Abstract
The motion of three bodies can be solved perturbatively when a tightly bound inner binary is orbited by a distant perturber, giving rise for example to the well-known Kozai-Lidov oscillations. We propose to study the relativistic hierarchical three-body orbits by adapting the Effective Field Theory techniques used in the two-body problem. This allows us to conveniently treat the inner binary as an effective point-particle, thus reducing the complexity of the three-body problem to a simpler spinning two-body motion. We present in details the mapping between the inner binary osculating elements and the resulting spin of the effective point-particle. Our study builds towards a derivation of three-body analytic waveforms.
Highlights
A triple system in nature often comes in hierarchical configurations [1]
We elaborate on the relation between the spin kinetic term and the Lagrange planetary equations in Appendix A, while in Appendix B, we provide details about the specific spin supplementary condition used in this article
The nonrelativistic general relativity (NRGR) approach to the two-body problem was designed to deal with extended compact objects
Summary
A triple system in nature often comes in hierarchical configurations [1]. In this kind of setting, a close (or “inner”) binary m1 − m2 is orbited by a distant perturber m3 (the “outer” object). We will obtain the action of a composite particle, whose spin is the orbital angular momentum of the inner binary, coupled to an external gravitational field. (iv) we will integrate out the remaining pointparticle orbital modes with frequencies ω > V=a3, doing an average over the period of the outer orbit In this way, we will get to a Lagrangian representing the dynamics of the three-body system as an interaction between the composite particle representing the inner binary and the outer body. (xiii) E 1⁄4 m − GNmμ=ð2aÞ: Total (mass and Newtonian) energy of the inner binary
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