Abstract— <p>The paper proposes an approach to constructing orbits in the vicinity of a Sun–Earth libration point, which ensures the approach of a spacecraft to asteroids flying nearby. The use of halo orbits near collinear L₁ and L₂ libration points, which are located at a distance of one and a half million kilometers from Earth, for the purpose of studying asteroids has three important advantages compared to previously implemented missions. Firstly, the trajectories of potentially hazardous asteroids approaching the Earth may pass by these libration points. Obtaining new scientific information about celestial bodies of this type is the most preferable in the context of the problem of asteroid–comet hazard. Secondly, the asteroid’s approach to both Earth and the spacecraft occurs at close moments in time, which could ensure the latter’s flight at a minimal distance from the surface of the celestial body and lead to the acquisition of fundamentally new data about the object of study. Thirdly, after approaching the asteroid, the spacecraft continues to operate near the libration point and can be used to solve other scientific problems. Using the example of the flight to the asteroids Apophis, 2001 WN₅ and 1997 XF₁₁, the results of calculations of such orbits for spacecraft that are already operating near the L₂ Sun–Earth libration point are presented (James Webb Space Telescope, Euclid and Spectrum-Roentgen-Gamma). The values of the characteristic velocity required to perform a maneuver of this type demonstrate the potential of the proposed concept.</p>