tl;dr

The moon has less gravity compared to Earth, so time ticks by about 58.7 microseconds quicker every day. As more countries and private companies set their sights on future lunar missions, astronomers want to ensure perfect synchrony with a unified clock. Currently, a moon mission runs on the time of the nation that’s operating the spacecraft.

Sounds so weird but makes sense. Lunar time it is!

Moon Time 🌝

Maybe for astronomy, but it seems pointless. If you're shipping a load from Terra to Luna, wouldn't you want all the clocks to be perfectly synchronized? People in the Martian and asteroid colonies aren't going to need to get up at dawn to feed the chickens. One time for the whole solar system. imho