I have been doing a physics depth study on the topic of "how gravitational waves affect the phase shift of light (in a vacuum)" and have found it difficult to find a source, at least one I am able to understand, on what factors affect the strength of gravitational waves. I am sure that strength is inversely proportional to the square of the distance, but I am not sure about other factors such as the mass of the spiraling bodies, the velocity at which they orbit each other, and "chirp mass" whatever that is. Also, if anyone could give a quick explanation of what inspiral is/how it works, that would be greatly appreciated.
1 Answer
If your source has a 2nd mass moment described by:
$$I^{ij} = \sum_k {\mu(x_k) x^i_k x^j_k} $$
With $x^i_k$ being the i-th spatial coordinate of the k-th mass $\mu(x_k)$ in orbit around the source with center-of-mass at $x_{CM}$, then this produces (to first order) a gravitational perturbation that looks like:
$$ h^{ij}(t,x) \approx \frac{2G}{rc^4} \frac{d^2}{dt^2}\big[ I^{ij}(t-\frac{r}{c}) \big]$$
With $r$ being the Euclidean distance between your observation coordinate $x$ and $x_{CM}$