Hey folks. I am running an arctic exploration campaign. In the game, it is currently summer and the players are subject to Midnight Sun. The sun isn't going to go down for a several weeks, just dip close to the horizon a little. I made it clear to the players at the start that this affects any item that mentions regaining charges at "dawn".

It seems like in the description for the Orb of Time it relays the relative position of the sun to the players, kind of like the clock in Minecraft. So would it just constantly tell them it's morning until the solstice, and then that it's afternoon?

The sun isn't actually mentioned in the description of the Orb of Time, so I think that it would function normally.  The sun does still move around in the sky in the arctic so you would still be able to roughly keep track of the passage of time based on the sun's position.  If "nighttime" is reported, then that would correspond with a certain portion of the "day".  At least that's how I'm interpreting this -- I think that some other interpretations are also reasonable.