The Neo-Babylonian Empire was a period of Mesopotamian history which began in 626 BC and ended in 539 BC. During the preceding three centuries, Babylonia had been ruled by their fellow Akkadian speakers and northern neighbours, Assyria.
In order for a satellite to successfully orbit the Earth, it must travel a horizontal distance of 8000 meters before falling a vertical distance of 5 meters. A horizontally launched projectile falls a vertical distance of 5 meters in its first second of motion.
People on the ground had been occasionally seeing it for about two weeks at that point. Viewers would make it out as a red glowing object moving in an east-to-west orbit. Most satellites of the time, according to what little material I've been able to find on the black knight satellite, moved from west-to-east.