I am writing a book and need information. If two people were on a place where gravity is half Earth's, I know they'd weigh half as much as normal. My question is this: would their punches still hold the strength of a punch on Earth? Would punching one another send them double the distance? And how would falling long distances work? Would the damage from hat be halved?
1) The punch should be equally strong in both environments, so the person in the lower gravity place will fly further. Only problem would be the lower gravity affecting the stance of the puncher. Lower gravity means lower friction between the ground and the puncher's feet. Imagine punching someone on an ice rink to see why this might be a problem.
2) Yes, falling will hurt half as much given half the gravity.
A horizontal punch has a certain force traveling in a direction perpendicular to the gravitational force. The resultant force vector is the addition of the horizontal force and the vertical force of gravity. If the vertical force is less, the resultant vector is angled less, and is thus stronger in the horizontal direction.
Depends on how long they had been there, and how long the trip was. On a planet with half the gravity, depending on atmospheric pressure (marginally), this person who just arrived would be near superhuman until their excess muscle eventually atrophied away.
As far as punches go, if you've had martial arts training, you'd do better in a lower G environment than most other combat disciplines This is only due to the fact that most martial arts teach you to be very grounded while attacking. Kind of like visualizing yourself as a thorn sticking out of the ground at an angle. Anything that the tip of your attack touches will be applying force directly to the ground you are standing on.
Now grappling, that'd be interesting. you'd need to come up with something that doesn't rely on an opponent's weight to bring them down. Take down maneuvers won't mean much at all since leverage is often applied through the use of your weight and the opponent's weight.
I'd imagine joint locks and grasping maneuvers would play a much better role.
Any punch that doesn't pin the opponent via a blocking force or a grasping hold will have less damage occur. The opponent's body will tend to bounce away, which removes some of the energy of the impact in a way you do not want. Instead pinning them to the ground to punch or grabbing their clothing and punching them will markedly improve performance for damaging results. It is the different between punching a free standing balloon and punching one pinned to a wall.
The physics, yes, but the stance, no. It completely depends on the type of kick. Some come down, some come up, and some strike straight out. Some yes and some no. With a punch you almost always have 2 contacts with the ground. With kicks you almost always only have 1 contact with the ground. With either, if you grasp your opponent, the contacts with the ground increase, usually adding 2 more contacts. The more contacts you have with the ground the more force you can apply and the greater the damage. It means the opponent and you are not going to bounce away from each other as much.