Binary Star System

[mjtobias]

Hi all,

 

I'm currently writing a young adult fantasy book series and it takes place on a planet in a binary star system. What I'd like is information on whether I'm correct in my assumptions and what daily life would be like on such a planet. 

 

I am imagining a sun and planet very much like ours (with some minor differences). The difference is, in my book the sun is also orbited by a red dwarf star. Imagine if this were the case for our galaxy...say, instead of Jupiter, there was a red dwarf orbiting the sun at approximately the same rate as Jupiter (would it orbit faster? Slower? Could it be either?)

 

I've created a rought image (definitely not to scale!) to show what I mean and attached it to this post.

 

In the image, I've labeled the red dwarf's approximate position in certain years of it's orbit (I imagine a 12 year orbit).

 

Is such a system possible? If so, what would daily life be like on such a planet? Would some nights be more like all-night dusk? Or does a red dwarf not put out enough light for that?

 

Any and all help would be greatly appreciated! I would like to get the science right ;)

 

Thanks!

 

[Eclogite]

I am concerned about the stability of the system. Modelling of the solar system has shown a small, but significant possibility that Jupiter's gravitational influence may eject Mercury from the system in a few hundred million years, or crash it into Venus. You may need to move it further out. Some researchers have modelled the possible stability of planets in binary systems. A search on google scholar should turn something up.

 

Red dwarfs are between 1/10 and 1/1000 as bright as the sun. It is roughly five times as far away as the sun. The decrease in illumination is proportional to the square of the radius, so we are looking at a reduction of 25. It's complicated in that when we are on the same side as the red dwarf the reduction is only 16 and on the opposite side it is 36.

 

If we assume a red dwarf 1/100 as bright as the sun then it will appear, on average 1/2500 as bright as the sun. For comparison the moon is 400,000 times brighter than the sun¹. So, your red dwarf is certainly going to light up the "night" sky. Even if it is a very faint red dwarf, when it is at its most distant (but not eclipsed by the primary) it will still be ten times brighter than a full moon.

 

1. Obviously this is meant to read the sun is 400,000 times brighter than the moon. (And this poster is 400,000 times dimmer than a dead aadrvark on merry-go-round.) Thanks to Moontanman for spotting the error.

[Moontanman]

I am concerned about the stability of the system. Modelling of the solar system has shown a small, but significant possibility that Jupiter's gravitational influence may eject Mercury from the system in a few hundred million years, or crash it into Venus. You may need to move it further out. Some researchers have modelled the possible stability of planets in binary systems. A search on google scholar should turn something up.

 

Red dwarfs are between 1/10 and 1/1000 as bright as the sun. It is roughly five times as far away as the sun. The decrease in illumination is proportional to the square of the radius, so we are looking at a reduction of 25. It's complicated in that when we are on the same side as the red dwarf the reduction is only 16 and on the opposite side it is 36.

 

If we assume a red dwarf 1/100 as bright as the sun then it will appear, on average 1/2500 as bright as the sun. For comparison the moon is 400,000 times brighter than the sun. So, your red dwarf is certainly going to light up the "night" sky. Even if it is a very faint red dwarf, when it is at its most distant (but not eclipsed by the primary) it will still be ten times brighter than a full moon.

 

 

Can I assume you got that switched? 

[Eclogite]

Yes indeed. I can't think of anything that would make the moon go supernova! :)

 

I shouldn't post when I wake up too early. I shall leave the error in the post as a reminder to myself to be more careful in future.

[mjtobias]

I am concerned about the stability of the system. Modelling of the solar system has shown a small, but significant possibility that Jupiter's gravitational influence may eject Mercury from the system in a few hundred million years, or crash it into Venus. You may need to move it further out. Some researchers have modelled the possible stability of planets in binary systems. A search on google scholar should turn something up.

 

Red dwarfs are between 1/10 and 1/1000 as bright as the sun. It is roughly five times as far away as the sun. The decrease in illumination is proportional to the square of the radius, so we are looking at a reduction of 25. It's complicated in that when we are on the same side as the red dwarf the reduction is only 16 and on the opposite side it is 36.

 

If we assume a red dwarf 1/100 as bright as the sun then it will appear, on average 1/2500 as bright as the sun. For comparison the moon is 400,000 times brighter than the sun¹. So, your red dwarf is certainly going to light up the "night" sky. Even if it is a very faint red dwarf, when it is at its most distant (but not eclipsed by the primary) it will still be ten times brighter than a full moon.

 

1. Obviously this is meant to read the sun is 400,000 times brighter than the moon. (And this poster is 400,000 times dimmer than a dead aadrvark on merry-go-round.) Thanks to Moontanman for spotting the error.

 

Thank you so much for this, it is very helpful and enlightening (pun intended ;)).

 

Now, about mercury being ejected, when I plan my fictional system, I can always just plan on one planet, the earth-like planet, so that wouldn't be a problem...or would there be other problems?

 

If the RD (red dwarf) is 10 times brighter than a full moon, would it still light up the night sky on FE (fictional earth) if it is as far away as Jupiter? Would it be more like a really, really bright full moon (still relatively dark) or more like a day, with the sky being blue rather than black? Think of it from a FE inhabitant's perspective. How would they experience such a thing? Obviously, once FE is on the other side of the sun, day and night would be relatively normal, with the exception of a second, much less bright sun during the day...am I right about this?

 

I'd also like for FE to have multiple moons...perhaps 3. Would this be possible? One of my plot points has to do with the instability of tides and seas. It was my *assumption* that multiple moons would contribute to this. Is this right?

 

Again, thanks so much for your help. I will be contacting you via private message to discuss attribution, unless you'd rather I didn't.

