The paper considers non-spherical objects with low gravitational attraction, such as asteroids, satellites of the planet and comets. We considered possibility of a mission to small bodies of the solar system of irregular shape on the example of the asteroid Apophis. The authors of the article suggest using a nanoclass spacecraft with an electric rocket propulsion system for a long mission to study Apophis. The purpose of this work is to determine the necessary costs of the working body for all stages of the mission, which includes reaching the asteroid, forming and maintaining a given orbit relative to it. The gravity of the Earth, Sun, and asteroid is taken into account when modeling the controlled movement of the spacecraft. When a spacecraft is moving relative to an asteroid, its gravitational field is described as a superposition of the gravitational fields of two rotating massive points. In this paper, it is proposed to divide the mission into two sections for preliminary ballistic design. The first optimal speed heliocentric flight Earth-asteroid Apophis with the alignment of the speed of the spacecraft and the asteroid. The second is the movement in the vicinity of the asteroid, which includes the optimal speed maneuver for forming the working orbit and maintaining the working orbit for a given time.

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This work aims to simulate the flight of a spacecraft with an electric propulsion system to the near-Earth asteroid 2011ES4. A control law was formed that ensures the minimum fuel consumption when the engine is running without shutdowns. The simulation of the flight of the spacecraft to the point of the asteroid’s orbit closest to the Earth is carried out. An additional study was also carried out, which simulates the flight of a spacecraft with a liquid-propellant engine. A comparison of the flight simulation results using two different propulsion systems was made. A comparison of the mass flow rate, the relative velocity between the spacecraft and the asteroid, and the flight times using these propulsion systems is made.

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