Edit: I tried using strokes of a circle and unionizing it with a curved line, repeating and then masking the overlapping part to create the overlap effect. I'm trying to achieve the look of the overlapping paths from earth around the various celestial beings such as the moon.
This visual effect is not as complex as it can be looking at the first glance :)
As @confused suggested you have to use some kind of Blend tool, for example, in Adobe Illustrator:
- Create 2 circles.
- Split them with Scissors tool and remove the bottom parts.
- Draw 2 curved lines underneath to simulate that curvy tail effect from your reference.
- Apply the Blend tool to both pairs of lines - circles and curved lines.
- Adjust or crop lines if needed to prevent overlapping lines.
- Change colors of lines as you want.
I've created a short screencast to demonstrate the process in action. You can watch it here:
Hope this help you :)