B Distance Expansion When Moving Away from an Object?

[Karagoz]

In a physics video on YouTube it's told that moving away from an object causes eextension of the length.

(Link: from 6:00, but video is Norwegian)

Imagine:

From planet B to planet C, the distance is 20 light years.
And from planet A to planet B the distance is 20 light years.
We are on planet B and observing it from there.

A rocket is moving towards the planet C with velocity 0.9685c relative to us.

In this case the Lorentz factor will be ca 4.

In the picture below, the rocket is right below the planet B.

So the astronauts will see the distance to the planet C as 20/4 = 5 light years. This is called length contraction.

But they are moving away from planet A. So they'll observe the distance to planet A as 4*20 = 80 light years.

Is this true?

Does the distance contraction happen only if the object is moving towards the other object?

And the distance will extend if the object is moving away from the other object?

Or the distance both to planet A and B will contract?

 

[Nugatory]

Is this true?

No.

 

[PeroK]

Or the distance both to planet A and B will contract?

Yes!

 

[Janus]

As far as the rocket is concerned, the distance between planets A and B and the distance between planets B and C will both be 5 light years and the total distance between planets A and C will be 10 light years.

 

[Orodruin]

So the astronauts will see the distance to the planet C as 20/4 = 5 light years. This is called length contraction.

So they'll observe

As always with relativity, you have to distinguish what an observer actually sees at some moment, i.e., what light signals arrive to the observer at that moment, from how things appear in that observer's inertial frame, i.e., what time and space coordinates the observer assigns to different events. This is a very common source of confusion and a bad use of language in my opinion. The typical thing to do in relativity is to deal with space-time coordinates and this is typically what is meant by colloquial phrases such as "observer A sees". I try to avoid such phrases when teaching and instead stick to more precise formulations.