Longest possible eclipse in double star system

I have a planetary system that consists of two close stars:

1. A Sun-like star - small but bright
2. A much larger, but much darker star (about 5-10 times larger)
3. A habitable planet orbiting both of the stars. This planet does not have a moon

Because of the planet's stable axis and lack of a moon, the only "winter" here will be the eclipse of that double star. When the larger one passes in front of the bright one, there will be darkness (or shade) over the whole habitable planet, because only the darker star is visible. And this makes a short, but really strong, winter.

Question: how long could this eclipse last? I know that this eclipse should last for a few hours in most systems, but can it last for (in extreme conditions and resonance of planet and star orbit speed) like 3 or 4 days with a day of partial eclipse? I need planet temperatures to get as cold as possible, because in first day without sun, there is not a significant decrease of temperatures. (we can barely get to 0 celsius).

Hint - other star can be born elsewhere and come later to that star system, so their orbits could be slower (could be?).

Optional Question B is - how slow could two stars rotate without splitting each other? Or can we slow down that planet enough to stay in shadow for a long time? (Without significant change of the planet radius and gravity compared to earth). That one orbit should last hundred of years, but eclipses/winter should come in a reasonable earth way.

Thanks for answers. I know that there are some binary star system eclipses threads, but they're about other variants of binary stars and do not answer my question about slow eclipses.

posted almost 6 years ago

Miki‭

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