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A small Assist (Read 5212 times)
abyssoft
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A small Assist
12/15/14 at 14:06:51
 
Trying to craft a system with the following setup
 
Tight Quaternary system AB-CD with a sub-stellar companion b.
 
I'm needing assistance with getting the tight Quaternary system setup, the sub-stellar companion can be dealt with later.
for all four stellar bodies:
m =2.2967175E+30 kg  
r = 830375 km
initial e = 0
i should be between 0 and 5
 
initial separation of binary AB at 0.041 au and CD at 0.041 au.
initial separation between the pairs at 0.303 au.
 
The problem I keep encountering is my various attempts at the system very quickly flies apart, and I'm not quite sure why; but I think it may have to do with the order I'm putting it together.
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abyssoft
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Re: A small Assist
Reply #1 - 12/16/14 at 16:39:30
 
I was correct.  
 
I finally got it to work by :
1) creating(editing) Star A to 2 * Mass of star (or mass of primary binary)  
2) Create Star B 2 * Mass of star (or mass of secondary binary) reference Object as Star A
3) run simulation for a few mins
4) Set the mass of Star A and Star B in half (or the more massive element in respective binaries)
5) Create Star C with 1 Mass of Star (or the less massive element of primary binary) reference Object as Star A  
6) Create Star D  with 1 Mass of Star (or the less massive element of secondarybinary) reference Object as Star B
 
What didn't work was creating AC and then trying to create B orbiting barycenter that always flew apart, it seems that the barycenter calculation doesn't work;
But at least I now know how to build this system.
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Tony
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Re: A small Assist
Reply #2 - 12/16/14 at 17:19:31
 
I tried something similar yesterday, but it flew apart.  I was going to code it from scratch, but seems you've got it.
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abyssoft
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Re: A small Assist
Reply #3 - 12/16/14 at 22:18:29
 
It's part of a con-world I'm working on.
 
There are a total of 5 sub-stellar companions and 2 belts both having a fair z component.
Both belts are obvious to the inhabitants of the 2nd planet. The inner due to zodiac light and the outer due alignment with nearby stars frequently causes occultations.
 
The first planet is an earth massed high density mars sized high albedo world
The second is in the habitable zone of the tight double binary
Then comes the first belt (not modeled in the simulation, contains lots of dust, pebbles, and boulders; very few large bodies)
3rd planet could have been a twin (about 3/4 ths the mass) of the 2nd but is currently outside the conservative HZ but is in the optimistic HZ and will be in the conservative HZ during the final 10% of the systems time on the Main sequence
4th planet is a ringed gas giant (4 Mjup)
5th planet is low density high albedo ringed gas giant similar to Saturn but Jupiter massed.  
outer belt similar to our Kuiper belt but higher density of objects with almost all in the 1-20 km range (not modeled in the simulation)
 
Moons
1st = moonless
2nd = 8 small moons totaling in mass to 1/8 th of the planets.
3rd = moonless
4rd = 4 large moons, 6 small, all orbit significantly far from the planets so as to be distinguishable.
5th = 2 large moons, 4 small, not know to the people of planet 2.
 
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Re: A small Assist
Reply #4 - 12/16/14 at 23:31:55
 
Ok now It's proving quite difficult to keep the planets bound lol.
 
If I end up getting the system worked out I'll post the sim for sure.
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« Last Edit: 12/17/14 at 10:21:20 by abyssoft »  
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phoenixshade
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Re: A small Assist
Reply #5 - 12/21/14 at 22:50:01
 
Greetings, one and all, after a long absence.
 
I'm seeing what I can do with this problem. I set up the quaternary the old-fashioned way: I did the math.
 
The first step was to consider one tight binary. First, we look at the universal formula for gravity, F = Gm1m2/r2. Since m1 and m2 are equal, this becomes F = Gm2/r2. Next, we set this equal to centripetal force, F = mv2/R. This is a different R, equal to half the distance between the stars (since they orbit their mutual center), so substituting R=0.5r into the equation gives F = mv2/0.5r, or F = 2mv2/r. Now we can set this equal to gravity and solve for our initial v: Gm2/r2 = 2mv2/r. This reduces to Gm/r = 2v2, or v = √(Gm/2r). Plugging in the numbers gives v = 111.8197 km/s.
 
Next, we repeat the process, treating each binary as a single object of mass 2m located at its barycenter. By the same calculations, we get v = 58.17067 km/s.
 
Dropping into GravSim, I created the four stars with appropriate mass, then adjusted them via Edit Objects (state vector). This was problematic at first; I had to manually edit the .gsim to make all four stars "Floating." Otherwise, it was forcing Star Ab to use Star Aa as a Reference Object, making its velocity relative to Star Aa instead of equal and opposite... equivalent to setting its initial velocity to zero. (Hey Tony, any chance we can get "Floating" in the Reference Object drop-box when editing state vectors??) To make everything nice and easy, the first tight binaries start on the y-axis (x=0), each 0.0205 au from the origin. Both stars of the second binary start on the x-axis (y=0), with x-values of 0.2825 and 0.3235 au (0.303 +/- 0.0205). Getting the tight binaries to orbit is now easy: for the first pair, all the initial velocity is in the x direction; one is positive 111.8197 and the other negative. For the second pair, the velocity is all in the y direction.
 
Now, to get the pairs to orbit each other, we could give each pair a push of 58.17067 km/s in opposite y directions, but rather than doing that, I gave all of the relative y velocity to the first pair by doubling the value. (This way, I didn't have to mess with the already assigned y velocities for the second tight binary.) Since their relative motion is the same, the resulting orbits are identical.
 
In all cases, I assigned positive or negative values to produce anti-clockwise rotation.
 
Here's the resulting .gsim. You might have to click the "floating/absolute" button on the graphics options... otherwise it tracks on one of the stars and things look a little weird.
 
Working on planets, but what distance did you have in mind to represent the HZ? Based on their mass, I'd estimate that each of these four stars have about twice our sun's energy output, or about 8 times solar output in total. I believe that, based on the inverse square law, that would put the HZ around sqrt(8) or about 2.83 au, so that's my starting point for planet 2. Thoughts?
 
By the way, if you want to change anything, I recommend you do it with state vectors. Trying to mess with orbital parameters WILL result in chaos (and not the fun kind). Trust me.
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« Last Edit: 12/22/14 at 01:18:15 by phoenixshade »  
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abyssoft
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Re: A small Assist
Reply #6 - 12/23/14 at 00:55:35
 
Thanks phoenixshade.
 
It's a good starting point for me.
 
 
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Tony
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Re: A small Assist
Reply #7 - 12/23/14 at 08:19:12
 
Taking Phoenixshade's sim and setting all objects to have the first object as its reference object allows you to make the system orbit its barycenter.
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abyssoft
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Re: A small Assist
Reply #8 - 12/23/14 at 14:51:44
 
Now if there was a way to simulate the suns rise/set on this world.
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abyssoft
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Re: A small Assist
Reply #9 - 12/26/14 at 16:00:09
 
Found a way to simulate the sun rise/sets
 
An application called Space engine.
 
it has a bit of a steep learning curve and definitely makes one do all the maths.
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