The few-body problem of particles with only gravitational interactions

Deepak Dhar

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arXiv · 2309.07144

The few-body problem of particles with only gravitational interactions

Deepak Dhar

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Abstract

In this article, I discuss the motion of $N$ point masses in non-relativistic mechanics, when the interaction between them is purely the Newtonian gravitational interaction, with $N$ greater than or equal to 2. The dynamical equations of motion cannot be solved in closed form, for general initial conditions, for any $N$ greater than 2. However, the qualitative behavior of the solutions can be understood from general considerations. I discuss in particular motion the three masses on a line, and the counter-intuitive case of four masses on a line that leads to all particles escaping to infinity in a finite time.

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Deepak Dhar. 2023-09-06. The few-body problem of particles with only gravitational interactions. https://arxiv.org/abs/2309.07144

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