In 1979, The Concorde 001 chased a solar eclipse by flying at 56,000 ft. over the Sahara Desert at a speed of Mach 2. The jet stayed in the umbra of the moon for a record 74 minutes. – WTF Fun Facts
Source: https://www.vice.com/en_us/article/8q8qwk/the-concorde-and-the-longest-solar-eclipse