Some future space missions measure distances of laser links and angles with unprecedented precision, allowing us to test theories of gravity up to the two-post-Newtonian （2PN） order. Besides, investigation of an intermediate-range force has been of considerable interests in gravitational experiments. Inspired by these ideas, within the framework of the scalar-tensor theory with an intermediate- range force, its 2PN approximation is obtained with Chandrasekhar＇s approach. It includes the 2PN metric and equations of motion for general matter without specific equation of state. The conserved quantities to the 2PN order are isolated with the aid of the energy-momentum complex. We also discuss the prospect of testing and distinguishing the intermediate-range force with the orbital motions of celestial bodies and spaeecrafts.
As an extension of the＂teleparallel＂equivalent of general relativity,f（T）gravity is proposed to explain some puzzling cosmological behaviors,such as accelerating expansion of the Universe.Given the fact that modified gravity also has impacts on the Solar System,we might test it during future interplanetary missions with ultrastable clocks.In this work,we investigate the effects of f（T）gravity on the dynamics of the clock and its time transfer link.Under these influences,theΛ-term and theα-term of f（T）gravity play important roles.Here,Λis the cosmological constant andαrepresents a model parameter in f（T）gravity that determines the divergence from teleparallel gravity at the first order approximation.We find that the signal of f（T）gravity in the time transfer is much more difficult to detect with the current state of development for clocks than those effects on dynamics of an interplanetary spacecraft with a bounded orbit with parameters 0.5 au≤a≤5.5 au and 0≤e≤0.1.
Searching for an intermediate-range force has been considerable interests in gravity experiments. In this paper, aiming at a scalartensor theory with an intermediate-range force, we have derived the metric and equations of motion （EOMs） in the first post- Newtonian （1PN） approximation for general matter without specific equation of state and N point masses firstly. Subsequently, the secular periastron precession ω of binary pulsars in harmonic coordinates is given. After that, ω of four binary pulsars data （PSR B1913＋16, PSR B1534＋12, PSR J0737-3039 and PSR B2127＋11C） have been used to constrain the intermediate-range force, namely, the parameters G and λ. α and λ respectively represent the strength of the intermediate-range force coupling and its length scale. The limits from four binary pulsars data are respectively A = （4.95 ±0.02）× 10^8 m and a = （2.30±0.01）× 10^8 if β = 1, where fl is a parameter like standard parametrized post-Newtonian parameter βPPN. When three degrees of freedom （α, λ and β = β - 1 ） in lσ confidence level are considered, it yields α = （4.21 ±0.01）× 10^4, λ= （4.51 ±0.01）× 10^7 m and β = （-3.30 ±0.01）× 10^-3. Through our research on the scalar-tensor theory with the intermediate-range force, it shows that the parameter α is directly related to the parameter γ （α = （1 - γ）/（1 ＋ γ））. Thus, this presents the constraints on 1 - γ by binary pulsars which is about 10^-4 for three degrees of freedom.
