Orbits of the three-body problem with large potential
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918380653510656 |
|---|---|
| author | Moeckel, Richard |
| author_facet | Moeckel, Richard |
| contents | Consider the planar three-body problem with masses positive $m_1,m_2,m_3$ position vector $q(t) = (q_1(t),q_2(t),q_3(t))\in\mathbb{R}^6$. Let $$U(q) = \frac{m_1m_2}{r_{12}}+\frac{m_1m_3}{r_{13}}+\frac{m_2m_3}{r_{23}}$$ where $r_{ij}=|q_i-q_j|$. Assume that the angular momentum is nonzero so that triple collision is impossible and fix any negative energy.. Then given any constant $K>0$ there are solutions with $U(q(t))\ge K$ for all $t\in\mathbb{R}$. These solutions will have a single close approach to triple collision. The configuration will always be a tight binary with $m_1, m_2$ close and the distance from the binary to $m_3$ diverging as $t\rightarrow\pm\infty$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_08833 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Orbits of the three-body problem with large potential Moeckel, Richard Dynamical Systems Consider the planar three-body problem with masses positive $m_1,m_2,m_3$ position vector $q(t) = (q_1(t),q_2(t),q_3(t))\in\mathbb{R}^6$. Let $$U(q) = \frac{m_1m_2}{r_{12}}+\frac{m_1m_3}{r_{13}}+\frac{m_2m_3}{r_{23}}$$ where $r_{ij}=|q_i-q_j|$. Assume that the angular momentum is nonzero so that triple collision is impossible and fix any negative energy.. Then given any constant $K>0$ there are solutions with $U(q(t))\ge K$ for all $t\in\mathbb{R}$. These solutions will have a single close approach to triple collision. The configuration will always be a tight binary with $m_1, m_2$ close and the distance from the binary to $m_3$ diverging as $t\rightarrow\pm\infty$. |
| title | Orbits of the three-body problem with large potential |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2603.08833 |