2 3 0 D O C . 5 6 G L O B U L A R S T A R C L U S T E R S
56. “A Simple Application of the
Newtonian Law of Gravitation to
Globular Star Clusters”
[Einstein 1921f]
Published ca. 18 March 1921
In: Festschrift der Kaiser Wilhelm Gesellschaft zur Förderung der Wissenschaften zu
ihrem zehnjährigen Jubiläum dargebracht von ihren Instituten. Berlin: Springer, 1921, pp.
There is hardly any doubt that one can safely extrapolate Newton’s law beyond
the distances for which it has been verified. This confidence is also supported by
the general theory of relativity, which provides a rational foundation for Newton’s
law such that an extrapolation to bodies that interact over larger distances appears
all the more justified. However, the general theory of relativity allows for consid-
erable deviations from the Newtonian law in a spatially finite universe, yet only in
the case where the mean density of the stellar matter in the investigated, gravitating
complex is not substantially larger than that of the rest of the universe.
In the following we shall apply the Newtonian law of gravitation to spherical
star clusters. The main difficulty then is to find some consequences that can be
tested, the reason being that our actual knowledge about the movement of stars in
these clusters is exceedingly limited. The positional changes of stars during the
time spans available to us are too small to be noticeable with our present means of
observation. Furthermore, over these long distances, stars are not bright enough
to allow for an investigation of their movements along the radius of vision by
means of Doppler’s principle. All one has is the image of the star cluster, pro-
jected parallel to the radius of vision, and even this only for the brightest stars in
the cluster.
Yet one knows the approximate distances of the star clusters and with this
their approximate true radius. This estimate is based upon the proven rule that
stars of the same spectral type share approximately equal size and approximately
equal absolute brightness. This assumption allows us to derive their distance from
the apparent luminosity of stars, namely, by comparison with stars of the same
spectral type, but closer to us. If one now knows the distance of a star that is close
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