D O C . 1 8 F L U C T U A T I O N S O F L U N A R L O N G I T U D E 8 9
18. “Comment about Periodical Fluctuations of
Lunar Longitude, Which So Far Appeared to Be
Inexplicable in Newtonian Mechanics”
[Einstein 1919b]
Submitted 24 April 1919
Published 8 May 1919
In: Königlich Preußische Akademie der Wissenschaften (Berlin). Sitzungsberichte (1919):
433–436.
As is well known, there are small systematic deviations of the observed lunar lon-
gitudes, the causes of which have not yet been derived with certainty. So far, an em-
pirical periodic term with a period of 273 years could be separated. The remaining
deviations also seem to be, at least approximately, of a periodic character, whereby
the period is almost 20 years and the magnitude is of the order of one second of arc.
These latter ones are discussed in the following.
C. F. Bottlinger has tried to give an explanation of these deviations in the paper
titled “Die Gravitationstheorie und die Bewegung des Mondes” (Freiburg i. Br.,
1912. C. Troemers Universitätsbuchhandlung) which was awarded a prize by the
University of Munich. In this he followed up an important cosmological idea of
Seeliger1
by introducing the hypothesis that the gravitational force lines suffer ab-
sorption when penetrating gravitational masses.
But it appears that these deviations can be very simply explained without intro-
ducing a new hypothesis, as I shall briefly outline in the following. In my opinion,
they are not a periodic oscillation of the motion of the moon, but rather variations
of the rotational movement of the earth, upon which our measure of time is based.
The tide raised by the moon increases the momentum of inertia of the earth rel-
ative to the earth’s axis, and it does so by an amount that depends upon the angle
which the line earth-moon forms with the equatorial plane of the earth. Conse-
quently, the moment of inertia of the earth, and thus its rotational velocity, passes
1
Seeliger, “Über die Anwendung der Naturgesetze auf das Universum” (Ber. d. Bayer.
Akademie [1909], p. 9). I also should have quoted this investigation in my paper “Kosmol-
ogische Betrachtungen zur allgemeinen Relativitätstheorie” (these Berichte 6 [1917], 142).
What has been explicated there in §1 is the idea of Seeliger, whose paper was at the time,
unfortunately, unknown to me.
[p. 433]
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[p. 434]