Based on your description, the fast-moving objects you observed in the sky could potentially be artificial satellites. Satellites are man-made objects that orbit the Earth and can be visible from the ground under certain conditions. There are numerous satellites in orbit around the Earth, including those used for communication, weather monitoring, scientific research, and more.
When observing satellites, they often appear as bright points of light moving steadily across the sky. The apparent speed and direction of their movement can vary depending on factors such as their altitude, orbit, and your location on Earth. Some satellites may appear to be chasing or overtaking one another if they happen to be in similar orbits but at slightly different speeds.
To confirm whether the objects you observed were indeed satellites, you can consult various satellite tracking websites or smartphone applications that provide real-time information on satellite positions and predictions for your specific location and time. These resources can help you identify known satellites and determine if their trajectories correspond to what you witnessed.