Zero velocity surfaces are deduced in the restricted three-body problem by using the .Jacobi-inlegral. These .surfaces are the boundaries of the Hill-regions: regions where the motion of the third, massless particle around the two primaries i.s not possible. V. Szebehely generalized this result for the planar elliptic restricted three-body problem. In a recent paper - Mako and Szenkovits (2()(M) presented a generalization of this result for the spatial elliptic restricted throe-body problem, where the existence of an invariant relation was proved -analogous to the .Jacolri integral in the restricted problem. For small eccentricities, this invariant relation can be approximated with zero velocity surfaces, given by implicit equations, delimiting the pulsating Hill-regions. In this paper we present the polynomial representation of these zero velocity surfaces.
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机译：通过使用.Jacobi-inlegral，可以在受限三体问题中推导出零速度曲面。这些表面是Hill区域的边界：在该区域中，第三个无质量粒子无法绕两个基元运动。 V. Szebehehe将该结果推广到平面椭圆约束三体问题。在最近的一篇论文中-Mako和Szenkovits（2（）（M）提出了关于空间椭圆约束苏体问题的该结果的推广，其中证明了不变关系的存在-与约束中的.Jacolri积分相似对于较小的偏心距，可以用隐式方程式给定零脉动希尔区域的零速度表面近似该不变关系，在本文中，我们给出了这些零速度表面的多项式表示。
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