Concorde planes would have been able to keep up with sunsets, even at the equator
If you started at a location on Earth where the Sun was setting and travelled westward at the speed Earth turned to the east, then you could remain in a state of constant sunset. In 2014, an ex-NATO pilot, a photographer and a filmmaker attempted to follow the sunset around the globe, through all 24 time zones, as a publicity campaign for a watch. They didn’t quite make it, but their effort provides a look into the science of sunset chasing.
If you wanted to follow the sunrise or sunset, you would need to stay in the same position relative to the Sun as the Earth turns underneath you. To do that at the equator, where the planet is at its maximum circumference around its axis of rotation, you’d have to fly at 1,609 kilometres (1,000 miles) per hour. That’s extremely fast – most commercial planes fly at a cruising speed of 740 to 925 kilometres (460 to 575 miles) per hour, whereas the US Navy’s Blue Angels air display team flies at a maximum speed of 1,126 kilometres (700 miles) per hour during air shows