# Two suns

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1. Oct 3, 2014

### kirinmew

I apologize in advance for my low understanding, but please play along if you can.

I'm working on a story and in the story I want to toy with the idea of the solar system containing two suns and one planet. The story will be fantasy so it doesn't need to follow our laws of physics totally, but at least mostly.

How I imagine it working is the one planet will orbit two suns in an 'eight' pattern. One sun is bigger than the other, so one sun will orbit the larger sun.

With that, pretend this planet is habitable; the biology works like ours, similar ecosystems and terrains. What would the seasons look like? And how would I make a calander? This is where my brain stops comprehending this two sun idea.

If anyone can give me some advice or school me a little on how the days and seasons would work, I would greatly appreciate it.

Sorry again if this is a ridiculous question and if its in the wrong fourm.

2. Oct 3, 2014

### Simon Bridge

The figure 8 pattern would not be stable.
The stars would have to be very close together ... they'd be orbiting each other at 2-4 times the distance the Earth orbits the Sun.

Seasons on Earth are due to the Earth's axial tilt - the hemisphere closest to the Sun gets summer ... in your case there would also be cooler times when one star eclipses the other and hottest when the planet is between the stars. Between stars, also, there would be no night.

You could imagine that the planet strays to the edge of the inhabitable zone going around the top and bottom of the "8" for snow and extreme cold ... but gets very hot weather when in between.

3. Oct 3, 2014

### kirinmew

Okay thank you for the reply! That brought much needed knowledge to my question.

Would it be possible to instead have the planet orbit one sun but still have a two sun solar system ( I know that might contradict the name?) But could another sun be in the solar system, or close enough that it effects the planet without being chaotic?

4. Oct 3, 2014

### Simon Bridge

One possibility is to have the stars as a distant binary pair and the planet orbits one of them.
This would make the non-primary sun a very bright star in the sky - something for astrologers to think about.
It also lets you have different color stars ;)

If the stars were in strongly elliptical orbits, then the close approach part may be associated with cataclysmic events (the companion disturbing comets etc) and hot weather. SF and fantasy has lots of these.

5. Oct 3, 2014

### kirinmew

I think I will do that instead (:. Thank you so much for your help!

6. Oct 3, 2014

### DrStupid

It can be much more than a bright star. If the planet orbits a red dwarf like Proxima Centauri in 7 times the distance between Earth and Moon and the red dwarf is orbiting a sun-like star in the distance between Sun and Mars, than both suns would have the same apparent magnitude (around 40 % of the brightness of Sun on Earth). This system should be stable because the orbit of the planet has only 3,4 % of the radius of the Hill sphere of the primary star and the planet could be habitable because it is within the common habitable zone of both stars.

That would look like this: http://tinyurl.com/kepe7ll

Last edited: Oct 3, 2014
7. Oct 3, 2014

### Simon Bridge

I used to have a solar-system generator for SF and the "planet orbits a dim star which orbits a bright star" was a favorite.
Wouldn't there be a risk of the planet being tide-locked to the red dwarf?

8. Oct 4, 2014

### DrStupid

In the situation above the planet would most probably be tide-locked but that does not necessarily need to be a risk. A tide-locked planet with a sufficiently dense atmosphere could still be inhabitable. To prevent tide-locking the primary star need to be heavier. But I'm afraid there is an upper limit because the variations of total irradiance increase with the distance from the primary star.

9. Oct 7, 2014

### Anthony23

Wouldn't the planet have to be close enough to the red dwarf where it would be receiving lethal radiation? That would render the planet quite inhospitable for humans, unless there is going to be a non-human race on this planet.

10. Oct 8, 2014

### DrStupid

That depends on the luminosity of the red dwarf.

