Restricted three body problem (numerical simulation of gravitational attraction)

In summary, the conversation is about implementing a numerical simulation of the three body restricted problem, where two massive bodies are affected by the potential created by a third, smaller body. The simulation shows that when the third body is placed close to one of the bigger ones, it moves in circles around it while the bigger bodies move around the center of mass. However, the goal is to demonstrate the randomness of the system, but the initial conditions cause the third body to be thrown out to infinity too quickly. The speaker is looking for a way to choose initial conditions that will result in a longer simulation, possibly for a presentation. Another person suggests playing with the parameters and using the highest precision available to reduce rounding and truncation errors. The conversation ends with
  • #1
Silviu
624
11
Hello! I am implementing the three body restricted problem numerically (2 of them are massive and the 3rd one is not affecting them, so it is just moving in the potential created by them). I implemented it and if I put the 3rd one close to one of the big ones it moves in circles around it, while the big one moves around the center of mass of the 2 big ones, as expected. However I want to show the randomness of the system, but for all the initial conditions of the 3rd one (position, momentum and mass), it gets thrown out to infinity too fast (the ones I saw on the internet evolve for quite a while). I understand that this is random, but how can I choose the initial conditions so that it lasts longer (I actually need it for a presentation and I want to show it for half a minute or so). Thank you!
 
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  • #2
I'm afraid there is no general method to find the initial conditions. You need to play with the parameters. How about this?
 
  • #3
I think these types of simulations can be very sensitive to rounding/truncation errors in the math. You might try using the highest precision available, if you're not doing that already.
 
  • #4
Hello. Can you help me with creating such a simulation? I'm trying to create one myself.
 

1. What is the restricted three body problem?

The restricted three body problem is a mathematical model used to study the motion of three celestial bodies that are mutually attracted by gravitational forces. It assumes that one of the bodies is significantly smaller than the other two and is therefore considered to have a negligible effect on the overall system. This simplifies the problem and allows for a more manageable solution.

2. What is numerical simulation?

Numerical simulation is a method of solving complex mathematical problems using a computer. In the context of the restricted three body problem, it involves using numerical methods to approximate the trajectories of the three bodies under the influence of their gravitational attraction. This allows for a more accurate and detailed analysis of the system.

3. How is the restricted three body problem useful?

The restricted three body problem has many practical applications in the field of astrodynamics. It can be used to study the motion of satellites, spacecraft, and other celestial bodies in our solar system. It also has applications in other fields such as physics, astronomy, and engineering.

4. What are some challenges in simulating the restricted three body problem?

One of the main challenges in simulating the restricted three body problem is the complexity of the mathematical equations involved. These equations are highly nonlinear and can be difficult to solve analytically. This is why numerical simulations are often used instead. Another challenge is ensuring the accuracy of the simulation, as even small errors in the initial conditions or numerical methods can lead to significant deviations in the results.

5. How can the restricted three body problem be solved numerically?

There are several numerical methods that can be used to solve the restricted three body problem, such as the Runge-Kutta method and the Bulirsch-Stoer method. These methods involve discretizing the equations and using iterative techniques to approximate the solution. Many software programs and computer codes have been developed specifically for simulating the restricted three body problem, making it more accessible for researchers and scientists.

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