The Gemorrah rules that Shabbos comes by itself and it not dependent on a Beis Din, contrary to Moadim which are dependent on Kiddush HaChodesh כדאיתא בב"ב קכ"א.
I understand that "Beit Din" in the Gemorrah means our acting as a result of astronomical phenomena. For example, Yom Tov can only come a certain number of days after the Beis Din has ascertained that there was indeed a New Moon. This applies even nowadays, according to the Gemorrah in Rosh HaShannah. What the Gemorrah says about Yom Tov and Beis Din would be analogous to our acting due to a certain number of rotations of the earth. The Gemorrah means that Shabbos comes independant of astronomical phenomena. Therefore the answer that Shabbat comes independent of astronomical phenomena is valid.
Also, even if your question were at least a ספק, it isn't worse than what the Shulchan Aruch in Siman שדמ deals with (what to do if you find yourself in the desert and you aren't sure what day Shabbos is). You still have to keep Shabbos m'Chumrah. In your case, you know for sure when the last Shabbos was.