We explicitly worked out the orbital effects induced on the trajectory of a test particle by the the weak-field approximation of the Kerr-de Sitter metric .
It results that the node , the pericentre and the mean anomaly undergo secular precessions proportional to k , which is a measure of the non linearity of the theory .
We used such theoretical predictions and the latest observational determinations of the non-standard precessions of the perihelia of the inner planets of the Solar System to put a bound on k getting k \leq 10 ^ { -29 } m ^ { -2 } .
The node rate of the LAGEOS Earth ’ s satellite yields k \leq 10 ^ { -26 } m ^ { -2 } .
The periastron precession of the double pulsar PSR J0737-3039A/B allows to obtain k \leq 3 \times 10 ^ { -21 } m ^ { -2 } .
Interpreting k as a cosmological constant \Lambda , it turns out that such constraints are weaker than those obtained from the Schwarzschild-de Sitter metric .