# What parameters descibe a gravitational wave?

What are the parameters of gravitational waves and how does the configuration of the system that creates those waves affect the result?

My current state of missunderstanding is:

• Frequency (due to rotation of two masses areound each other)
• Polarisation (plane, in which the masses rotate around each other)
• Amplitude (mass of objects)
• have you read en.wikipedia.org/wiki/Gravitational_wave ? Commented Nov 30, 2022 at 11:24
• Yes... just before I wrote my question (which contains the link to exactly that wikipedia article) Commented Dec 1, 2022 at 5:57

Edit: For a circular orbit, the observed strain amplitude can be written: $$$$h = -\frac{4G \omega_{\phi}^2 \mu a^2}{rc^4} \left[\frac{(1 + \cos^2 i)}{2} \begin{pmatrix} 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0\\0 & 0 & -1& 0\\0 & 0 & 0 & 0 \end{pmatrix} \cos(2\omega_{\phi} t) + \cos i \begin{pmatrix} 0 & 0 & 0 & 0 \\0 & 0 & 1 & 0\\ 0 & 1 & 0& 0\\0 & 0 & 0 & 0 \end{pmatrix} \sin(2 \omega_{\phi} t) \right],$$$$ where $$\omega_\phi$$ is the orbital angular frequency, $$\mu$$ is the reduced mass - $$m_1m_2/(m_1+m_2)$$, $$a$$ is the semi-major axis (which can be rewritten in tems of $$\omega_\phi$$ and $$(m_1+m_2)$$ using Kepler's third law), $$i$$ is the orbital inclination ($$i=90^{\circ}$$ is "edge-on") and the two matrices correspond to the "plus" and "cross" polarisation resepectively.