Orbital Mechanics Question - Speculative

[MrMattHoffman]

Hello,
I am not a physicist or a physics student. I am an author, and I am trying to see if a Trinary star system I've dreamed up could work, and if so, what are the details as applies to my book. I hope someone can take the time to help me with this.
The situation is this: I have imagined a star system with a yellow (sun-like) star and a small red dwarf (perhaps 1/4 mass of the yellow star) orbiting each other closely, and a single earth-like planet in the habitable zone around these two. So far so good. The complication is another star (which for my story is a small, hot blue, but I know that's really not likely - perhaps it was captured?) which orbits the 'binary and planet' arrangement in a very elliptical orbit. The idea is that the star only approaches close to the main system for a very short period of time, and only rarely. I am working with the idea of a 500 year orbit for the tertiary star, but that number is flexible.
I have several specific questions about this arrangement, but any data, even hard math, would be useful. Primarily, though, these are my questions:
1) Is a 500 year orbital period possible? Too short?
2) What is the shortest period of time the tertiary sun would be close to the planet? I want it to effect the planet - something in the story called 'The Burning' - but I don't want life destroyed. Could it be as short as a single year that it effects the planet? A handful of years, some getting hotter, then cooling off?
3) Is there any way you can suggest that I can understand what this would look like from the planet's surface? I need to be able to describe the blue sun as it moves through it's orbit.
Thank you so much in advance for any help with this!
Matt

 

[mfb]

In general, longer periods are no problem in terms of orbital mechanics - you have to be careful in order to get a stable planetary orbit anyway, if the third star influences it frequently.

A short "burning time" is problematic. To get a stable planetary orbit, the fly-bys cannot be too close. A more massive blue star would help there, but that increases the luminosity a lot. It is easier if the yellow star is smaller than the sun.

To test some numbers (year always means Earth years):
Yellow star 0.8 solar masses, luminosity 0.4 times solar luminosity
Red dwarf 0.2 solar masses, luminosity <=1% solar luminosity
Life is certainly possible at ~0.7 AU (same light intensity as on earth).

Blue star 2 solar masses, 20 times the solar luminosity. Minimal distance 4 AU, to increase radiation by ~130% (90% to 180% depending on the phase). Probably too much, but let's see what happens:
A period of 500 years is long enough to have approximately escape velocity of the stars: This is 24km/s or 5 AU/year relative velocity. Those burning phases would last ~1-2 years.

In terms of the blue star, there is not much we can change:
- increasing its mass reduces the fly-by time a bit, but increases the luminosity extremely
- reducing the minimal distance reduces fly-by time, but increases the intensity too much and gives problems with the orbital stability
We can make it fainter, of course, and I think this is necessary to ensure that life can survive. It will increase the time a bit, but not too much.

If the binary star can get smaller, it is easier:
Red dwarf 0.5 solar masses, 6% solar luminosity, 0.6 solar radius
Red dwarf 0.2 solar masses, <1% solar luminosity, 0.3 solar radius
Orbiting each other in a close orbit (<0.05 AU)
Planetary orbit: 0.25 AU, again chosen to have light similar to earth

Third star: Sun-like, 2 AU minimal distance (giving ~25% increase in luminosity), maximal relative velocity 4.8 AU/year. This would probably increase surface temperature significantly, but last less than a year. You can play with the luminosity here, if you like, this does not change numbers a lot.

3) Is there any way you can suggest that I can understand what this would look like from the planet's surface? I need to be able to describe the blue sun as it moves through it's orbit.

Like a third sun: It goes up and down every day, and shifts its position slightly every day.

Star data is taken from this table. I wouldn't worry about the combination of 3 different stars, there is always a possible capture scenario.

 

[Vanadium 50]

The idea of a "small, hot blue" is problematic, because they don't really exist. Blue stars are heavy. The closest you are likely to get are a handful of small objects called "subdwarf B" and "subdwarf O" stars, at about half a solar mass.

Something that big will perturb the orbit of every other object in your solar system.

But why are you making this hard? Make the red dwarf a flare star and you're done, no?

 

[MrMattHoffman]

@ mfb, thanks for your thoughts on this. I'm glad my initial idea was at least semi-plausible. The burning can work over three years, with the first year being a 'waxing' year, and the third being a 'waning' year, and the middle year being just horrible, but not lethal. People may die, but many would live.
@Vanadium 50, Well, no, it doesn't work. There are several reasons why.
First, 3 is a symbolic number in the trilogy. Three heroes, three gods, three types of magic and, three suns.
Second, I chose a trinary star system because the story needs some 'sci-fi' feel to it
Third, the planet has no moon. It's core would cool if it weren't for the appearance every 500 years or so. The intense gravitational disruptions would cause geothermal and seismic activity, and helps to keep the core molten.
Fourth, the hard radiation released by a flare would likely sterilize the planet, and I need people to live.
Yes, I know. Us authors can be a real pain! ;-)
Please see the following link to see a crude illustration of the system I am envisioning. http://technospiritualist.com/
And does anyone know a way I can visualize this? As in what it would look like from the surface?
Thanks, All!

 

[Drakkith]

I'm not sure your system would be stable. I feel the 3rd stars gravity may end up causing long term stability issues with the other two unless it is very far away. Not too mention problems with the planets orbit itself. If the planet is getting so close that severe tidal effects are felt, then I think its orbit is going to be severely disrupted.

