## Quasi-Periodic Solution of a Spiral Type for Photogravitational Restricted 3-Bodies Problem

**Authors:** Sergey V. Ershkov

Here is presented a new type of exact solutions for photogravitational restricted 3-bodies problem (a case of spiral motion). A key point is that we obtain the appropriate specific case of spiral motions from the Jacobian-type integral of motion for photogravitational restricted 3-bodies problem (when orbit of small 3-rd body is assumed to be like a spiral). Besides, we should especially note that there is a proper restriction to the type of spiral orbital motion of small 3-rd body, which could be possible for choosing as the exact solution of equations for photogravitational restricted 3-bodies problem. The main result, which should be outlined, is that in a case of quasi-planar orbital motion (of the small 3-rd body) the asymptotic expression for component z of motion is proved to be given by the proper elliptical integral.

**Comments:** 12 Pages. Allocation in blue color in the text differs from the published version (see "Conclusion", examples of elliptic integrals)

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### Submission history

[v1] 2012-04-27 16:04:15

[v2] 2014-05-13 19:46:10

[v3] 2014-05-14 06:05:56

[v4] 2015-02-10 00:44:58

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