Let us take it from the beginning.
The aberration of the light from a star can be
stated very simple:
We will always see the star where it was at
the time of emission.
That means that the aberration is the angle
between the observed position of the star and
its real position.
Both are positions in our rest frame.
Let v be the orbital speed of the Earth. v = 29.78 km/s
Let a star be at the ecliptic north pole, a distance d from the Sun.
Let our observer be at the north pole (no diurnal aberration).
Let his coordinate system be such that the x-axis is tangential
to Earth's orbit, the y-axis is pointing towards the Sun and
the z-axis is pointing towards the Sun.
At any time, the true position of the star in the observer's
rest frame is:
-ax = 0, y = 1 AU, z = d.
Since the star in the observer's rest frame is moving
at the speed v in the negative x-direction, the observed
position of the star will at any time be:
x = -vt, z = d
where t is the transit time for the light to go from
the star to the observer.
The angle to the observed star in the x-z plane is:
__vt__
\ |
\ | aberration angle ++ = arcsin(v/c) ree 20.5"
\ ++ |d
ct\ |
\ |
\|
-------O--->x
At any time, the observer will observe the star 20.5"
in the negative x-direction from the true position of
the star at x = y = 0.
Since the rest frame of the observer is rotating once
per year, the observer will during a year observe
the star to move along a circle with radius 20.5".
This is annual stellar aberration.
Since there is a distance between the observer and
the star in the y-direction, the observer will observe
the star to be an angular distance from its true position.
If d = 100 pc, this angle will be 0.01" (per definition of parsec)
This angle is parallax, and depend on the distance to the star.
It has nothing to do with stellar aberration.
Note that the parallax is perpendicular to the aberration.
Typo.
the z-axis is pointing towards the star.
(The z-axis will point a small angle from the star;
the parallax. This is not aberration. See below.)
The x-axis is pointing in the same direction as Earth's velocity in the
solar system.
Den 06.03.2026 20:47, skrev Paul B. Andersen:
Let us take it from the beginning.
The aberration of the light from a star can be
stated very simple:
We will always see the star where it was at
the time of emission.
That means that the aberration is the angle
between the observed position of the star and
its real position.
Both are positions in our rest frame.
Or better:
In the observer's momentarily comoving inertial frame
of reference.
Let v be the orbital speed of the Earth. v = 29.78 km/s
Let a star be at the ecliptic north pole, a distance d from the Sun.
Let our observer be at the north pole (no diurnal aberration).
Let his coordinate system be such that the x-axis is tangential
to Earth's orbit, the y-axis is pointing towards the Sun and
the z-axis is pointing towards the Sun.
Typo.
the z-axis is pointing towards the star.
(The z-axis will point a small angle from the star;
-athe parallax. This is not aberration. See below.)
The x-axis is pointing in the same direction as
Earth's velocity in the solar system.
At any time, the true position of the star in the observer's
rest frame is:
-a-ax = 0, y = 1 AU, z = d.
------------------
Since the star in the observer's rest frame is moving
at the speed v in the negative x-direction, the observed
position of the star will at any time be:
-ax = -vt, z = d
where t is the transit time for the light to go from
the star to the observer.
The angle to the observed star in the x-z plane is:
-a __vt__
-a \-a-a-a-a |
-a-a \-a-a-a |-a aberration angle ++ = arcsin(v/c) ree 20.5"
-a-a-a \ ++ |d
-a-a ct\-a |
-a-a-a-a-a \ |
-a-a-a-a-a-a \|
-a-------O--->x
At any time, the observer will observe the star 20.5"
in the-a negative x-direction from the true position of
the star at x = y = 0.
Nobody has caught my error above!
Let me correct it:
Since the star in the observer's momentarily comoving
inertial frame of reference is moving at the speed v
in the negative x-direction, the observed position of
the star will be where the star was at the time of
emission:
-ax = vt, z = d
where t is the transit time for the light to go from
the star to the observer.
The angle to the observed star in the x-z plane is:
-a-a-a-a-a __vt__
-a-a-a-a |-a-a-a-a /
-a-a-a-a |-a-a-a /-a-a aberration angle ++ = arcsin(v/c) ree 20.5"
-a-a-a d| ++ /
-a-a-a-a |-a /ct
-a-a-a-a | /
-a-a-a-a |/
-a----O--->x
At any time, the observer will observe the star 20.5"
in the-a positive x-direction from the true position of
the star at x = y = 0.
The rest is correct.
Since the rest frame of the observer is rotating once
per year, the observer will during a year observe
the star to move along a circle with radius 20.5".