11. Oct 8, 2014

### Staff: Mentor

There are stable figure-8 orbits. Actually, there are many different classes of non-trivial orbits around two suns. See this science article for more details. Some animations can be found here.
It is unclear how a planet would hit one of those orbits, but you can always assume some unlikely capture process.
For the discussed system with one star far away, close to the seasons on earth (maybe more or less extreme depending on the axial tilt). For the other orbits... it's complicated.
I guess every cycle would get its own unit - similar to days, months (not exactly, but close to the period of the moon) and years on earth. Days would still be the rotation of the planet (unless it is tidally locked), and you would probably get two kinds of years, one for the sun close to the planet, and one less important year for the orbit of the sun far away. This second year could be significantly longer than the lifetime of your calendar-making species and also less important, but the motion of the second sun relative to the stars would be easy to track.

12. Oct 9, 2014

### DrStupid

13. Oct 9, 2014

### Staff: Mentor

Okay, let's call them figure-8-like orbits: Orbits where two stars orbit each other and the planet is not bound to any of them, but follows a complex path, frequently switching between those stars. If I remember correctly, some of them look like an 8.

14. Oct 10, 2014

### snorkack

Earth orbits the Sun at only a bit over 13 times the orbital period of Moon around Earth.

Yet the orbit of Moon is not chaotic. Sun strongly perturbs the orbit of Moon, but all these perturbations are periodic and stay within their respective fixed ranges.

It is therefore reasonable to assume that even a massive star that Sun orbits with period of at least around 13 years in case of circular orbit, or that stays outside around 5 AU (times the cube root of the mass of the stars), should not make Earth orbit chaotic and the perturbations should stay periodic in their ranges.

Imagine that Proxima were to orbit Sun on the orbit of Jupiter. Around 11 years, so slightly close, but Proxima also is 1/8 the mass of Sun, so not as much perturbation as a massive star would cause.
Now, some scale of brightness.
Full Moon is 400 000 times dimmer than Sun.
The brightest fixed star, Sirius, is 30 000 times dimmer than full Moon.
The brightest wandering star, Venus, is about 2000 times dimmer than full Moon
All stars combined in a moonless night are about 1000 times dimmer than full Moon
I have not found exactly how bright the airglow is in absence of aurora, but estimates go up to 10 times the brightness of stars, so 100 times dimmer than full Moon.

Now, Proxima is inherently 18 000 times less bright than Sun. Proxima does emit as much as 1/500 the energy of Sun, but most of it is infrared, so the ratio of visible light perception is as stated.
To simplify computation, let us assume that Proxima is on a circular orbit 5,0 AU from Sun. (The actual orbit of Jupiter is slightly further, average 5,20 AU, and elliptic between 4,95 and 5,46 AU).
Assuming Earth is on a circular orbit at 1 AU, then the distance to Proxima at opposition should be 4,0 AU. At conjunction, it should be 6,0 AU, and at quadrature, from Pythagoras triangles, 4,9 AU.
Now, Proxima at opposition should be 288 000 times dimmer than Sun - and this means about 40 % brighter than full Moon. Not a big qualitative difference.
But Proxima would be perhaps just 70 arc seconds across. Meaning that the light is concentrated into a spot only slightly bigger than Venus at its biggest. Too small to resolve by naked eye - and, unlike the disc of Moon, concentrated in a spot that dazzles.
Also, would the contrast between reddish light of Proxima and only slightly yellowish-white Moon be a conspicuous one?

15. Oct 10, 2014

### snorkack

I think you should call the distant star period something else than a year. It is necessarily very different in both its length and importance.

And the motion of the second sun relative to stars will not be directly that easy to track, nor that important. With effort you can make out the brighter stars around Moon. But who cares if Moon is in Capricorn, apart from astrologers? Whereas full Moon, new Moon, waxing or waning Moon are easy to spot and also of immediate practical importance. Sure, if Moon is in Capricorn and so is Sun then it therefore is new Moon. But the immediate logic of tracking, if you do care where Moon is, is opposite - new Moon, winter (Sun in Capricorn that is invisible in sunlight) - therefore Moon in Capricorn.

Now imagine that Proxima is on Jupiter´s orbit, and as bright as Moon.

