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.

• Hi Miki, and welcome. I doubt you can have a planet orbiting both stars of a double-star system and being habitable at the same time, especially if the stars aren't something like blue giants. The necessary orbital radius for the planet would almost certainly be too large. I'm guessing that you could get away with type O, B or maybe A for the hotter one, but almost certainly not F, G, K or M. This is not conducive to your requirement of a Sun-like (G-type) star being the more luminous.
– user
Commented Feb 8, 2019 at 12:44
• Also, I'd like to point out that larger stars typically shine brighter for to their increased rate of stellar nucleosynthesis and larger surface area. So, a larger yet darker star may not be possible.
– user44399
Commented Feb 8, 2019 at 13:44
• @B.fox There are large K and M type stars, so that alone is not an impossibility. In particular, a red giant might meet OP's requirements there. I'm still not sure one can get sufficient luminosity with a subgiant star to provide sufficiently high temperature at sufficient distance to allow a planet to orbit both stars' barycenter, though; someone better versed than me in astronomy might need to chime in on that.
– user
Commented Feb 8, 2019 at 14:56
• Let's ignore the details for a moment and suggest that a star and a larger-in-diameter body are orbiting a barycenter and your planet is orbiting the both of them. The orbital speeds would need to be such that the "orbit of the larger object around the bright star" and the orbit of the planet are almost identical. The more identical they are, the longer the winter. But that barycenter causes a complex orbit, it's never as if the central star is stuck with pin. Intriguing, but it might not be possible insofar as we understand the math today. (The universe does throw us curve balls...)
– JBH
Commented Feb 8, 2019 at 22:41
• You might want to check out How would life be on Earth if the Sun was replaced a binary star system? and How long is a solar-solar eclipse in a Binary Star System?, if you haven't already.
– user
Commented Feb 9, 2019 at 13:08

SHORT ANSWER You probably need to make the system contain a white dwarf star orbited by a gas giant planet and by a Earth-like planet orbiting just slightly farther than the gas giant planet. Due to the extreme improbability of surviving planets in the habitable zone of a white dwarf, that star system would probably have to have been created by highly advanced aliens for some reason.

I would suggest that you make the small bright star as small as you plausibly can and replace the larger dimmer star with a gas giant planet or a brown dwarf with a much greater radius.

Thus, if the giant planet or brown dwarf is wider than the star, its shadow will expand with distance becoming wider and wider with increased distance from the star. And if you make the giant planet or brown dwarf very close to the star, compared to the diameters of the star and the dark object, the shadow of the dark object may cover a significant percentage of the orbit of any planets orbiting farther out - a percentage equal to that of the diameter of the planet or brown dwarf compared to that of its own orbit.

If the planet to be eclipsed orbits in exactly the same orbital plane as the inner planet, the length of its eclipses should be the same percentage of its orbit as the diameter of the inner planet or brown dwarf is of its own orbit.

If the gas giant planet or brown dwarf has a diameter of 0.5 percent of it's orbital circumference, its shadow should be 0.5 percent of the orbital circumference of the outer planet, which thus would be in eclipse for 0.5 percent of its year.

So if your eclipse by the inner planet or brown dwarf lasts for five Earth days, for example, and is 0.5 percent of the outer planet's year, for example, the total length of the outer planet's year would be 1,000 Earth days or about 2.737 Earth years.

But that is assuming that the inner planet or brown dwarf is motionless and only the outer planet is moving.

If, on the other hand, the inner planet or brown dwarf orbits the star and the outer planet is motionless, the eclipse would have to last for 0.5 percent of the inner planet's year. So for the eclipse to last for five Earth days, for example, the year of the inner planet or brown dwarf would have to be 1,000 Earth days or about 2.737 Earth years long.

But both these calculations are wrong, because both the inner planet or brown dwarf and the outer planet have to be moving in orbit around the star to keep from falling into it.

Because the inner planet has to be moving faster than the outer planet, the inner planet will catch up to the outer planet and eclipse it for a while before pulling ahead of it.

In order for an eclipse of one planet by an inner planet to last as long as possible, the two orbits must be as close as possible to make the relative orbital speeds of the two planets as close as possible.

Because the planets in our solar system have absolutely and relatively widely spaced orbits, each planet in our solar system has a significantly wider orbit and slower speed than the next innermost planet. Thus each planet is overtaken in orbit and passed by the next innermost planet in a short time.

