In orbit, objects are weightless because both the objects and the spacecraft have the same speed and direction, and both are affected by the same gravitational influence. We use the spacecraft as the frame of reference. Because the objects are not in motion relative to the spacecraft, they appear to float.
In Earth orbit, the objects are still affected by Earth’s gravity, but yet they float. Flat-Earthers use it to disprove spaceflight. In reality, the objects float because we are using the spacecraft as the frame of reference, which is also moving by the same amount and is affected by the same gravity as the objects themselves.
If the thrusters of the rocket are activated, the rocket is affected by a force that does not directly affect the astronaut. So, the astronaut will feel being pushed toward the back of the spacecraft by the same amount it is accelerated forward.
On the lunar surface, the astronaut does not float because he is not in orbit. He lacks the speed to go against lunar gravity. The gravity of the Moon pulls him toward the surface just like on Earth, only one-sixth as strong.
- Weightlessness – Wikipedia