 

[mfb]

I'm not sure your system would be stable. I feel the 3rd stars gravity may end up causing long term stability issues with the other two unless it is very far away. Not too mention problems with the planets orbit itself. If the planet is getting so close that severe tidal effects are felt, then I think its orbit is going to be severely disrupted.

I agree. Tidal effects are probably not possible, and the third star should have a large distance relative to the planetary orbit. I tried to have a ratio of ~10, which is certainly possible (and observed!) for circular orbits, so I hope it is possible for elliptic orbits as well.

The lack of tidal forces is not a problem: you don't need a moon to keep the interior molten, size alone is sufficient and tidal effects on the planet are negligible anyway. Tidal effects can keep the core of moons molten.

The burning can work over three years, with the first year being a 'waxing' year, and the third being a 'waning' year, and the middle year being just horrible, but not lethal. People may die, but many would live.

Good, that is certainly possible.

 

[Bandersnatch]

I'll add my twopence to what others have said:


I think the perturbations issue can be very well hand-waved here. As long as the author skims over the details of the orbital parameters, we can happily assume the system is in some sort of stable resonance.
It could be useful to find out whether the planet stays outside the primary's Hill sphere at closest approach.That should let us know what's the closest "safe" distance we can use. Alas, I don't know how to calcuate it for a system with two large masses.


Take a look at this picture:
http://www.atlasoftheuniverse.com/startype.gif

It illustrates some basic relationships between stellar attributes like mass, luminosity, temperature and lifetime.
Basically, the more massive a star, the more luminous and hotter, and the shorter its lifespan.
The colour depends on temperature. Stars start to look vaguelly blueish around at least 7500. You probably want the two solar masses example that mfb used in his calculations.

This tells us that the blue star must be much younger than 1 billion years, leaving too little time for the proper development of the planets from their formation to the emergence of a thriving ecosystem - should the blue star be native to the system.

You'll have to assume a relatively recent capture scenario then.



Since the blue star is more massive than the other two combined, the system won't look like the one in your drawing.
The stars will orbit their common barycentre, which will lie closer to the blue star than the other pair.
It'll look a bit like what you can see in the animation here, only less symmetrical:
http://en.wikipedia.org/wiki/Gravitational_two-body_problem
Where one of the bodies is in our case the pair of smaller stars.


To visualise the system, I'd recommend using Celestia(http://www.shatters.net/celestia/), or some other free planetarium software.
In this program, navigate to "36 Oph A-B"(press enter and type). This is the barycentre of two of the three stars in the trinary system 36 Ophiuchi.
That it is a trinary is actually of little interest to us, as the third star's(36 Oph C) orbit is too long and never approaches closely the other two.
However, the components A & B orbit each other every ~560 years, and their orbits around the barycentre are highly eccentric(ellipsoidal), with the closest approach at ~6AU - almost exactly like in the system you want.
With more massive components, like in your story, the details will be a bit different, but I suppose it's close eough a match.

You can lock on to one of the two stars, pretending it's the two dimmer stars in your story, and advance the time to see the changes in the sky.
It's a crazy dance.
You can select the other one while centred on the first, and watch how the distance, angular size, and magnitude changes.

One of the interesting things it tells us, is that even at the farthest point in its orbit, the star is much brighter than a full Moon is - and that's just a yellow dwarf!

 

[MrMattHoffman]

Fantastic! Thanks for the tips. I've downloaded the Celestia program. Working on a way to visualize how it would look from a planet's surface.
Thanks again!

 

[Bandersnatch]

I've created your system as an addon for Celestia.
It might not be 100% accurate as orbital mechanics go, but I suppose it should do for your needs.

here's a link:
https://drive.google.com/folderview?id=0B6hJly6aYB0ZM0dFWElJVHVjdUU&usp=sharing
(let me know if you can't access the folder, whether because I borked the setup or you can't use google drive, and I'll rehost it to the service of your choice or send you an email)

1.Copy the whole folder "Hoffman's System" into your "extras" folder of the Celestia instalation.
2.Run the program as usual.
3.Press enter and type "hoffman".
4.Navigate to "hoffman's star" which is your blueish star (the other two are barycentres)
5.From there you can press enter again and navigate to "the world" - which is your planet, or one of the two other stars with fancy names: "the mother" and "the father".

Ctrl+G switches the view to the surface.
You might want to turn orbits, star names, ecliptic and whatnot in the render options to get a better insight on what's going on.


I have used Earth as a model for your planet, so that you might have an easier time orienting yourself around. Keep in mind that the axial tilt is the same too, so that's going to influence the way the sky changes just like it does in reality.


I've used the setup mfb proposed, with 2, 0.8 and 0.2 solar masses for the stars; 500 year period for the A+BC system at 90 and 60 AU from the barycentre respectively, both orbits with 0.97 eccentricity; ~12 days period for the B+C system at 0.1 and 0.025 AU and fully circularised.
The planet orbits at 0.7 AU with the period of ~211 days.
I've added some modest obliquity and inclination to the orbits to make them look less artificial.

I admit that whatever calculations I had to do were rather half-arsed, so if anyone wants to suggest a correction or two, be my guest.


At present the system has the bright star approach the planet to the minimum distance of roughly 4 AU, at which point it's as bright as the brighter of the other two companions at -27 apparent magnitude. Effectively, there are periods with no night on the planet.

And finally, here's a link to the addon creation guide:
http://www.lns.cornell.edu/~seb/celestia/addon-intro.html
It's relatively easy to modify the two important files(.ssc and .stc) in notepad, if needed be.