How about a smooth change in direction? This might be weird enough to be interesting in its own right. In that case picture a satellite in a highly elliptical orbit, where you catch it near apogee, and assuming conditions are such that you can see it (big enough shiny surface/close enough to earth for human eyes, sunlit) then the earth could “outrun” it for a bit while the sat. is at its slowest, and the craft might trace a loop out in the sky, or (presumably) some other curve depending out your relative line of sight, etc.
Edit: trying to remember if there was a more official name for this orbit. Perhaps a Molniya orbit could give the ground based observer a loop?
How about a smooth change in direction? This might be weird enough to be interesting in its own right. In that case picture a satellite in a highly elliptical orbit, where you catch it near apogee, and assuming conditions are such that you can see it (big enough shiny surface/close enough to earth for human eyes, sunlit) then the earth could “outrun” it for a bit while the sat. is at its slowest, and the craft might trace a loop out in the sky, or (presumably) some other curve depending out your relative line of sight, etc.
Edit: trying to remember if there was a more official name for this orbit. Perhaps a Molniya orbit could give the ground based observer a loop?
https://www.google.com/amp/s/www.researchgate.net/figure/A-3...