You cannot be Sirius

When I was young, I was under the impression that Shabbos ends when one could see three stars. Later, I discovered it was actually three medium-sized stars. What a useless rule, I thought. Unless you're going to specify actual stars (which the Jews, not being (the likes of Gersonides being exceptions) astronomers wouldn't), that becomes completely meaningless.

A couple of weeks ago I look out of the window around צֵאת הַכּוֹכָבִים and saw Sirius, Rigel and Betelgeuse—the three brightest stars in the (northern) sky—and for the first time, the rule made sense to me.

Then I wondered how soon after sunset it would be possible to see Sirius, the brightest star in the sky. Shabbos goes out at least three quarters of an hour after sunset; Sirius, by contrast, is visible much earlier. The skies having been cloudless recently, I've been looking at the sky after sunset trying to see how early I could see Sirius.

So far, the earliest was today, when, having determined last night where in relation to objects on the horizon as seen from my balcony, I ought to look, I managed to spot it a mere eleven minutes after sunset.

I wonder whether I can pull that figure still earlier...