Astronomers always assumed that would be the rule in other star systems, until exoplanets were discovered and it was found that many solar systems are very different from ours, including some star systems where the planets orbit very close together both relatively and absolutely.

The smallest absolute difference between two exoplanet orbits is between Kepler-70b and Kepler-70c. Kepler-70c orbits only 0.0016 Astronomical Units, or about 240,000 kilometers, or about 149,129 miles, farther out from Kepler-70 than Kepler-70b.

The smallest relative difference between two exoplanet orbits is between Kepler-36b and Kepler-36c. Kepler-36c orbits only 11 percent, or 0.013 Astronomical Units, or about 1,944,772.3 kilometers, or about 1,208,425 miles, farther out from Kepler-36 than Kepler-36b.

So if planet c orbits 11 percent farther from their star than planet b, their relative orbital speed should be easy to calculate. I believe the relative orbital speeds of planets b and c would be proportional to the square route of a constant divided by the radii of their orbits, and so if the orbital radius of planet b is 1.00 and that of planet c is 1.11, their relative orbital speeds should be in the ratio of 1.00 and 0.949 if my calculations are correct.

In order for the bright star in the system to be very small in diameter, significantly smaller than a gas giant planet or a brown dwarf, it will have to be a very dim red dwarf.

The dimmest red dwarf star that I know that has planets orbiting in its habitable zone is TRAPPIST-1, a spectral type M8V or M8.2V. TRAPPIST-1 has a radius of 0.121 plus or minus 0.003 that of the Sun. The Sun has an equatorial radius of about 695,000 kilometers and thus a diameter of about 1,390,000 kilometers. So TRAPPIST-1 should have a radius of about 84,095 kilometers and thus a diameter of 168,190 kilometers.

The largest planet in our solar system, Jupiter, has an equatorial radius of 71,492 kilometers and thus an equatorial diameter of 149,984 kilometers. Thus if Jupiter orbited TRAPPIST-1 its shadow would be a cone that tapered to a point, but it would do so very slowly.

If a gas giant planet was a little bit more massive than Jupiter it would be a little bit bigger than Jupiter. But making a gas giant planet a lot bigger than Jupiter would make it smaller and denser than Jupiter. Jupiter is near the largest size possible for a gas giant planet.

That is, Jupiter is close to the largest size possible for a cold gas giant planet orbiting far from its star. astronomers have discovered many "hot Jupiters", gas giant planets orbiting close enough to their stars to receive as much radiation as Earth does, or even much closer to their stars, close enough to have temperatures much hotter than Earth's. And the high temperatures of some "hot Jupiter's makes their gases expand and swells up the diameters of those planets.

The list of largest exoplanets includes several which are two, or three, or four times the radius of Jupiter. https://en.wikipedia.org/wiki/List_of_largest_exoplanets3

But if your planet that is eclipsed is orbiting in the habitable zone of its star, and if the gas giant planet that eclipses it has to have an orbit almost identical in size in order to make the eclipses last as long as possible, the gas giant planet should be only slightly hotter than the habitable outer planet and thus it might not be swollen up much due to heat.

Brown dwarfs are objects more massive than gas giants and less massive than stars, with masses ranging from about 13 times that of Jupiter to about 75 to 80 times that of Jupiter. Because of their greater mass, brown dwarfs are many times as dense as Jupiter and so have similar diameters, rarely getting much larger.

Thus the radius of the red dwarf star should be decreased to make it even smaller and dimmer than TRAPPIST-1.

Star EBLM J0555-57Ab has a radius of about 0.84 that of Jupiter, and thus about 60,0853 kilometers, and a diameter of about 120,106.5 kilometers, smaller than a gas giant planet the same size as Jupiter.

Possibly the red dwarf star could be replaced with a white dwarf star.

The smallest white dwarf star is listed as GRW +70 8247, with a radius 0.005 that of the Sun.

GRW +70 8247 has a radius of about 3,478.5 kilometers, or a diameter of 6,957 kilometers, making it smaller than Jupiter, and even smaller than all the planets in our solar system except for Mars and Mercury. So a Jupiter-sized,or even Earth-sized, planet orbiting a white dwarf star the size of GRW +70 8247 would cast a shadow that got wider and wider with increasing distance from the planet.

Of course highly advanced and powerful aliens wopuld probably have to assemble that star system, bringing in the inner and outer planets from other star systems to orbit that star, since it would be unusual for planets, especially a habitable planet, to naturally orbit around a white dwarf star.