Abstract We consider an interstellar interloper moving at a relatively large distance from a circular binary star. We use the analytical method of separating rapid and slow subsystems, the rapid subsystem being the binary and the slow subsystem being the interstellar interloper. We show that due to the higher than geometrical symmetry of the problem, in addition to the conservation of the energy and the projection of the angular momentum on the axis of the rotation of the binary, the square of the angular momentum is also conserved. In the course of the time evolution, the vector of the angular momentum rotates about that axis at the constant angle to the axis. After obtaining this general counterintuitive result, we focus at the case where the interstellar interloper is coplanar with the binary. We provide an explicit equation of the motion of the interloper. Then we calculate analytically the angle of deflection of the interloper from the straight line. We analyze the difference in the angle of deflection between this three-body problem and the corresponding two-body problem: we show that this difference remains almost constant (a negative constant) at the range of the eccentricities of the interloper trajectory relatively close to unity and linearly increases (by the absolute value, remaining negative) with the eccentricity as the latter becomes much greater than unity.

中文翻译：

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圆形双星和星际闯入者：解析解

摘要 我们考虑一个星际闯入者在距离圆形双星相对较大的距离处移动。我们使用分离快速子系统和慢速子系统的解析方法，快速子系统为双星，慢速子系统为星际闯入者。我们证明，由于问题的对称性高于几何对称性，除了能量守恒和角动量在二元旋转轴上的投影外，角动量的平方也守恒。在时间演化过程中，角动量矢量围绕该轴以与该轴成恒定角度旋转。在获得这个普遍的违反直觉的结果后，我们关注星际闯入者与双星共面的情况。我们提供了闯入者运动的明确方程。然后我们分析计算闯入者从直线的偏转角。我们分析了这个三体问题和相应的二体问题之间偏转角的差异：我们表明，在相对接近统一的闯入者轨迹的偏心率范围内，这种差异几乎保持不变（负常数）并且随着偏心率线性增加（按绝对值，保持为负），因为偏心率变得远大于 1。