Physics Motion-- when we travel in an AC compartment of a train which is moving very smoothly?

How do we come to know that its actually moving especially when its dark and we have no access to check whether the train is in motion.

We don't, the only way to know that its moving is we notice acceleration (a change in velocity). Either the speed changes or the direction (a curve in the track).

The Earth does more than 66,000 mph around the Sun at this very moment. We don't feel a thing!

Vibration, noise etc. It is possible if it is very quite and very smooth that you won't be able to tell that it is moving.

You don't. If the train is not accelerating, it is an inertial reference frame. No experiment done inside the train can indicate whether the train is moving relative to something outside the train.

This is the entire point of special relativity.

You cannot.