Re: Relativistic aberration

Den 01.08.2024 13:39, skrev Richard Hachel:

 The event that occurred at the supernova located at 15,000 ly has just been recorded by the Earth observer.
He notes E = (x, y, z, To, t)
Let x = 12000, y = 9000, z = 0, To = -15000, t = 0.
This is how I write in Hachel notation.

A very stupid notation!
Giving the position of a star in  Cartesian coordinates
would obviously include the distance to the star, and then
in addition giving the distance to the star in light years
or years is redundant.
Astronomers give the position to the star as an angle
in a spherical coordinate system. The angle is given as
observed from the Sun.
The distance is given in parsecs (or ly) and will be determined
by parallax or other method.
The Earth is orbiting the Sun, which will mean that
an observer on the Earth will see the direction to
the star varying during the year. The star will appear
to move along an ellipse with major axis 40.98 arcsecs.
The direction to the star observed from the Sun will be in
the centre of the ellipse.
https://paulba.no/pdf/Stellar_aberration.pdf

 An observer crosses the Earth at this moment at a few thousand kilometers, his speed is 0.8c (his rocket has very advanced technology, and he is heading on the Ox axis).

Along the x-axis?
So his velocity is 37⁰ from the direction to the star.

 It is clear, at the risk of being absurd, and of not having understood anything at all about the theory of relativity that the events will be simultaneous for the two observers who will be conjoined at this moment.
 Their watch will mark t = 0 (since they are triggered at this moment).
 We want to know what the coordinates of the supernova event will be in the new reference frame of the rocket, and what the commander will write on his on-board carent.

Due to aberration he will see the supernova in a very
different direction than the person on Earth.
https://paulba.no/pdf/AberrationDoppler.pdf
equation (19)
The rocket will see the supernova
an angle 12.7⁰ from the x-axis.

 Let E'=(x,y,z,To,0) since not yet knowing the Poincaré-Lorentz transformations, we can only guess the other four coordinates.
 But you, Paul, who knows the TL and who knows a little about SR, can you give the five new coordinates in RH mode?

The aberration above is from the LT.
It is obviously meaningless to transform the distance,
there is no way the rocket man can measure it.
It is measured by other means.

 Don't be afraid to make mistakes, we are here to learn and understand, and even if you make a mistake, it will allow us to go further.
 If you don't make a mistake, it's because you have already understood this point perfectly.

Did you have a point?
--
Paul
https://paulba.no/