Research on space manipulators powered by jet propulsion represents a groundbreaking exploration in space technology. Along-track capture mode, as opposed to head-on mode, offers advantages such as lower relative velocity and reduced thrust demand, making it more suitable for space manipulators in target capture scenarios. Accurately calculating the Time to Go (TGO) is imperative for successful target capture. However, TGO estimation methods commonly employed in head-on capture modes are not directly applicable to along-track capture modes. To address this challenge, distinct TGO estimation methods for capturing non-maneuvering targets in along-track capture mode are proposed in this study. By ingeniously transforming the linear guidance equations, we derive the flight arc length of the manipulator and subsequently obtain an analytical expression for TGO estimation based on the predicted collision point. This estimation method exhibits strong versatility and can be applied to the residual flight time estimation for trajectory planning of general manipulator missions involving spatial object capture. By employing retro proportional navigation (RPN) and its extended variant as guidance frameworks and comparing them with classical methods, the proposed TGO estimation method demonstrates high precision and effectively enhances the success rate of manipulator capture.