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Thank you :) I use Adobe Illustrator. That's a vector graphics editor. But you can also use Inkscape, it's free. Illustrator allows you to work with shapes, in this case with circles. Photoshop is a raster graphics editor. Perfect for photos, but usually not for logos, because you cannot draw a perfect circle, it will always be pixelated. For the animation I used Adobe After effects :)

Upvote because you also mentioned Inkscape. Great tool for those without deep pockets for Adobe products.