The arrival times of gravitational waves and optical light from orbiting binaries provide a mechanism to understand the propagation speed of gravity when compared to that of light or electromagnetic radiation .
This is achieved with a measurement of any offset between optically derived orbital phase related to that derived from gravitational wave data , at a specified location of one binary component with respect to the other .
Using a sample of close white dwarf binaries ( CWDBs ) detectable with the Laser Interferometer Space Antenna ( LISA ) and optical light curve data related to binary eclipses from meter-class telescopes for the same sample , we determine the accuracy to which orbital phase differences can be extracted .
We consider an application of these measurements involving a variation to the speed of gravity , when compared to the speed of light , due to a massive graviton .
For a subsample of \sim 400 CWDBs with high signal-to-noise gravitational wave and optical data with magnitudes brighter than 25 , the combined upper limit on the graviton mass is at the level of \sim 6 \times 10 ^ { -24 } eV .
This limit is two orders of magnitude better than the present limit derived by Yukawa-correction arguments related to the Newtonian potential and applied to the Solar-system .