NASA is embarking on an unprecedented mission to rescue the Neil Gehrels Swift Observatory, which has been operational since 2004 and is currently experiencing orbital decay due to atmospheric drag. A private spacecraft named Link, developed by Katalyst Space Technologies, is scheduled to launch next month with the goal of boosting Swift's altitude. This mission is significant as it marks the first attempt by a private spacecraft to capture a U.S. government satellite. Swift's future is uncertain, as atmospheric conditions vary with solar activity, which can affect its orbital position. NASA's modeling team is continuously updating predictions based on various factors, including solar weather and tracking data from the U.S. Space Force. Currently, Swift is expected to maintain a critical altitude of at least 185 miles (300 kilometers) above Earth into early fall 2025, providing a favorable window for Link's mission. The project has garnered considerable interest within the flight dynamics community, highlighting the collaborative effort to refine orbital predictions and ensure the success of this innovative rescue operation.