Re: Relativistic aberration

Le 02/08/2024 à 21:49, "Paul.B.Andersen" a écrit :

Den 01.08.2024 23:03, skrev Richard Hachel:
equation (19)
The rocket will see the supernova
an angle 12.7⁰ from the x-axis.
(From Earth the supernova is seen in the direction 37⁰ from the x-axis)
 Here is how an observer moving at 0.8c will observe the universe:
The stars in front of him will be much closer to each other and
much brighter.
 This phenomenon is called "beaming".

We will now move on to numerical applications.
We have an observer on Earth who has just noticed the explosion of a supernova in the sky and who sends its coordinates to Paul B Andersen. Paul B Andersen takes out his telescope, and at the indicated location, finds the supernova. He notes E = (12000, 9000.0, -15000.0).
He then asks for spatial confirmation from the commander of a rocket
which crosses the Earth on the x-axis, but since he knows the laws of aberration of the position of the stars, Paul, thanks to an ultra-fast computer, sends the correct coordinates in the rocket's reference frame.
So he sends: position in x':
x'=(x+Vo.To)/sqrt(1-Vo²/c²) (attention negative To)
Or again, which is the same thing:
x'=[x+sqrt(x²+y²+z²)Vo/c]/sqrt(1-Vo²/c²)
<http://news2.nemoweb.net/jntp?aGJtGFi-pcZdeYKlbLrP7fJkFGw@jntp/Data.Media:1>
x'=40000
Or for the rocket: E'=(40000,9000,0,-41000,0)
We will note that always, always, always, for two joint observers, t=t'=0.
Which translated means "they see the same universe present" but not with the same spatial coordinates.
R.H.