Parallax—Lunar Parallax found from Direct Observation—Solar Parallax
deduced from the Transit of Venus—Distance of the Sun from the
Earth—Annual Parallax—Distance of the Fixed Stars.
THE parallax of a celestial body is the angle under which the radius of
the earth would be seen if viewed from the centre of that body; it
affords the means of ascertaining the distances of the sun, moon, and
planets (N. 130). When the moon is in the horizon at the instant of
rising or setting, suppose lines to be drawn from her centre to the
spectator and to the centre of the earth: these would form a
right-angled triangle with the terrestrial radius, which is of a known
length; and, as the parallax or angle at the moon can be measured, all
the angles and one side are given; whence the distance of the moon from
the centre of the earth may be computed. The parallax of an object may
be found, if two observers under the same meridian, but at a very great
distance from one another, observe its zenith distances on the same day
at the time of its passage over the meridian. By such contemporaneous
observations at the Cape of Good Hope and at Berlin, the mean horizontal
parallax of the moon was found to be 3459ʺ, whence the mean distance of
the moon is about sixty times the greatest terrestrial radius, or
237,608 miles nearly.[4] Since the parallax is equal to the radius of
the earth divided by the distance of the moon, it varies with the
distance of the moon from the earth under the same parallel of latitude,
and proves the ellipticity of the lunar orbit. When the moon is at her
mean distance, it varies with the terrestrial radii, thus showing that
the earth is not a sphere (N. 131).
Although the method described is sufficiently accurate for finding the
parallax of an object as near as the moon, it will not answer for the
sun, which is so remote that the smallest error in observation would
lead to a false result. But that difficulty is obviated by the transits
of Venus. When that planet is in her nodes (N. 132), or within 1-1/4° of
them, that is, in, or nearly in, the plane of the ecliptic, she is
occasionally seen to pass over the sun like a black spot. If we could
imagine that the sun and Venus had no parallax, the line described by
the planet on his disc, and the duration of the transit, would be the
same to all the inhabitants of the earth. But, as the semi-diameter of
the earth has a sensible magnitude when viewed from the centre of the
sun, the line described by the planet in its passage over his disc
appears to be nearer to his centre, or farther from it, according to the
position of the observer; so that the duration of the transit varies
with the different points of the earth’s surface at which it is observed
(N. 133). This difference of time, being entirely the effect of
parallax, furnishes the means of computing it from the known motions of
the earth and Venus, by the same method as for the eclipses of the sun.
In fact, the ratio of the distances of Venus and the sun from the earth
at the time of the transit is known from the theory of their elliptical
motion. Consequently the ratio of the parallaxes of these two bodies,
being inversely as their distances, is given; and as the transit gives
the difference of the parallaxes, that of the sun is obtained. In 1769
the parallax of the sun was determined by observations of a transit of
Venus made at Wardhus in Lapland, and at Tahiti in the South Sea. The
latter observation was the object of Cook’s first voyage. The transit
lasted about six hours at Tahiti, and the difference in duration at
these two stations was eight minutes; whence the sun’s horizontal
parallax was found to be 8ʺ·72. But by other considerations it has been
reduced by Professor Encke to 8ʺ·5776; from which the mean distance of
the sun appears to be about ninety-five millions of miles. This is
confirmed by an inequality in the motion of the moon, which depends upon
the parallax of the sun, and which, when compared with observation,
gives 8ʺ·6 for the sun’s parallax. The transits of Venus in 1874 and
1882 will be unfavourable for ascertaining the accuracy of the solar
parallax, and no other transit of that planet will take place till the
twenty-first century; but in the mean time recourse may be had to the
oppositions of Mars.
The parallax of Venus is determined by her transits; that of Mars by
direct observation, and it is found to be nearly double that of the sun,
when the planet is in opposition. The distance of these two planets from
the earth is therefore known in terrestrial radii, consequently their
mean distances from the sun may be computed; and as the ratios of the
distances of the planets from the sun are known by Kepler’s law, of the
squares of the periodic times of any two planets being as the cubes of
their mean distances from the sun, their absolute distances in miles are
easily found (N. 134). This law is very remarkable, in thus uniting all
the bodies of the system, and extending to the satellites as well as the
planets.
Far as the earth seems to be from the sun, Uranus is no less than
nineteen, and Neptune thirty times farther. Situate on the verge of the
system, the sun must appear from Uranus not much larger than Venus does
to us, and from Neptune as a star of the fifth magnitude. The earth
cannot even be visible as a telescopic object to a body so remote as
either Uranus or Neptune. Yet man, the inhabitant of the earth, soars
beyond the vast dimensions of the system to which his planet belongs,
and assumes the diameter of its orbit as the base of a triangle whose
apex extends to the stars.
Sublime as the idea is, this assumption proves ineffectual, except in a
very few cases; for the apparent places of the fixed stars are not
sensibly changed by the earth’s annual revolution. With the aid derived
from the refinements of modern astronomy, and of the most perfect
instruments, a sensible parallax has been detected only in a very few of
these remote suns. α Centauri has a parallax of one second of space,
therefore it is the nearest known star, and yet it is more than two
hundred thousand times farther from us than the sun is. At such a
distance not only the terrestrial orbit shrinks to a point, but the
whole solar system, seen in the focus of the most powerful telescope,
might be eclipsed by the thickness of a spider’s thread. Light, flying
at the rate of 190,000 miles in a second, would take more than three
years to travel over that space. One of the nearest stars may therefore
have been kindled or extinguished more than three years before we could
have been aware of so mighty an event. But this distance must be small
when compared with that of the most remote of the bodies which are
visible in the heavens. The fixed stars are undoubtedly luminous like
the sun: it is therefore probable that they are not nearer to one
another than the sun is to the nearest of them. In the milky way and the
other starry nebulæ, some of the stars that seem to us to be close to
others may be far behind them in the boundless depth of space; nay, may
be rationally supposed to be situate many thousand times farther off.
Light would therefore require thousands of years to come to the earth
from those myriads of suns of which our own is but “the remote
companion.”