The relevant period for the immediate practical use of Proxima would be the period of Proxima relative to Sun. But, since Proxima is moving much slower than Sun, this period is close to the period of Sun (that is, Earth orbit around Sun). This period, therefore, is the (solar) year - unlike the case of Moon which moves much faster than Sun and whose period therefore is close to its orbital period and very different from the year.

Now, assume that Proxima also orbits in prograde direction as Jupiter does - the same direction as Moon orbits and Earth rotates.
Note that, looking from Sun, a full moon overtakes Earth, whereas Jupiter is overtaken by Earth.

Jupiter is brighter than any stars in the sky except Venus which never gets far from Sun. It follows that the opposition of Jupiter is easy to track, but of no practical importance: Jupiter outshines any single star, but not the combined light of all stars and skyglow, so Jupiter in opposition does not shine significant useful light on ground the way full moon does.

So imagine Proxima instead of Jupiter - slightly brighter than full Moon.

Then the exact opposition of Proxima would be both conspicuous and practically important.

Moon circles the Earth in 24 hours 50 minutes, so it rises 50 minutes later each day. Fixed stars, and Jupiter, circle the Earth in about 23 hours 56 minutes, so they rise 4 minutes earlier each day.

For an evening owl, exactly full moon would rise at sunset, and climb higher in the east as the twilight fades in the west, so there would not be real darkness at full moon - or before full moon, under waxing gibbous moon. But the next evening after full moon? Twilight gets as dark as the light of full moon when Sun is 9 or so degrees under horizon, so in tropics where sun sets vertically or nearly so, it would get quite dark in 40 minutes or so after sunset. Unless full, or waxing gibbous, moon is in the sky. One night after exact full moon, and all of a sudden evenings get quite dark before Moon finally rises 50 minutes after sunset - and even then it takes time to climb higher from horizon and spread useful light on horizontal ground.

Now imagine Proxima. As bright as Moon, but unlike Moon its rise gets 4 minutes earlier each evening. So on the exact opposition, it rises at sunset, and you can watch the opposition approach over a period of something like ten days, as it rises progressively earlier in dusk and is correspondingly higher as the twilight fades. Something that is both easy to detect and immediately practically important. And which happens not 12 times a year, each month, but just once a year.

Approximately. Because Jupiter does orbit Sun relative to stars, with period of about 12 years. The motion relative to stars is somewhat harder to detect in case of Proxima, and less practical importance. But what does matter, actually, is the motion relative to Earth axis.

Because the Sun still rises and falls in sky. Days get longer and shorter, at sufficient latitude disappear altogether. The warmth of the Sun varies with its height and day length, and winds and rains follow.

If, one year, Jupiter reaches exact opposition on 1st of January, or Proxima does and shines useful light on otherwise long and dark winter nights then on the next year, it does not do the same. It reaches exact opposition in early February instead. In 6 years, Proxima will be in opposition/full in summer nights when the nights are short and light anyway, and in winter nights it is in conjunction/new, so winter nights are about as long as dark as on Earth for that year.

So, the seasonality of Proxima´s oppositions and conjunctions will regularly change with its orbit, and that is a significant cycle of about 12 years. How about, Year of Rat?

But the orbital cycle will not be exactly 12 or some other integer number of years. The orbital period of Jupiter is actually 11,8618 years.

So suppose you want to fix the cycle to years to the seasonality of Jupiter´s orbit. So that Year of Rat always means Jupiter is in opposition in January, Year of Ox always means Jupiter is in opposition in February, et cetera.

In 12 years, Jupiter has accomplished one orbit, but also is about 0,138 years into next. If one Year of Rat, Jupiter opposition was on exactly 1st of January, then in 12 years, it will be about 5th of January.
So the result will be that in about 90 years you will need a, well, leap year. One Rat Year had Jupiter opposition in the very end of January. The result will be that 11 years after that Rat Year, Jupiter will be in opposition in the beginning of January, and in 12 years after such Rat Year, in beginning of February.

So you will have to skip a year. Which one?
There are 12 cycle designations. Rat, Ox, Tiger, Hare, Dragon, Snake, Horse, Goat, Monkey, Cock, Dog, Pig.

