NASA has been asked to create a time zone for the moon. Here's how it would work
Briefly

The new lunar time zone, Coordinated Lunar Time (LTC), is all about ensuring the success of future, multinational missions to the moon, said Michelle Hanlon, the executive director of the Center for Air and Space Law at the University of Mississippi.
The creation of a lunar time zone would require international agreements, similar to how UTC zones are set on Earth using a weighted average measurement of atomic clocks.
Due to the moon's lower gravity and motion relative to Earth, moon time passes 56 microseconds faster each earth day. An ensemble of clocks deployed to the moon might be used to set the new time standard.
Hanlon emphasized the importance of establishing a unified approach to space travel through the LTC for international collaboration amongst the 36 nations involved in the Artemis partners mission to the moon.
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