If something is thrown out of a spaceship that is traveling at near light speeds, several things would occur depending on the perspective of different observers and the properties of the object being thrown. Let's consider a few scenarios:
Observer inside the spaceship: From the perspective of someone inside the spaceship, if an object is thrown, it would behave according to the laws of motion as experienced in their frame of reference. The object would continue moving in a straight line at a constant velocity unless acted upon by external forces, just like in everyday situations. However, it's important to note that the object's velocity would be relative to the spaceship, not to an external observer.
Observer outside the spaceship: An observer outside the spaceship, such as an observer on Earth, would see the spaceship and the object moving at extremely high speeds relative to them. Due to time dilation effects predicted by special relativity, time would appear to pass more slowly for the spaceship and the object from the perspective of the external observer.
If the object is thrown with a velocity relative to the spaceship, both the spaceship and the object would continue moving forward at nearly the speed of light, each with their respective velocities. The object's trajectory would be affected by the velocity of the spaceship, and it would not simply "drop" behind the spaceship.
From the perspective of the external observer, they would see the object and the spaceship appear contracted in the direction of motion (length contraction) due to the relativistic effects. The object's motion would appear slower than expected, and its energy and momentum would increase as it approaches the speed of light, following relativistic equations.
It's important to note that as an object with mass approaches the speed of light, it requires an increasing amount of energy to accelerate it further, and its relativistic mass would also increase. This means that reaching or exceeding the speed of light is not possible for objects with mass, according to our current understanding of physics.
In summary, from the perspective of an observer inside the spaceship, the object would behave as expected in their frame of reference. From the perspective of an external observer, the object's motion would be affected by the spaceship's velocity, and relativistic effects would come into play, leading to apparent time dilation, length contraction, and energy/momentum increase as the object approaches the speed of light.