet twice with a difference of a "year", you'll see exactly the same (as the entire system is in the same state), but you need to give a different answer. For a deterministic method, that's a contradiction. –  questionguy Jul 8 at 20:50

Edit (massive rewrite in response to comments)

There's nothing "out there" that will tell you what day of the week it is. The concept of a week is determined by religion or culture but there's no objective reason why a week should have seven days. From 1793-1805 the French Republic had a calendar with a 10-day week.

If you wanted to try to extrapolate our idea of a week to other planets, be aware that the planets in our solar system have very different day lengths. One Venus day is 243 Earth days, while the planets Jupiter through Neptune all have days that are less than one Earth day.

It doesn't happen in our own solar system, but it's theoretically possible for a planet to have one side always facing its star. Then it would be impossible to define a day in the way that you've intended.

Even if you wanted to know what day of the year it is, that's possible but quite hard. In particular you would have to account for things like time zones, leap years, and daylight savings, which are not empirically observable phenomena. A few hundred years ago the definition of noon was when the sun was at its highest point in the sky. I think that definition is closer to what you're asking, but that's not the calendar system that we currently use.

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Although this is interesting, it doesn't directly answer the question. –  LDC3 Jul 4 at 22:36
    
More specifically, it answers the 'related note' only. Improve the quality of the answer by also addressing the primary question. –  Jeremy Jul 5 at 20:23
    
Yeah I'm new here... trying again. –  Matthew Jacobs Jul 5 at 21:12

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