## 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:** 185 times

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*