Would you designate a specific year as the leap year - so that it is always, for example, Pig Year shipped after 84 or 96 years when Jupiter is far enough from cycle that you must skip from Dog Year to Pig Year? Or would you do the leap year at any year of the cycle, whenever the accumulated deviation reaches one month?

16. Nov 6, 2014

### Simon Bridge

"simply" add mass to it ... it does seem to be a new and exciting use of the word "simple" that I was not previously aware of.

Smallest possible star:
http://www.space.com/21420-smallest-star-size-red-dwarf.html

Least massive star known is OTS44, at 11.5JM (Jupiter Masses) it is actually an M9.5 brown dwarf rather than a full star.
Jupiter already has a decent effect on planetary orbits at just 1JM - adding another 10 or so Jupiters in that orbit would do more than just make a dimly glowing ball. Getting it into the range of an official star would mean adding much more mass. The resulting system would look quite different - and what does that do to orbits in the habitable zone of the primary?

http://en.wikipedia.org/wiki/List_of_least_massive_stars
(Caution - seems to have a bunch of errors in it. Double-check the data before use.)

You can get very close binary stars though - Centaurus A and B get about 11AU from each other at closest approach.

17. Nov 6, 2014

### Staff: Mentor

The stars of W Ursae Majoris have a semi-major axis of just 2.5 solar radii, so close they are touching each other.

18. Nov 6, 2014

### DaveC426913

This problem has already been solved my one Mr. A.C. Clarke.

Simply drop a replicating TMA-2 into it and wait.

:D

19. Nov 6, 2014

### DaveC426913

You're remembering incorrectly.

But I was just being tongue-in-cheek with my comment.

(They never had an epilogue to the film showing the state of the solar system after Jupiter's mass changed so dramatically - what with planets peeling off in random directions..

Last edited: Nov 6, 2014
20. Nov 6, 2014

### DaveC426913

This. Is. Fascinating. Mesmerizing. I had no idea orbital mechanics could be so complex.

http://suki.ipb.ac.rs/3body/index.php

Last edited: Nov 6, 2014
21. Nov 6, 2014

### dragoneyes001

you're right it was 2010 a space odyssey

22. Nov 6, 2014

### Simon Bridge

... yah: that would be one way to get a double-sun in the sky, and funny seasons too I guess.

... going the "increase density" route.
Maybe a sufficiently miniscule drop of red matter, or reversing the polarity of the local tachyon field with an x-matter pulse resonator?
Why the possibilities abound :)

23. Nov 7, 2014

### Staff: Mentor

Okay, so completely ignoring physics at one point, we can get physics right at a different point? Yeah, well...

24. Nov 7, 2014

### snorkack

Qualitatively, not much. I established it before. Sun has huge effect on orbit of Moon. Does not stop Moon having a periodic orbit.
So, how about that Proxima Centauri on Jupiter orbit I described above? As bright as full Moon. Would you skip Pig Year and have Rat Year right after Dog Year every time a leap year is needed? Or would you skip any year, whatever year the deviation totals one year?

25. Nov 16, 2014

### lpetrich

One can calculate how much of a perturbation it makes, and it's actually rather easy to do an order-of-magnitude estimation. It is

(perturber's tidal force or differential gravity force) / (primary's gravity force)

For primary's mass M and distance a, and perturber's mass M' and distance a', with the primary and the perturber orbiting each other, we have
$$\text{(ratio)} = \frac{\frac{GM'a}{a'^3}}{\frac{GM}{a^2}} = \frac{M'/a'^3}{M/a^3} = \frac{M'}{M+M'} \left( \frac{\omega'}{\omega} \right)^2$$
for angular velocities ω and ω'.

So as long as the planet orbits its star with a smaller period than the stars' orbits of each other, the planet is safe. The limit of the same period is for orbits at the star's "Hill sphere".

Here are two rules of thumb regarding stability:

A planet's orbit around one star is stable if aplanet <~ (1/3) * astars

A planet's orbit around two stars is stable if aplanet >~ 3 * astars

They are from numerical calculation of simulated planets' orbits.