To date, there has been a lot of on-orbit satellite fragmentations since a Thor-Able upper stage exploded in space in 1961. Considering that even sub-millimeter-size debris are a big threat to operational satellites, then it can be said that detailed debris modelling is becoming an urgent task for sustainable space development. For accurate modelling, it is essential to know the accurate time of breakup. However, there is no effective method which can estimate the time precisely. Therefore, this study aims at constructing a new method for estimating the time of breakup precisely. This study focuses on orbital plane as a parameter and derives a new equation. This equation constraints orbital planes of fragments at breakup by using orbital elements of the broken-up object. The advantage of this equation is that the fragments can be evaluated by only inclination and right ascension of the ascending node which can guarantee relatively high accuracy even in a long-term propagation. For the estimation, this study proposes a hybrid method which combines the advantages of the constraint equation and the close approach analysis. As a result, by using officially reported data, it was confirmed that this hybrid method can estimate the time of breakup with an error of 1 min or less. It was also suggested that the difference in the estimated time between the hybrid method and the close approach analysis causes a large difference in predicted fragments.
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