Final answer:
After a collision, if it's inelastic, the pod and the space station move together with the combined mass and a shared center of mass velocity. The final velocity after docking can be calculated using the conservation of momentum. Inertia and momentum conservation also explain how an astronaut could move in microgravity by throwing objects.
Step-by-step explanation:
Understanding the Motion of Pods After Collision with the Space Station
After the collision occurs, the pod's trajectory will follow the motion of the space station. According to the principles of conservation of momentum and energy, the two will move together as a single system. If the collision is elastic, the kinetic energy of the system is conserved, and the velocities of the objects can be swapped or altered but the total kinetic energy and the total momentum stay the same. However, if the collision is inelastic, which seems to be what the problem implies since the satellites are docking, the two objects will stick together, and some kinetic energy may be lost to other forms of energy such as heat or sound.
To estimate the final velocity after docking, you would use the conservation of momentum. The combined mass moves together with the center of mass velocity unchanged by the collision. This remains true in any inertial frame of reference. However, from the frame in which one satellite is at rest, the other satellite approaches with the relative velocity, and vice versa, which explains why the velocities seem different in different frames. For an astronaut motionless at the center of a space station, they can move themselves by using inertia. They could throw an object in one direction, which would propel them in the opposite direction due to the conservation of momentum.
In scenarios where gravitational force is involved, such as the Soyuz payloads, their initial acceleration towards each other can be calculated using Newton's law of universal gravitation. The time for them to drift together and collide can be estimated using kinematic equations based on these initial accelerations and the distance between them.