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.