Orbit of figure eight 3 or more bodies

In summary, the orbit of figure eight 3 or more bodies is a complex and fascinating phenomenon in celestial mechanics. It involves three or more celestial bodies orbiting around each other in a unique figure eight pattern, with each body exerting gravitational forces on the others. This type of orbit is unstable and requires precise initial conditions for it to occur. The figure eight orbit has been observed in various systems, including moons orbiting around planets and stars orbiting around each other. Studying these orbits helps us better understand the dynamics of the solar system and other celestial bodies.
  • #1
renegade05
52
0
If I wanted to set up some initial conditions for a 3 body figure eight orbit, what would I have to set the position and velocity vectors?

Say I have three vector inputs:
initial position <x,y>
initial velocity <x,y>
mass of bodies <m1,m2,m3>

The solutions for position use
f=mi*x''
f=SUM(mi*mj*r/|r|^2)

and equating the two to get a differential equation.

Hope this make sense.

See this for a reference of what I am trying to do:
http://www.ams.org/samplings/feature-column/fcarc-orbits3
 
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  • #2
We discussed this on my website. You can find some info here:
http://www.orbitsimulator.com/cgi-bin/yabb/YaBB.pl?num=1181200864/0
http://www.orbitsimulator.com/cgi-bin/yabb/YaBB.pl?num=1250625868/0#0
 

1. What is the "figure eight" orbit in celestial mechanics?

The "figure eight" orbit, also known as the three-body problem, is a type of orbit in celestial mechanics where three objects (usually stars or planets) are in orbit around each other in a shape that resembles the number eight.

2. How is the "figure eight" orbit different from other types of orbits?

The "figure eight" orbit is unique because it involves three bodies, whereas most other types of orbits involve only two bodies. Additionally, the "figure eight" orbit is a stable orbit, meaning that the three bodies will continue to orbit each other indefinitely without any external forces acting upon them.

3. What factors affect the stability of the "figure eight" orbit?

The stability of the "figure eight" orbit is affected by the masses and distances of the three bodies. If the masses are too similar or the distances are too close, the orbit may become unstable and deviate from the figure eight shape.

4. Can the "figure eight" orbit exist in our solar system?

The "figure eight" orbit has not been observed in our solar system, as it is a rare and highly specific type of orbit. However, it is theoretically possible for three celestial bodies in our solar system to have a "figure eight" orbit if the conditions are just right.

5. What applications does the study of "figure eight" orbits have?

The study of "figure eight" orbits has applications in celestial mechanics and astrophysics, helping us better understand the complex dynamics of multiple body systems in space. It also has practical applications, such as in the design and navigation of spacecraft or the study of exoplanetary systems.

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