Circular binary star and an interstellar interloper: The analytical solution.

• An analytical solution for the motion of an interstellar interloper around a circular binary • This physical systems has a higher than geometrical symmetry • In the general case, the angular momentum of the interloper rotates around the binary's axis • Explicit equation of the motion for an interloper coplanar with the binary • Correction of the angle of deflection of the interloper due to the 3-body nature of the system 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. [ABSTRACT FROM AUTHOR]