Mikolaj Kruzynski, Polish Space Agency; Zygmunt Anio?, Polish Space Agency; Krzysztof Armiski, Polish Space Agency; Dorota Mieczkowska, Polish Space Agency; Marcin Teofilewicz, Polish Space Agency; Edwin Wnuk, Polish Space Agency; Tomasz Zubowicz, Polish Space Agency; Justyna Golebiewska, Astronomical Observatory Institute, Faculty of Physics, A.Mickiewicz University; Monika K. Kaminska, Astronomical Observatory Institute, Faculty of Physics, A.Mickiewicz University; Julia Pietrzak, Astronomical Observatory Institute, Faculty of Physics, A. Mickiewicz University; Marek Poleski, Faculty of Power and Aeronautical Engineering, Warsaw University of Technology
Keywords: re-entry, ballistic coefficient, orbit propagation, atmosphere drag
Abstract:
The number of satellites orbiting the Earth is still increasing. We are also observing growing number of decaying objects. There are dozens of decays every year and almost 30,000 objects have entered the atmosphere since the beginning of the space era. Most of that objects will burn up during re-entry, but not all of them – Objects of large size and mass can survive entering the atmosphere. With that in mind, a satellite object falling to the ground may pose a threat to both people and infrastructure. Therefore, monitoring and predicting the moment of decay is important to reduce dangers for population and property on the ground.
This, however, is a challenging task. This is mainly due to fact that one needs to account for various phenomena acting on decaying object. This leads to structurally complex algorithms built upon advanced models of perturbing forces. Moreover, the inherent property of the problem is that the propagation of the satellite motion for such low orbits is subject to elevated levels of uncertainty. One of the biggest sources of the uncertainty of the predicted moment of decay is atmospheric drag, which influence grows as the altitude decreases.
Modelling the drag (perturbing) force is difficult due to two main reasons. First, a reliable forecast of the dynamic state of the atmosphere is required. This is a difficult task due to spatial distribution of the model and limited number of measurements. Second, an exact characteristic of a physical properties of the object entering the atmosphere is needed. This, however, may change due to the interaction of object and atmosphere during decay and there is no technologically feasible manner to directly observe or measure the phenomenon. The factor which are of most interest to the problem include object mass, cross-sectional area, drag coefficient depending on the shape and material of which the satellite is made make up the value of the ballistic coefficient (BC). Unfortunately, in the latter case, the value is difficult to estimate, and the estimate is prone to aggregate the uncertainty resulting also from other sources or factors.
In practice, the problem of BC estimation is handled in various manner. Some typically used methods include:
an approach based on the previously known physical characteristics of a decaying object. Known size and weight limit the range of BC values. However, such an approach may cause too much uncertainty in the case of objects with an irregular shape and a large span of individual dimensions. In addition, it is impossible to apply to objects whose dimensions are unknown a priori, e.g. objects resulting from fragmentation;
the use of data contained in the orbital catalog space-track.org. In the orbital catalog saved in the TLE format, the coefficient B* is included. After making appropriate calculations, it is possible to estimate the BC;
method based on the historical orbital elements of the object. Using proprietary in-house software, the average BC was determined and the prediction of the decay moment of selected objects was performed;
an approach to determine the parameter during the orbit determination process by including this parameter in the state vector. We used the least squares (LSQ) and Kalman filter (KF) techniques in our calculations. This approach allows for determining the instantaneous BC, but it can be used only when we have a sufficiently large number of observations.
Each of these approaches has its limitations. In this work, the applicability of individual approaches and the results obtained in each of them were verified. The analysis was carried out for objects that have re-entered the atmosphere in recent years and compared. As a result, information was obtained on the impact of the atmospheric models used and the effectiveness of individual BC estimation methods on the quality of prediction of the moment of re-entry.
Date of Conference: September 19-22, 2023
Track: Atmospherics/Space Weather