Plane Circular Restricted Three-body Problem In Modified Newtonian Dynamics

As a major competitor of the dark matter theory,the modified Newtonian dynamics contains not only a gravitational constant but also an acceleration constant,which explains a series of problems such as the rotation curve of galaxies delicately.The modified Newtonian dynamics has been widely studied at the galaxy scale,Those results are expected to make precise corrections to the modified Newtonian dynamics theory.Based on the special solutions of the two-body problem and the circular restricted three-body problem of classical Newtonian dynamics,this paper is devoted to the restricted three-body problem in modified Newtonian dynamics.We work out the Lagrangian points and the Hill curves are similar to those in the Newtonian dynamics.Besides,we apply results above to the Earth-Moon system,the Sun-Earth system and the Sun-Jupiter system,aims to check those results numerically.In contrast,the location and number of Lagrangian points,as well as the profile of the Hill region are dependent on both the acceleration constant and the mass ratio of main celestial bodies.Quantitative analysis and interpretation of above difference are given in this paper.These findings open up a new avenue for testing the modified Newtonian dynamics.