jock123:
If anything the bullets would travel better and further on the Moon: a vacuum means they wouldn't be impeded by an atmosphere, and under the lower gravity on the moon they wouldn't fall as fast.
Actually, even better, I think that if you fired the bullet at exactly the right speed on an atmosphere-free sphere like the moon, gravity wouldn't bring it down to the ground
at all, and it would keep going round the moon in extremely low orbit indefinitely. I think I'm right in saying that the reason satellites can stay in orbit round the earth without coming back down is only the lack of any air friction in space. (It's not because you sudddenly get free of the earth's gravity when you enter space, which you obviously don't).
I think you have to make the satellites go forward at exactly the right speed, so that the gravitational pull back to earth is exactly balanced by their forward force (which if too fast to be countered by the gravity, would send them off in a straight line into space).
I believe that if you built a continuous vacuum tube all the way round the earth, even at ground level, and fired a bullet (or anything) along it at just the right speed, it would orbit the earth inside the tube forever.
However, I may be wrong, of course. If someone whose knowledge of physics is better than mine (which wouldn't be difficult!) wants to contradict and correct me (or explain it more clearly!), feel free.
I don't think any of this really answers the question of
why they'd take guns to the moon, unless they were planning to conduct orbiting bullet experiments along the lines outlined above. I suppose having one of the Thom[p]sons fire a bullet into the distance, only to have it come round from behind many hours later to hit him or his colleague might have been quite entertaining.
But Jock's probably right that a gun or two simply seemed like an expedition-y thing to take to an unknown place. Unless the guns were for protection in the event of accidentally landing the rocket back down (or being forced down)in a hostile part of earth. Their rocket-building programme had been hindered by armed spies, of course (one of whom had shot Tintin in the head), and the baddies had also tried to steal the unmanned prototype rocket by taking it off course. So maybe Baxter wanted to take no chances.