In the exploration mission of small bodies orbiting operation is very significant in terms of fuel saving and scientific observation of small bodies. Although the force field around a small body is strongly perturbed, there is a family of stable orbits which is called "Terminator Orbit". While the terminator orbit is stable, it also has disadvantages. The terminator orbit's orbital plane must always face the sun and lack flexibility in orbit design. Moreover, since the orbital plane lies in night side, optical observation of the small body is extremely restricted. Therefore, this study extends the terminator orbit concept to a group of stable orbits which includes the terminator orbit and does not suffer from impact with surface or escaping. This extended terminator is called "Quasi-Stable Terminator Orbit (QSTO)" in this study. This work aims to reveal the solution space and the usability of QSTO. Thus, we succeeded in analytically deriving the existence range of the long-term QSTO and verified that numerical and analytical solutions coincide well. As a result, the calculation time required for solving the existence range of the long-term stable QSTO can be greatly shortened, and it became possible to obtain the range when changing the strength of the small body's gravity and the SRP in accordance with various missions in a short time.