Classical Mechanics Animation in Python | 3 - Body Problem

The 3 - Body Problem is one of the most complex and mostly an unsolvable problem of Classical and Celestial Mechanics. The problem focuses upon the characteristics of the motion of three objects of similar mass in an isolated system exerting force on each other.

The 3-body system is chaotic and highly unpredictable. It has no analytical solution (except for a few special cases such as 3 identical bodies with identical orbits) and its equations can only be solved numerically on a computer. They can turn abruptly from stable to unstable and vice versa.

For this simulation, three stars of similar mass were considered. The model is simulated under the effect of Gravitational Force Field and in Python using Spyder. The packages used were NumPy, SciPy and Matplotlib. The differential equations obtained for the 3 - body system were first solved using a SciPy module, Odeint, and then were Non-Dimensionalised for further processing.

If you liked the simulation then, please Like and Share among your friends. For more such exciting stuff, Subscribe to my channel.

[alejandromoreno]

This is the only video that has actually made me understand what the three body problem is.

[huseyinkagantoy]

The three-body problem is a classic challenge in celestial mechanics that involves predicting the motion of three celestial bodies interacting through gravitational forces. It has been a subject of study for centuries, dating back to the time of Newton, and remains an important area of ​​research due to its complexity and importance in understanding planetary systems and galactic dynamics.

In this problem, gravitational forces between three objects are taken into account, leading to a coupled system of ordinary differential equations (odes) that describe the positions and velocities of the objects over time. The gravitational force between two objects is given by Newton's law of universal gravitation, which states that the force is proportional to the product of their masses and inversely proportional to the square of the distance between them.

Unlike the simpler two-body problem, which has analytical solutions that describe the motion of two bodies under the influence of gravity, the three-body problem lacks general analytical solutions. this is due to the inherent complexity and nonlinearity of the interactions between the three bodies. As a result, numerical methods are often used to approximate solutions numerically.

Numerical methods involve discretizing differential equations and integrating them over time to predict the motion of objects. Various numerical techniques such as Euler's method, Runge-Kutta methods or adaptive step size methods are used to solve the ode system and simulate the behavior of the three-body system.

One of the most striking aspects of the three-body problem is its chaotic behavior. Even under simple initial conditions, the motion of objects can become quite unpredictable and sensitive to small changes. This chaos arises from the nonlinear nature of gravitational interactions and has profound consequences for understanding the dynamics of planetary orbits and galactic structures.

Studying the three-body problem has important applications in astrophysics, celestial mechanics and space exploration. Understanding the dynamics of three-body systems is crucial for modeling planetary motion, predicting celestial events such as gravitational waves, and planning space missions to explore distant regions of the universe.

Overall, the three-body problem represents a fundamental challenge in theoretical and computational physics, pushing the boundaries of our understanding of complex dynamical systems and the behavior of gravitational forces in the cosmos.

[Samuftie]

Looks amazing! What is the Python package and do you have github repo for this?

[tommccrae]

Silly question... Why don't they collide and merge into one big star?

[rupamkundu]

Have you used the 4th order RK? or proceeded with the Euler soln?

[aSpyIntheHaus]

There's always one problem maker! If it's not green it's red! Today it's red!

[rpids]

why didn't the suns hit reach other?

[viddeshk]

Ooh my God. The 3 body problem. Do you have the code?

[REACTIONU]

Well these elegts are really freaking fast

[jasonlin]

Due to mometum conservation, those 3 bodys would be always all moving in a plane.
Why you demo in 3D ?