XIII. On the Precession of a Viscous Spheroid, and on the remote History of the Earth.
By G. H. Darwin, M.A., Fellow of Trinity College, Cambridge.
Communicated by J. W. L. Glaisher, M.A., FM.S.
Received July 22,—Read December 19, 1878,
The following paper contains the investigation of the mass-motion of viscous and
imperfectly elastic spheroids, as modified by a relative motion of their parts, produced
in them by the attraction of external disturbing bodies ; it must be regarded as
the continuation of my previous paper/" where the theory of the bodily tides of such
spheroids was given.
The problem is one of theoretical dynamics, but the subject is so large and complex,
that I thought it best, in the first instance, to guide the direction of the speculation
by considerations of applicability to the case of the earth, as disturbed by the sun
In order to avoid an incessant use of the conditional mood, I speak simply of the
earth, sun, and moon ; the first being taken as the type of the rotating body, and the
two latter as types of the disturbing or tide-raising bodies. This course will be justi-
Roche radius, whereas Fig. 3 is a rather extended disk case (run 9).
The extension of a disk is indicated by Jdisk/Mdisk, where Jdisk is the
total angular momentum of the starting disk. For the disks in Figs 2
and 3, Jdisk/Mdisk are0:692 GM!aR and 0:813 GM!aR, respectively.
Figure 3 The same snapshots as in Fig. 2 but for run 9 of a more extended disk
(Jdisk=Mdisk ¼ 0:813 GM!aR). At t ¼ 1,000 the largest moon mass is 0.71ML.
[Ida et al., Nature, 1997]FIG. 2. Snapshots of the circumterrestrial disk projected on the R–z plane at t = 0, 10, 30, 100, 1000TK for runs (a) 29a
centered at the coordinate origin stands for Earth. Circles represent disk particles and their size is proportional to the physic
[Kokubo et al., Icarus, 2000]
N = 1,000