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Gravitationally bound hierarchies containing three or more components arevery common in our Universe. In this paper we study {\em periodic}gravitational wave (GW) form, their polarizations, response function, itsFourier transform, and energy loss rate of a triple system through threedifferent channels of radiation, the scalar, vector and tensor modes, inEinstein-aether theory of gravity. In the weak-field approximations and withthe recently obtained constraints of the theory, we first analyze the energyloss rate of a binary system, and find that the dipole contributions from thescalar and vector modes could be of the order of${\cal{O}}\left(c_{14}\right){\cal{O}}\left(G_Nm/d\right)^2$, where $c_{14} \;(\equiv c_{1} + c_{4})$ is constrained to $c_{14} \lesssim{\cal{O}}\left(10^{-5}\right)$ by current observations, where $c_i$'s are thefour coupling constants of the theory. On the other hand, the "strong-field"effects for a binary system of neutron stars are about six orders lower thanthat of GR. So, in this paper we ignore these "strong-field" effects and firstdevelop the general formulas to the lowest post-Newtonian order, by taking thecoupling of the aether field with matter into account. Within thisapproximation, we find that the scalar breather mode and the scalarlongitudinal mode are all suppressed by a factor of${\cal{O}}\left(c_{14}\right)$ with respect to the transverse-traceless modes($h_{+}$ and $h_{\times}$), while the vectorial modes $(h_{X}$ and $h_{Y}$) aresuppressed by a factor of $c_{13} \lesssim {\cal{O}}\left(10^{-15}\right)$.Applying the general formulas to a triple system with periodic orbits, we findthat the corresponding GW form, response function, and its Fourier transformdepend sensitively on both the configuration of the triple system and theirorientations with respect to the detectors.

Gravitational wave forms, polarizations, response functions and energy losses of triple systems in Einstein-Aether theory