Astronomical Curiosities: Facts and FallaciesGore, J. Ellard (John Ellard)
Science
Astronomical Curiosities: Facts and Fallacies
Gore, J. Ellard (John Ellard)
Astronomy -- Miscellanea; Solar system -- Miscellanea
In the spectrum of the gaseous nebulæ, the F line of hydrogen (Hβ) is
visible, but not the C line (Hα). The invisibility of the C line is
explained by Scheiner as due to a physiological cause, "the eye being
less sensitive to that part of the spectrum in which the line appears than
to the part containing the F line."[364]
An apparent paradox is found in the case of the gaseous nebulæ. The
undefined outlines of these objects render any attempt at measuring their
parallax very difficult, if not impossible. Their distance from the earth
is therefore unknown, and perhaps likely to remain so for many years to
come. It is possible that they may not be farther from us than some of the
stars visible in their vicinity. On the other hand, they may lie far
beyond them in space. But whatever their distance from the earth may be,
it may be easily shown that their attraction on the sun is directly
proportioned to their distance--that is, the greater their distance, the
greater the attraction! This is evidently a paradox, and rather a
startling one too. But it is nevertheless mathematically true, and can be
easily proved. For, _their distance being unknown_, they may be of any
dimensions. They might be comparatively small bodies relatively near the
earth, or they may be immense masses at a vast distance from us. The
latter is, of course, the more probable. In either case the _apparent_
size would be the same. Take the case of any round gaseous nebula.
Assuming it to be of a globular form, its _real_ diameter will depend on
its distance from the earth--the greater the distance, the greater the
diameter. Now, as the volumes of spheres vary as the cubes of their
diameters, it follows that the volume of the nebula will vary as the cube
of its distance from the earth. As the mass of an attracting body depends
on its volume and density, its real mass will depend on the cube of its
distance, the density (although unknown) being a fixed quantity. If at a
certain distance its mass is _m_, at double the distance (the _apparent_
diameter being the same) it would have a mass of eight times _m_ (8 being
the cube of 2), and at treble the distance its mass would be 27 _m_, and
so on, its _apparent_ size being known, but not its _real_ size. This is
obvious. Now, the attractive power of a body varies directly as its
mass--the greater the mass, the greater the attraction. Again, the
attraction varies _inversely_ as the square of the distance, according to
the well-known law of Newton. Hence if _d_ be the unknown distance of the
nebula, we have its attractive power varying as _d_{3} divided by _d_{2},
or directly as the distance _d_. We have then the curious paradox that for
a nebula whose distance from the earth is unknown, its attractive power on
the sun (or earth) will vary directly as the distance--the greater the
distance the greater the attraction, and, of course, conversely, the
smaller the distance the less the attractive power. This result seems at
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