In this paper we use \Delta P = -1.772341 \pm 13.153788 s between the phenomenologically determined orbital period P _ { b } of the PSR J0737-3039A/BÂ Â double pulsar system and the purely Keplerian period P ^ { ( 0 ) } = 2 \pi \sqrt { a ^ { 3 } / G ( m _ { A } + m _ { B } ) } calculated with the system ’ s parameters , determined independently of the third Kepler law itself , in order to put constraints on some models of modified gravity ( f ( R ) , Yukawa-like fifth force , MOND ) .
The major source of error affecting \Delta P is not the one in the phenomenologically measured period ( \delta P _ { b } = 4 \times 10 ^ { -6 } s ) , but the systematic uncertainty \delta P ^ { ( 0 ) } in the computed Keplerian one due to the relative semimajor axis a mainly caused , in turn , by the errors in the ratio \mathcal { R } of the pulsars ’ masses and in \sin i .
We get | \kappa| \leq 0.8 \times 10 ^ { -26 } m ^ { -2 } for the parameter that in the f ( R ) framework is a measure of the non linearity of the theory , | \alpha| \leq 5.5 \times 10 ^ { -4 } for the fifth-force strength parameter ( for \lambda \approx a = 0.006 AU ) .
The effects predicted by the strong-acceleration regime of MOND are far too small to be constrained with some effectiveness today and in the future as well .
In view of the continuous timing of such an important system , it might happen that in the near future it will be possible to obtain somewhat tighter constraints .