Re: Relativistic aberration

Den 01.08.2024 22:44, skrev Richard Hachel:

Le 01/08/2024 à 20:04, "Paul.B.Andersen" a écrit :

Richard, you pride yourself of being the only person who has ever
correctly explained the Langevin paradox, but when I ask you to explain
a very simple example of said paradox, you chicken out!
>
One stationary clock on Earth, and two aeroplanes flying at
very low altitude in opposite directions around the Earth,
could it be simpler?

 I will answer you obviously, but not now, because the answer is too complicated, and you risk forfeiting a fight that you could win.

I risk to loose a fight I could win? :-D
I will take the risk!

 We must go more slowly and talk about the Langevin first, because the punch in the face is already quite colossal.

WE must talk?
I have solved the problem according to SR.
Why do YOU have to talk more about the Langevin first, have you
after 40 years still not all the equations and knowledge you need?

 In your example, it is true that it is very simple in appearance and we say to ourselves what could be simpler, one remains on the ground, the others turn in different directions but at the same speed.
 However, in the frame of reference of airplanes, it is the earth that turns around them, and the subject remaining on the earth does not describe a circle, but a very complex ovoid.

Have you ever been in an aeroplane? Did the fact that the ground
was moving at the speed 850 km/h relative to you make the Earth
turn into a complex ovoid? :-D
The equator is a circle, even when it is rotating.

 I prefer not to take this example, at least for the moment, and not until you have had all the insights that I have had for 40 years.
 R.H.

A pretty lousy excuse for chickening out. :-D
I have all the insight I need to solve the problem according to SR.
I am asking YOU to solve it according to YOUR theory.
You don't have teach me YOUR theory to solve the problem according
to YOUR theory.
Try?
---------------------------------------
The triplets Ginette, Elise and Wanda are co-located on
the equator. They all have an atomic clock.
Ginette are always stationary on the Equator.
Elise is travelling eastwards at low altitude in an aeroplane.
Wanda is travelling westwards at low altitude in an aeroplane.
Both are travelling once around Earth at equator.
Note that the altitude of the aeroplanes is so low
that the gravitational blue shift can be ignored.
 From the time they are co-located, to they again are co-located
after Elise's and Wanda's journey, Ginette's clock shows that
the duration of their journey is τ_G = two sidereal days.
Please find what the duration of the journey will be
measured by Elise and Wanda, τ_E and τ_W.
Some data:
Circumference of Earth at equator L = 40075 km
Sidereal day Tday = 86164.0905 s
Ginette's speed in the non rotating Earth centred frame of
reference (ECI frame), v = L/Tday = 465.1 m/s
SR predicts:  τ_E − τ_G = −259.2 ns,  τ_W − τ_G = +155.5 ns
But that's not the right answer, is it?
--
Paul
https://paulba.no/