In a manner different from the two-way satellite time and frequency transfer (TWSTFT) via geostationary satellites which has been employed for subnanosecond time transfer between widely separated earth stations, TWSTFT via non-geostationary satellites has a problem attaining subnanosecond accuracy because of satellite motion. The impact of satellite motion on the accuracy of TWSTFT via non-geostationary satellites is wholly attributed to the non-reciprocal geometric path. We have analysed the non-reciprocal geometric path caused by satellite motion in order to evaluate the accuracy of TWSTFT via non-geostationary satellites. Our analysis shows that the non-reciprocal geometric path introduces significant error to the accuracy of subnanosecond time transfer. Using a numerical model, we have demonstrated that ordinary orbit estimation can correct the non-reciprocal geometric path in TWSTFT via non-geostationary satellites to subnanosecond accuracy. Residuals of the non-reciprocal geometric path correction with respect to the orbit estimation accuracy and baseline length are presented. As an example of a non-geostationary satellite orbit, we employed an orbit of a quasi-zenith satellite orbiting the Earth in a period of one day, in synchronization with the Earth's rotation and with an orbital inclination of 45°.