Circling around an object movement

[mortal barn]

I'm trying to create a movement system similar to that of Bopl Battle where the player can stick to a platform and circle around, so it can go on the side and upside down and loop around.

In my game there is just one platform and I don't need jumping, the player just needs to be able to circle around it, the platform is a rectangle with rounded edges.

[heavy delta]

you could just put an empty transform in the center of the planet, then put the player as child transform onto that transform (player.transform.parent = thatTransform)

then you can simply rotate the center transform and the character will rotate with it

for a more math based situation you could do this
planetCenterPosition + Quaternion.Euler(0f, 0f, yourDesiredRotationInDegrees) * (Vector3.up * centerToCharacterDistance);

there is a version of this for 2d too but this works for 2d and 3d space
so you take the center and add to it an up vector of a certain distance, and that vector is rotated by your desired rotation