Legal jurisdiction on the moon

If a murder was committed on the surface of the moon, whose law would it fall under?

Probably the country that sent the astronauts to the moon.

A more interesting question would be what happens if there’s a murder on the international space station thingy. I’d assume the major players have some sort of treaty about such things…

I imagine it’d be the same as if there were a murder at the South Pole. There’s no internationally recognised sovereignty there, but there is a scientific base with personnel from a number of countries.

So would it be under the jurisdiction of the murderer or the victim’s country?

It seems that it would depend. From here, the US Marshals have the authority to enforce US law on US citizens in Antarctica.

Also, here is the UN Office for Outer Space Affairs. There’s a lot to wade through, but they do have a law section. As far as the ISS goes, basically it says that whoever launched the object retains jurisdiction. Each section of the ISS is owned by one of the member countries and their own law applies in their part of the station.