D O C U M E N T 1 9 7 J U L Y 1 9 2 1 1 3 7
Accordingly, may I request that you annul the mentioned ms. and at the same
time pardon my impetuousness.
As my simple solution to this paradox will soon be appear-
ing in the mentioned journals, I do not want to bore you here
with the details. But one thing I do have to say is that this
whole incident gave me cause to regard your derivation of
the true aberration (§7 of your art. in the Ann[alen] d[er]
Phys[ik] of
1905)[3]
henceforth as unsatisfactory, if not illu-
sory, even. For, just as in the case of the two stars (revolving
along a conical orbit), so also in the case of the Earth’s (observer’s) annual motion
one is not allowed simply to conclude the resultant aberration ellipse from the
Earth’s tangential uniform motion of the momentarily resting system .
For, please consider,—if we allowed our-
selves to apply your reasoning in the case of
the rotating Earth, then everyone would
want to apply the same also to the curvilin-
early orbiting star; that means transforming
from S1 to S (see figure), and likewise from
S2 to S (which would yield, even for the ap-
parent distance of the stars, the enormous
angle ) even though these stars are
not moving rectilinearly but curvilinearly.
(If they were moving rectilinearly, would be right, because S would see
each star from where it had emitted S light.) Thus if one is not permitted to make
use of the resting system (of the star) in the case of curvilinearly orbiting objects
(star), one is perhaps not permitted to do so in the case of the curvilinearly orbiting
observer, either. In any event, a careful analysis is called for to be able to prove that
one may do so.
This I shall take into account in my paper. May I ask you how you would carry
out such a proof?
It seems to me thoroughly necessary. For without such a proof, the following sit-
uation remains: We certainly can show how it is that the double stars, etc., exhibit
no extra aberration, but not how the stars describe the usual aberration ellipses.
Your clarification would be very helpful to me in working out the notes.
S
S*
(star)
Earth
S
S1
S2
S (observer)
S2
idem
from
system at rest from
S1
v
v
2--
c
- =
w
c
--- - =