Studying a direct re-entry from a Sun-Earth Libration Point Orbit: can ground uncertainty be kept under control?

In recent years, there has been an increasing attention to Libration Points Orbits (LPOs) in the Sun-Earth and Earth- Moon systems, because they represent a fundamental resource to obtain astrophysical and planetary observations. Even for this kind of missions an awareness of the end-of-life opportunities is crucial. In the present work, we keep on investigating the opportunity of an Earth's atmospheric re-entry. In the past, we have investigated this possibility in terms of trajectory design and ground casualty risk for three specific missions (SOHO, Herschel and Gaia). We showed that low-cost solutions can exist in terms of Dv-budget, according to the size of LPO, that the steep re-entry and the shorter period in the atmosphere cause the debris field to be significantly shorter in length and closer to the point of breakup than those associated with circular re-entries, and that, as in the case of circular re-entries, it is not possible to provide globally applicable recommendations in terms of demise. In this work, we aim at addressing the aspect related to the orbit determination and maneuver uncertainty to constrain the impact location. The sensitivity study performed in the past showed that the longitude of impact is linearly dependent to the time of flight, while the latitude depends on the inclination corresponding to the LPO and the osculating argument of pericenter at the entry into the atmosphere. After a review on the tracking procedures, we show how the Semi-Linear Method, usually applied in the context of asteroid dynamics and impact monitoring, could be used to study the ground uncertainty in the re-entry of LPO spacecraft. Moreover, we will simulate observations corresponding to a direct LPO re-entry in order to understand how the orbit determination campaign shall be conducted to bound the ground uncertainty.