# Gravitational waveforms for eccentric Lagrange triangles

## Abstract

Gravitational waves allow us to probe systems such as neutron star and black hole mergers either in addition to, or in lieu of more established methods of astronomy. Extensive study has been done in the case of binary mergers, culminating in the detection of gravitational waves in 2015. This body of work can be extended to include cases where there are three bodies in a periodic orbit. The Lagrange equilateral triangle orbit is of particular interest, since the trajectories can be found analytically. Previous work has looked at the circular case of the Lagrange triangle, where all three masses follow a circular orbit about the center of mass, and found that the waveforms look very similar to those coming from binary sources with similar orbital parameters. We extend the work to include eccentric Lagrange Triangles, where each of the masses follow ellipses with the same eccentricity, but oriented in different directions with different sizes. We find that in eccentric orbits, the shape of the gravitational waveforms remain similar to their binary counterparts.

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*Proceedings of the Samahang Pisika ng Pilipinas*

**42**, SPP-2024-PB-11 (2024). URL: https://proceedings.spp-online.org/article/view/SPP-2024-PB-11.