Welcome, Guest. Please Login.
Gravity Simulator
11/19/17 at 13:45:39
News: Registration for new users has been disabled to discourage spam. If you would like to join the forum please send me an email with your desired screen name to tony at gravitysimulator dot com.
Home Help Search Login


Pages: 1 2 3 4 
Send Topic Print
Chasing suns ... (Read 33594 times)
Tony
YaBB Administrator
*****




Posts: 1051
Gender: male
Re: Chasing suns ...
Reply #45 - 07/01/07 at 10:33:52
 
Actually, I realized the flower-shaped one is just 3 normal orbits, and would probably remain stable even if the masses were not equal.  It consists of two binary orbits.  The first one consists of two equal-massed (but they don't have to be) planets orbiting their common barycenter in circular orbits.  The second one consists of a planet and the barycenter of the first planet pair orbiting the barycenter of that system.  Try watching the simulation with the trails turned off.  You'll see what I mean.
Back to top
 
 
Email View Profile WWW   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1507
Gender: male
Re: Chasing suns ...
Reply #46 - 07/01/07 at 12:20:50
 
You're right Tony ...amazing how the trails can be ...complexing things. I also think that changing masses can work ...Maybe some work to do  Wink .  
Here's another one , also from Chen . In this case 4 equal masses start in the y-direction , also at given distances . The system starts good , but due to the low accurancy ( remember the 4 significant digits ) the orbits change ...
However the system stays stable . The period of this system is about 8 years . It was run for more than 500 years .  
Back to top
 

Chen41111.gif
Email View Profile   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1507
Gender: male
Re: Chasing suns ...
Reply #47 - 07/04/07 at 12:38:01
 
The system above is not stable in the long term , although it seemed to be so . This may be a result of the "poor" accurancy of the initial conditions , or may be inherent . I don't know.  
Here are the initial conditons ( from the work of dr Chen ) .  
"Earth",5.9736e+24 kg  
"Rx Ry Rz Vx Vy Vz of planets"
"E", 1.10153e+10,0,0,0,-2.82011e+0,0
"E", 3.9966e+9,0,0,0,3.52200e+2,0
"E", -3.9966e+9,0,0,0,-3.52200e+2,0
"E", -1.10153e+10,0,0,0,2.82011e+0,0
 
Another 4 body system is this one (also from the same author :  
"Earth,5.9736e+24
"Rx Ry Rz Vx Vy Vz of planets"
"E", 9.70470e+9,0,0,0,2.83396e+01,0
"E", 2.19975e+9,0,0,0,4.04237e+02,0
"E", -2.19975e+9,0,0,0,-4.04237e+02,0
"E", -9.70470e+9,0,0,0,-2.83396e+01,0
The system has a period af about 6 years and keeps its form for 100 years , but suddenly the planets escape from their orbit , evolving to a typical 4-body motion as can be seen hereunder .
Back to top
 

Chen41111pi.gif
Email View Profile   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1507
Gender: male
Re: Chasing suns ...
Reply #48 - 07/04/07 at 13:58:24
 
Here is finally an example of a choreography with distinct masses ( ref : Chen )  Smiley:  
The planets have resp. 1 , 5 and 10 Earth masses . The inner planets have the biggest masses .  
Initial conditions are :  
"Earth1",5.9736e+24
"Earth2",2.9868e+25
"Earth3",5.9736e+25
"Rx Ry Rz Vx Vy Vz of planets"
"E", 1.8e+10,0,0,0,6.30687e+2,0
"E", 9.85935e+9,0,0,0,-4.55923e+2,0
"E", -6.72975e+9,0,0,0,1.64893e+2,0
The system seems stable . A small rotation is noticible , as a kind of precession .  
 
Chen defined several categories of orbits , depending upon the cyclic permutation .  
This orbit belongs to the same category as the criss cross .
Back to top
 

Chen31510pi.gif
Email View Profile   IP Logged
EDG
Ultimate Member
*****


oh, crumbs!!!

Posts: 611
Gender: male
Re: Chasing suns ...
Reply #49 - 07/04/07 at 23:56:28
 
OK, this is getting really silly now Smiley
Back to top
 
 

(formerly known as Mal)
View Profile WWW   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1507
Gender: male
Re: Chasing suns ...
Reply #50 - 07/05/07 at 08:27:21
 
The following choreography is a member of the same set as the flower  
It consists of 3 bodies . The first has 1 Earth masses , the 2nd 5 and the 3th 10 Earth masses.  
The outerst planet is at 2.54565e+10 m from the center .  
Orbital period is about 11 years .  
The system seems quite stable .  
Amazing how the 5 Earth mass body rotates in almost a square ...
Back to top
 

Chen31510pi2.gif
Email View Profile   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1507
Gender: male
Re: Chasing suns ...
Reply #51 - 07/05/07 at 10:21:14
 
Hereunder is a simulation with 4 distinct masses (1 ,5,8,2 Earth Masses ) from right to left . The outermost planet is 2.54 e+10 m from the center . Orbit period is about 12 years
It's a piity this system is unstable and degenerates quickly .  
From all the 4 body choreographies none of them was stable till now.  
Back to top
 

Chen41582pi2.gif
Email View Profile   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1507
Gender: male
Re: Chasing suns ...
Reply #52 - 07/07/07 at 02:38:44
 
Peanuts have arrived ..!!! Smiley
From the work of Chen who investigated retrograde orbits comes the following simulation .  
Two big masses ( 1 and 2 Earth masses in this case ) circle aroud each other . A third mass (0.01 Earths ) circles around them , or tries to. In fact it is pushed into a patatoo or peanut orbit .  
The orbit seems stable .  
 
Masses und coordinates used here are :  
"Earth1",1.19472e+25
"Earth2",5.9736e+22
"Earth3",5.9736e+24
"Rx Ry Rz Vx Vy Vz of planets"
"E", 3.31350e+9,0,0,0,1.16179e+02,0
"E", 1.19010e+10,0,0,0,-1.75825e+2,0
"E", -6.7470e+9,0,0,0,-2.30597e+2,0
Back to top
 

Chenpeanut.gif
Email View Profile   IP Logged
frankuitaalst
Ultimate Member
*****


Great site

Posts: 1507
Gender: male
Re: Chasing suns ...
Reply #53 - 07/07/07 at 03:09:35
 
The peanut system above seems to me to be possible in the real universe for several reasons :  
first double stars are quite common in the universe , second other orbits are possible with other sun masses , and third the peanut orbit seems stable if the initial conditions of the peanutplanet are changed ...
Herunder is a picture of the same system when the initial velocity was changed by more than 2% . The peanut orbit simply rotates but stays stable ...  
 
Moreover the system remains stable ( although the orbit rotates ) if a velocity component in the z-direction of the peanutplanet is added ( vz of 10% vy was added fi ) .
Back to top
 

Chenpeanutvelocity.gif
Email View Profile   IP Logged
Tony
YaBB Administrator
*****




Posts: 1051
Gender: male
Re: Chasing suns ...
Reply #54 - 11/12/07 at 11:34:07
 
Thread restored
There's a few threads that were generating error messages when viewed, including this one.  This thread should work again.
Back to top
 
 
Email View Profile WWW   IP Logged
Pages: 1 2 3 4 
Send Topic Print