Hayabusa2’s deployable camera (DCAM3) was deployed from the spacecraft near the asteroid Ryugu to successfully monitor the artificial cratering experiment. Scientific analyses of the observed impact ejecta require accurate determination of the camera’s position and orientation. However, in contrast to conventional spacecraft operations, DCAM3 lacked the capability to acquire orbit tracking data and attitude sensor data due to its limited onboard resources. Even though the optical images obtained by DCAM3 itself are the only source of geometric information, they were subject to significant distortion caused by the rolling shutter effect and lens distortion. This research is, therefore, designed to simultaneously estimate the image distortion and the orbital and attitude motions of DCAM3, relying solely on its image data. The relative geometry between the camera and the asteroid is reconstructed from the geographic information of the observed feature points by incorporating distortion effects. The proposed method involves segmenting the geometry reconstruction, with more than ten thousand feature measurements, into smaller-scale least-squares problems. The image-based estimation yields consistent distortion, orbit, and attitude solutions with pixel-scale accuracy. The analysis results indicate that DCAM3 experienced significant nutation of its optical axis during ballistic flight in a semi-elliptical orbit. In addition, these motions were sensitive enough to simultaneously determine system parameters, such as the gravitational parameter of Ryugu and the inertia moment of DCAM3. This paper illustrates the potential of deployable camera systems as a promising option for enhancing the scientific and engineering aspects of asteroid exploration.