One name and surname of someone sayingOn 3/3/2026, Paul B. Andersen wrote:
"I'm seeing/observing stars moving along
circles". Even you are not THAT stupid, trash.
Den 07.03.2026 06:51, skrev Maciej Wo+|niak:
On 3/3/2026, Paul B. Andersen wrote:
One name and surname of someone saying
"I'm seeing/observing stars moving along
circles". Even you are not THAT stupid, trash.
|
| I will give you exactly one name:
| James Bradley (1693rCo1762)
|
| He observed the stellar aberration of gamma Draconis
| and 35 Camelopardalis from December 1725 to January 1727.
|
| Since neither of the stars are at the ecliptic north pole
| (Dec ~51rU# for both), he observed that the stars were moving
|along ellipses with major axis ~ 40".
|
| He got it correct within one arcsec!
You, Maciej Wo+|niak, seem to be so incredible stupid and ignorant
that you don't know that annual stellar aberration does exist.
On 4/1/2026 10:18 PM, Paul B. Andersen wrote:
Den 07.03.2026 06:51, skrev Maciej Wo+|niak:
On 3/3/2026, Paul B. Andersen wrote:
One name and surname of someone saying
"I'm seeing/observing stars moving along
circles". Even you are not THAT stupid, trash.
|
| I will give you exactly one name:
| James Bradley (1693rCo1762)
|
| He observed the stellar aberration of gamma Draconis
| and 35 Camelopardalis from December 1725 to January 1727.
|
| Since neither of the stars are at the ecliptic north pole
| (Dec ~51rU# for both), he observed that the stars were moving
|along ellipses with major axis ~ 40".
|
| He got it correct within one arcsec!
You, Maciej Wo+|niak, seem to be so incredible stupid and ignorant
that you don't know that annual stellar aberration does exist.
You, Paul B. Andersen seem to be an extremly dumb
piece of lying shit, even considering the usual
level of relativistic scum. And stellar aberration is
no way the movement of stars along circles.
https://explainingscience.org/2019/05/28/stellar-aberration/
Read, cry, and shut up.
https://explainingscience.org/wp-content/uploads/2019/05/abberation-bradley-observations.png--
https://tinyurl.com/28v3y3ar
Den 02.04.2026 00:18, skrev Maciej Wo+|niak:
On 4/1/2026 10:18 PM, Paul B. Andersen wrote:
Den 07.03.2026 06:51, skrev Maciej Wo+|niak:
On 3/3/2026, Paul B. Andersen wrote:
One name and surname of someone saying
"I'm seeing/observing stars moving along
circles". Even you are not THAT stupid, trash.
|
| I will give you exactly one name:
| James Bradley (1693rCo1762)
|
| He observed the stellar aberration of gamma Draconis
| and 35 Camelopardalis from December 1725 to January 1727.
|
| Since neither of the stars are at the ecliptic north pole
| (Dec ~51rU# for both), he observed that the stars were moving
|along ellipses with major axis ~ 40".
|
| He got it correct within one arcsec!
You, Maciej Wo+|niak, seem to be so incredible stupid and ignorant
that you don't know that annual stellar aberration does exist.
You, Paul B. Andersen seem to be an extremly dumb
piece of lying shit, even considering the usual
level of relativistic scum. And stellar aberration is
no way the movement of stars along circles.
https://explainingscience.org/2019/05/28/stellar-aberration/
Read, cry, and shut up.
Yet again you demonstrate that you can't read.
But maybe you can look at a picture?
This is what Bradley observed:
https://explainingscience.org/wp-content/uploads/2019/05/abberation- bradley-observations.pngor
https://tinyurl.com/28v3y3ar
Bradley observed that the star during a year appeared to move
around an ellipse with major axis 40". In 1726!
On 4/2/2026 3:13 PM, Paul B. Andersen wrote:
https://explainingscience.org/2019/05/28/stellar-aberration/
This is what Bradley observed:
https://explainingscience.org/wp-content/uploads/2019/05/abberation-bradley-observations.png
https://tinyurl.com/28v3y3ar
Bradley observed that the star during a year appeared to move
around an ellipse with major axis 40". In 1726!
Did he also observed that it moved along this ellipse?
Den 02.04.2026 16:01, skrev Maciej Wo+|niak:
On 4/2/2026 3:13 PM, Paul B. Andersen wrote:
https://explainingscience.org/2019/05/28/stellar-aberration/
This is what Bradley observed:
https://explainingscience.org/wp-content/uploads/2019/05/abberation-
bradley-observations.png
https://tinyurl.com/28v3y3ar
Bradley observed that the star during a year appeared to move
around an ellipse with major axis 40". In 1726!
Did he also observed that it moved along this ellipse?
!!!! :-D
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