In the exploration of small bodies, the orbiting operation is very significant in terms of fuel consumption and scientific observation of small bodies. Although the force field around a small body is strongly perturbed, there is a family of stable orbits, called terminator orbits, that exist. However, although a terminator orbit is stable, it also has disadvantages. The orbital plane of a terminator orbit must always face the Sun and lacks flexibility in orbit design. Moreover, since the orbital plane lies in the night side because of the solar radiation pressure (SRP) shifting the equilibrium point, optical observation of the small body is extremely restricted. Therefore, the present study focuses on the perturbed terminator orbit, i.e., the quasi-terminator orbit (QTO), which is a stable orbit that does not suffer from impact with the surface or escape. The present study attempts to reveal the solution space and the usability of the QTO. We succeeded in analytically deriving the existence range of the long-term QTO and verified that the numerical and analytical solutions coincide well. As a result, the calculation time required for solving the existence range of the long-term stable QTO can be greatly shortened, and it becomes possible to quickly apply our findings to other missions by accounting for the gravity field and SRP of the mission-specific small body.
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