Past exam of the mathematics course of the University of Cambridge / 2023 / ii / Paper 4 / 37B / b

Use the total massWith the stated last-orbit estimate,The Kepler third law then givesA binary's dominant quadrupole radiation has two cycles per orbit, so the last-orbit frequency of a compact binary isOnly one significant figure is meaningful under the approximations.

A suitable Spatially flat FLRW metric isBoth source and detector are comoving, so cosmological redshift stretches the wave period in proportion to the scale factor. If $f_e$ is the local source frequency at emission and $f_o$ is the frequency measured in Earth's local frame, thenThe same relation applies to gravitational waves propagating on the FLRW background in the geometric-optics regime.