Asked by: Sam Gormley, via Twitter
Fundamentally, and ignoring the complications of Einstein’s Special Relativity, it’s the same time as it is here on Earth. But this is a bit of a cheat, of course, because we haven’t defined how we are measuring time.
There are many ways to define the ‘time’ at a particular location. Here on Earth our usual system (‘solar time’) is defined by the motion of the Sun in the sky (although we usually keep track of time with an atomic clock). This means that the local time depends on where you are on Earth and we get around this complication by having many different time zones.
Now, we could also define a similar time system based on the motion of the Sun as seen from the Moon. Such a system exists (Lunar Standard Time) but it is not much more than an interesting exercise in physics.
What is more useful, however, is a definition of time that doesn’t vary with location. This is called Universal Time (UT) and is a modern form of Greenwich Mean Time. It is the same everywhere in the Universe. So, the UT time on the Moon is the same as the UT time on Earth.