Sometimes the ships in orbit at a planet have very large orbits that are well outside the image of the planet.
To see this, load this save. Give whatever answer you want to the alien. Zoom out to see all of the sector, the move to the bottom of the sector to find planet Sika IV.
Zoom in to get close to the planet. You will see it is under siege by a fleet of two ships. It will be captured at the end of the turn, so go to the next turn.
After the planet is captured, look to see if the two ships are in very large orbits around the planet. If they aren't visible, zoom in more in increments until they are. This screenshot shows how far away they are.
You can also download and look at this video, which shows the ships in a large orbit. It also shows a graphic artifact that appears and vanishes in a tile that is two tiles to the lower left of the planet. There was a shipyard there before I destroyed it. The graphic artifact doesn't appear in the game and doesn't seem to cause this problem, so I don't know what it means. Maybe someone at Stardock can figure it out.
Here are two screenshots that show what a ship in a normal orbit looks like.
Continuing with the large orbits, a ship still has moves. Click on the "turn" button to go to it and move it to the right to go into orbit around Sika I. Zoom in to see if it has a normal orbit or a big orbit. In my testing it could be either way.
A shipyard is now idle, so go to it and select to build anything just to get out of the shipyard screen. To the upper right of the shipyard is planet Pertinax I. It has one ship in orbit. Sometimes is has a normal close orbit, and sometimes it has a large orbit. Zoom in as needed to see what kind of orbit it has.
Select the ship below the planet that was just built by the shipyard and move it to go into orbit around Pertinax I and see what kind of orbit they have. The orbit may still be the same or it may have changed to the other type.
There are many other planets that have one or more ships in orbit around them. They may have a normal close orbit or a large orbit. Move the ship or ships one tile away from the planet, then move them back into orbit. They may have normal or large orbits.
NOTE: Tiny ships can be hard to see, no matter what type of orbit they have. I haven't been able to find any consistent reason why the ships have the orbit type they get when moved to a planet. I haven't found any evidence that it affects the game. It just looks odd.
I hope there will be some differences in the way things work with the different types of orbits that can be detected to show why there is a difference so things can be fixed.