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Planet levels and day/night cycles

Good day/evening/night/morning.

I’d like your opinion on the possibility of implementing a planetary time of day system. That is, Where it is 12 noon at one position, if the player was to walk to the direct opposite side of the planet, it’d be dead night. 12 midnight. The player would be traversing times of day by walking around this small planet. The position of relative noon could change as a direct result of the system time, so that if the system time was 12 noon the relative ‘noon’ would be at the tip of the planet. At system time 12 midnight, the relative ‘noon’ would take place at the opposite end of the planet.

I know that this is theoretically achieved by incorporating a day/night skysphere on a planet level (and indeed the bottom of the planet is almost completely unlit) however at this point it’d be nice to have the skysphere at night. Here it is at the moment if you walk to the underside of the planet, with a day/night cycle implemented.

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Now, hopefully, if this makes sense, I was wondering what the best way to go about implementing this system would be. Would it just be a matter of implementing a standard day/night system and then some clever manipulation of the skysphere?

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How about you you rotate youre light (directional sunlight) with the skysphere round youre planet. one rotation 360 degrees= one day.

This does allow the sunlight to move, however the sky colour is unchanged. Perhaps the brightness of the skysphere could change with the player character’s up vector? Not sure if that makes sense.