The fourth gravity test and quintessence matter field

After the previous work on gravitational frequency shift, light deflection (Eur. Phys. J. C 59: 107–116, 2009) and perihelion advance (Eur. Phys. J. C 60: 175–179, 2009), we calculate carefully the fourth gravity test, i.e. radar echo delay in a central gravity field surrounded by static free quintessence matter, in this paper. Through the Lagrangian method, we find the influence of the quintessence matter on the time delay of null particle is presence by means of an additional integral term. When the quintessence field vanishes, it reduces to the usual Schwarzschild case naturally. Meanwhile, we also use the data of the Viking lander from the Mars and Cassini spacecraft to Saturn to constrain the quintessence field. For the Viking case, the field parameter α is under the order of 10−9. However, α is under 10−18 for the Cassini case.