We derive the equations of motion , the periastron shift , and the gravitational radiation damping for quasicircular compact binaries in a massive variant of the Brans-Dicke theory of gravity .
We also study the Shapiro time delay and the Nordtvedt effect in this theory .
By comparing with recent observational data , we put bounds on the two parameters of the theory : the Brans-Dicke coupling parameter \omega _ { BD } and the scalar mass m _ { s } .
We find that the most stringent bounds come from Cassini measurements of the Shapiro time delay in the Solar System , that yield a lower bound \omega _ { BD } > 40000 for scalar masses m _ { s } < 2.5 \times 10 ^ { -20 } \mathrm { eV } ( or Compton wavelengths \lambda _ { s } = h / ( m _ { s } c ) > 5 \times 10 ^ { 10 } km ) , to 95 % confidence .
In comparison , observations of the Nordtvedt effect using Lunar Laser Ranging ( LLR ) experiments yield \omega _ { BD } > 1000 for m _ { s } < 2.5 \times 10 ^ { -20 } \mathrm { eV } .
Observations of the orbital period derivative of the quasicircular white dwarf-neutron star binary PSR J1012+5307 yield \omega _ { BD } > 1250 for m _ { s } < 10 ^ { -20 } \mathrm { eV } ( \lambda _ { s } > 1.2 \times 10 ^ { 11 } km ) .
A first estimate suggests that bounds comparable to the Shapiro time delay may come from observations of radiation damping in the eccentric white dwarf-neutron star binary PSR J1141-6545 , but a quantitative prediction requires the extension of our work to eccentric orbits .