There are lots of information about this topic, but I'm still greatly confused about something:
Astronauts in the ISS are in free fall all the time because they have only gravity acting on them, but when it comes to their floating motion I just cannot grasp the concept. How can a body be floating seems counter-intuitive to me.
I "concluded" from researching various texts around the Internet: because an astronaut is falling at the same rate with the ISS, it will remain stationary; likewise, if an astronaut jumped a meter in the ISS, his new "surface" will be that one meter above, so he will remain at that point, float in a way.
What I still do not yet understand are two things: Why did the astronaut really float? I mean is my conclusion correct, or am I utterly misguided? I drew my conclusion from the classic elevator example; if the cable of the elevator were to broke, you'd just float. This makes sense, because it's not the person's motion that causes the floating. But in the ISS, people can push themselves in a direction and move. What caused that direction? Did the astronaut push themselves from a place? Please explain this in a simple way from Newton's Laws.
My second question is that if the astronaut were in a spaceship orbiting the Earth, but that he would never hit the spaceship's parts from inside, and pushed himself in a direction, would he continue forever in that direction-we are assuming there are no obstacles. If so, as I learnt from the Newton's 2nd Law, there must be no forces acting on him. But there is gravity.
I read in places that this might be the centrifugal force, and if it is, would make much sense. But I wanna know why it is the case by the definition, "Because they are accelerating at the same rate."