How earlier LSST would have discovered currently known long-period and hyperbolic comets?

Comets originating from the Oort Cloud are a rare and elusive group within our solar system, making them difficult to detect. However, these comets are some of the most pristine objects we can observe, offering vital insights into the formation of planetary systems, and thus, they are the subject of extensive scientific research and missions.The Legacy Survey of Space and Time (LSST), set to begin operations at the Vera C. Rubin Observatory in 2025, is anticipated to significantly enhance our ability to detect these comets. By regularly monitoring the Southern sky to a depth of magnitude 24 with high precision, the LSST will greatly improve our comet detection capabilities. However, predicting the future detection rates of the LSST is challenging due to our limited understanding of the underlying comet population. Previous identifications have been made by various surveys or individual observers, each with unknown selection biases.In this talk, we will explore an alternative method to estimate the LSST's performance by analyzing how early known comets on long-period or hyperbolic orbits would have been discovered if an LSST-like survey had been operational ten years prior to their perihelion. This approach cannot be used to make quantitative predictions for future incoming objects, but it still shows that LSST can potentially increase the discovery rate of long-period and hyperbolic comets by at least five times. We will present our findings, discuss the limitations of the method, and share the insights gained from this exercise.