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Hello, I have a couple of questions related to reference frames in Special Relativity.

Let's consider a rocket that is inertially moving towards a star with a relative velocity 0.9c.

I'd like to look at this example from both the rocket's and the star's perspectives.

My questions/comments are:

Let's consider a rocket that is inertially moving towards a star with a relative velocity 0.9c.

I'd like to look at this example from both the rocket's and the star's perspectives.

**In the reference frame of the rocket:**- The rocket is at rest and the star is moving towards the rocket.
- At time t(0), the distance between the rocket and the star is 10 light years.
- Since the distance between the two is 10 ly - and their relative velocity is 0.9c - the star will reach the rocket in 11.1 years.
- From the rocket's perspective, time is slowing down for the star, so only 4.8 years will have passed in the star's reference frame.

**In the reference frame of the star:**- The star is at rest and the rocket is moving towards the star.
- At time t(0), the distance between the rocket and the star is 10 light years.
- Since the distance between the two is 10 ly - and their relative velocity is 0.9c - the rocket will reach the star in 11.1 years.
- From the star's perspective, time is slowing down for the rocket, so only 4.8 years will have passed in the rocket's reference frame.

My questions/comments are:

- Is my math correct ;)
- Given that there is no acceleration involved in this example, can we safely assume that the two reference frames are fully symmetrical?
- When we switch the roles of "stationary" and "moving" between the star and the rocket, the proper distance between them doesn't change, right?
- The proper distance in this example is always in the reference frame of the stationary observer.

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