## Triangle Exact Solution of 3-Bodies Problem

**Authors:** Sergey V. Ershkov

Here is presented a system of equations of 3-bodies problem in well-known
Lagrange's form (describing a relative motions of 3-bodies). Analyzing of such a system,
we obtain an exact solution in special case of constant ratios of relative distances
between the bodies.
Above simplifying assumption reduces all equations of initial system to a proper
similar form, which leads us to a final solution: initial triangle of bodies
m_{1} , m_{2}, m_{3} is
moving as entire construction, simultaneously rotating over the common center of
masses as well as increasing or decreasing of it's size proportionally.

**Comments:** 9 pages.

**Download:** **PDF**

### Submission history

[v1] 30 Aug 2011

[v2] 10 Sep 2011

[v3] 13 Sep 2011

**Unique-IP document downloads:** 189 times

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