Restricted three body problem (numerical simulation of gravitational attraction)

Click For Summary
SUMMARY

The discussion focuses on implementing the restricted three-body problem numerically, specifically simulating the gravitational attraction where two massive bodies influence a third negligible mass. The user successfully simulates the expected motion but struggles to maintain the third body's trajectory for a longer duration. Key insights include the importance of selecting appropriate initial conditions and the potential impact of numerical precision on simulation outcomes. Participants suggest experimenting with initial parameters and using higher precision calculations to achieve longer-lasting simulations.

PREREQUISITES
  • Understanding of the restricted three-body problem
  • Familiarity with numerical simulation techniques
  • Knowledge of gravitational dynamics
  • Experience with high-precision arithmetic in programming
NEXT STEPS
  • Research methods for selecting initial conditions in chaotic systems
  • Explore high-precision libraries for numerical simulations, such as MPFR or GMP
  • Learn about error analysis in numerical simulations
  • Investigate visualizing gravitational simulations using tools like Matplotlib or Unity
USEFUL FOR

This discussion is beneficial for physicists, computational scientists, and software developers involved in simulating gravitational systems and those interested in numerical methods for chaotic dynamics.

Silviu
Messages
612
Reaction score
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!
 
Astronomy news on Phys.org
I'm afraid there is no general method to find the initial conditions. You need to play with the parameters. How about this?
 
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.
 
Hello. Can you help me with creating such a simulation? I'm trying to create one myself.
 

Similar threads

Undergrad Stable solutions to simplified 2- and 3-body problems?
  • · Replies 6 ·
Replies
6
Views
3K
Simulating the Three Body Problem
  • · Replies 9 ·
Replies
9
Views
3K
Undergrad Simulation of gravity on large bodies
  • · Replies 12 ·
Replies
12
Views
3K
Undergrad I made an N-body simulation program
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Gravitational attraction of bodies
  • · Replies 3 ·
Replies
3
Views
4K
Creating a Gravitational 2 body simulation
  • · Replies 6 ·
Replies
6
Views
2K
Undergrad Is momentum conserved as a body falls through a gravitational field?
  • · Replies 35 ·
2
Replies
35
Views
3K
High School Magnetic Attraction: Watching Magnets Move in Unison
  • · Replies 24 ·
Replies
24
Views
3K
High School Help Scaling Gravity Simulation
  • · Replies 7 ·
Replies
7
Views
2K
Graduate Solving N-Body Simulation Problems with Gravitational Equations
  • · Replies 8 ·
Replies
8
Views
3K