[Eclogite]

Your questions are interesting, but answering them pushes at the limits of my competence. (Which is good, because that's how I learn.) Let me delay a response while I check some things out, so I can give you an assured answer. By all means contact me by pm, though generally I'm just happy to help someone out in a field that is of general interest to me.

[pgrmdave]

If the RD (red dwarf) is 10 times brighter than a full moon, would it still light up the night sky on FE (fictional earth) if it is as far away as Jupiter? Would it be more like a really, really bright full moon (still relatively dark) or more like a day, with the sky being blue rather than black? Think of it from a FE inhabitant's perspective. How would they experience such a thing? Obviously, once FE is on the other side of the sun, day and night would be relatively normal, with the exception of a second, much less bright sun during the day...am I right about this?

The Apparent Magnitute of the Sun is about -27, and the apparent brightness of the moon is about -13. The star would be roughly a -18.5 if those numbers are correct (that the star would be an apparent 1/2500 of the sun's light). At that brightness, it would be similar to how the sun looks from Pluto at its furthest point. It would still be very bright - much brighter than the full moon, but you'd still be able to see some stars. The fact that it would be similar to the sun from pluto means that you can find a lot of reference images (artistic license, of course, but still) which should help.

[CraigD]

I am imagining a sun and planet very much like ours (with some minor differences). The difference is, in my book the sun is also orbited by a red dwarf star. Imagine if this were the case for our galaxy...say, instead of Jupiter, there was a red dwarf orbiting the sun at approximately the same rate as Jupiter (would it orbit faster? Slower? Could it be either?)

The classical gravity (which is a good enough approximation for this sort of questions) formula for how fast bodies orbit one another – that is, their orbital period, how long one revolution takes - is pretty simple:

[math]T= 2\pi\sqrt{\frac{a^3}{G \left(M_1 + M_2\right)}}[/math]

Where a is the semimajor axis (for a circular orbit, its radius)

 

From this, it’s easy to calculate that a red dwarf (which masses from about 80 to 500 times as much as Jupiter) the same distance from the Sun as Jupiter would have a slightly faster (about 4% to 22%), shorter period. Alternately, slightly (about 2% to 14%) increasing its distance from the Sun would keep its period the same, or if you increase it slightly more, give it a slightly slower, longer period.

 

Is such a system possible?

I’d have to model it, or find a paper modeling it, to be certain, but but my pretty confident guess is that a system with a red dwarf, even the smallest possible, in a 12 year orbit around the Sun (about the same as Jupiter), wouldn’t permit stable orbits for any inner planets.

 

At a first approximation, to permit the Earth and other inner planets to exist, you’d want to put the red dwarf far enough away that its gravitational force on the inner planets is similar to Jupiter’s. That would put it from about 9 to 22 times Jupiter’s distance from the Sun, way out in the Kuiper belt

 

If so, what would daily life be like on such a planet? Would some nights be more like all-night dusk? Or does a red dwarf not put out enough light for that?

Life on Earth in such a system would be pretty much like it is now, though a red dwarf in the Kuiper belt would be the brightest star in the sky, with an apparent magnitude of -8 to -12, from at least 16 times brighter than Venus to nearly half as bright as the Moon.

 

Turning from science to science fiction, note that “the ‘Verse” from the Firefly SF franchise and fandom feature a very un-solar-system containing 5 main-sequence stars and several smaller ones in a disk of diameter about 400 AUs (compare to Solar systems diameter, defined by the orbit of Neptune, of about 60). Gamers, fans, and pros have made lots of maps of the ‘Verse, leading to a pretty good consensus about it.

[mjtobias]

...my pretty confident guess is that a system with a red dwarf, even the smallest possible, in a 12 year orbit around the Sun (about the same as Jupiter), wouldn’t permit stable orbits for any inner planets.

 

At a first approximation, to permit the Earth and other inner planets to exist, you’d want to put the red dwarf far enough away that its gravitational force on the inner planets is similar to Jupiter’s. That would put it from about 9 to 22 times Jupiter’s distance from the Sun, way out in the Kuiper belt

 

Life on Earth in such a system would be pretty much like it is now, though a red dwarf in the Kuiper belt would be the brightest star in the sky, with an apparent magnitude of -8 to -12, from at least 16 times brighter than Venus to nearly half as bright as the Moon.

 

Turning from science to science fiction, note that “the ‘Verse” from the Firefly SF franchise and fandom feature a very un-solar-system containing 5 main-sequence stars and several smaller ones in a disk of diameter about 400 AUs (compare to Solar systems diameter, defined by the orbit of Neptune, of about 60). Gamers, fans, and pros have made lots of maps of the ‘Verse, leading to a pretty good consensus about it.

Hmmm. This is kind've a bummer. So, is there a scenario where an earth-like planet can exist in a binary star system where the 2nd star has at least some affect on the planet? I suppose the planet could orbit the RD which then orbits the larger and brighter star...is that possible?

 

Also, if I forego the binary star system and just have one sun, would multiple moons create unpredictable and unsteady seas and tides? If not, would there be a way to achieve this without radically altering the habitability of the planet?

[pgrmdave]

Also, if I forego the binary star system and just have one sun, would multiple moons create unpredictable and unsteady seas and tides? If not, would there be a way to achieve this without radically altering the habitability of the planet?

The tides would still be *predictable*, just complex. No matter how many moons, suns, and other orbiting bodies you add it will still be perfectly predictable, and any culture that comes about over hundreds/thousands of years will certainly be able to measure and predict them. Just like we have good examples of many early civilizations which had good working models of predicting the planetary motions, and the tides, the sun's position each day of the year, etc.

[Moontanman]

A planet could orbit both stars if the stars were close together.. .