Abstract: The forecasting and the location of long-lifetime orbits in close proximity of small celestial bodies are important concerns of orbital design for the near-small-body stage due to the weak gravity and considerable uncertainty of the physical characteristics and orbital dynamics.For the complex dynamical environment near irregular small celestial bodies，gravitational perturbations of J2，J3，J4 terms，solar radiation pressure（SRP）and eclipses are taken into account.A semi-analytical approach that can rapidly determine the type and existence region（range of initial orbital elements）of long-lifetime natural orbits around asteroids is developed based on averaged dynamics.An analysis is also conducted to assess the impact of factors，such as SRP，eclipses，and variations of the asteroid-probe system parameters，on the existence regions of these orbits.During the search for natural orbits around the potentially hazardous asteroid 99942 Apophis，two families of long-lifetime orbits are discovered.The first family consists of heliotropic orbits，which have a smaller existence region and are more sensitive to parameter uncertainties.The second family comprises terminator orbits，which exhibit a larger range of semi-major axes and demonstrate greater stability.The research indicates that SRP has a significant impact on the existence of long-lifetime orbits around irregular small celestial bodies.When considering the effects of SRP，the existence regions of these orbits are notably reduced.As the SRP strength becomes stronger，the heliotropic orbits tend to have higher eccentricities，while the terminator orbits have lower eccentricities，and the range of semi-major axes becomes smaller for both orbit families.

Key words: asteroid, irregular gravitational perturbations, solar radiation pressure, eclipse, frozen orbits