## 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)

**Download:** **PDF**

### 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

**Unique-IP document downloads:** 142 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.*

*
*