Chapter I: Magnitude and Distance of the Sun

138. _The Volume of the Sun._--The apparent diameter of the sun is about 32', being a little greater than that of the moon. The real diameter of the sun is 866,400 miles, or about a hundred and nine times that of the earth.

As the diameter of the moon's orbit is only about 480,000 miles, or some sixty times the diameter of the earth, it follows that the diameter of the sun is nearly double that of the moon's orbit: hence, were the centre of the sun placed at the centre of the earth, the sun would completely fill the moon's orbit, and reach nearly as far beyond it in every direction as it is from the earth to the moon. The circumference of the sun as compared with the moon's orbit is shown in Fig. 154.

The volume of the sun is 1,305,000 times that of the earth.

139. _The Mass of the Sun._--The sun is much less dense than the earth. The mass of the sun is only 330,000 times that of the earth, and its density only about a fourth that of the earth.

To find the mass of the sun, we first ascertain the distance the
earth would draw the moon towards itself in a given time, were the
moon at the distance of the sun, and then form the proportion: as
the distance the earth would draw the moon towards itself is to the
distance that the sun draws the earth towards itself in the same
time, so is the mass of the earth to the mass of the sun.

Although the mass of the sun is over three hundred thousand times that of the earth, the pull of gravity at the surface of the sun is only about twenty-eight times as great as at the surface of the earth. This is because the distance from the surface of the sun to its centre is much greater than from the surface to the centre of the earth.

140. _Size of the Sun Compared with that of the Planets._--The size of the sun compared with that of the larger planets is shown in Fig. 155. The mass of the sun is more than seven hundred and fifty times that of all of the planets and moons in the solar system. In Fig. 156 is shown the apparent size of the sun as seen from the different planets. The apparent diameter of the sun decreases as the distance from it increases, and the disk of the sun decreases as the square of the distance from it increases.

141. _The Distance of the Sun._--The mean distance of the sun from the earth is about 92,800,000 miles. Owing to the eccentricity of the earth's orbit, the distance of the sun varies somewhat; being about 3,000,000 miles less in January, when the earth is at perihelion, than in June, when the earth is at aphelion.

"But, though the distance of the sun can easily be stated in
figures, it is not possible to give any real idea of a space so
enormous: it is quite beyond our power of conception. If one were to
try to walk such a distance, supposing that he could walk four miles
an hour, and keep it up for ten hours every day, it would take
sixty-eight years and a half to make a single million of miles, and
more than sixty-three hundred years to traverse the whole.

"If some celestial railway could be imagined, the journey to the
sun, even if our trains ran sixty miles an hour day and night and
without a stop, would require over a hundred and seventy-five years.
Sensation, even, would not travel so far in a human lifetime. To
borrow the curious illustration of Professor Mendenhall, if we could
imagine an infant with an arm long enough to enable him to touch the
sun and burn himself, he would die of old age before the pain could
reach him; since, according to the experiments of Helmholtz and
others, a nervous shock is communicated only at the rate of about a
hundred feet per second, or 1,637 miles a day, and would need more
than a hundred and fifty years to make the journey. Sound would do
it in about fourteen years, if it could be transmitted through
celestial space; and a cannon-ball in about nine, if it were to move
uniformly with the same speed as when it left the muzzle of the gun.
If the earth could be suddenly stopped in her orbit, and allowed to
fall unobstructed toward the sun, under the accelerating influence
of his attraction, she would reach the centre in about four months.
I have said if she could be stopped; but such is the compass of her
orbit, that, to make its circuit in a year, she has to move nearly
nineteen miles a second, or more than fifty times faster than the
swiftest rifle-ball; and, in moving twenty miles, her path deviates
from perfect straightness by less than an eighth of an inch. And
yet, over all the circumference of this tremendous orbit, the sun
exercises his dominion, and every pulsation of his surface receives
its response from the subject earth." (Professor C. A. Young: The
Sun.)

142. _Method of Finding the Sun's Distance._--There are several
methods of finding the sun's distance. The simplest method is that
of finding the actual distance of one of the nearer planets by
observing its displacement in the sky as seen from widely separated
points on the earth. As the _relative_ distances of the planets from
each other and from the sun are well known, we can easily deduce the
actual distance of the sun if we can find that of any of the
planets. The two planets usually chosen for this method are Mars and
Venus.

(1) The displacement of Mars in the sky, as seen from two
observatories which differ considerably in latitude, is, of course,
greatest when Mars is nearest the earth. Now, it is evident than
Mars will be nearer the earth when in opposition than when in any
other part of its orbit; and the planet will be least distant from
the earth when it is at its perihelion point, and the earth is at
its aphelion point, at the time of opposition. This method, then,
can be used to the best advantage, when, at the time of opposition,
Mars is near its perihelion, and the earth near its aphelion. These
favorable oppositions occur about once in fifteen years, and the
last one was in 1877.

Suppose two observers situated at _N'_ and _S'_ (Fig. 157), near the
poles of the earth. The one at _N'_ would see Mars in the sky at
_N_, and the one at _S'_ would see it at _S_. The displacement would
be the angle _NMS_. Each observer measures carefully the distance of
Mars from the same fixed star near it. The difference of these
distances gives the displacement of the planet, or the angle _NMS_.
These observations were made with the greatest care in 1877.

(2) Venus is nearest the earth at the time of inferior conjunction;
but it can then be seen only in the daytime. It is, therefore,
impossible to ascertain the displacement of Venus, as seen from
different stations, by comparing her distances from a fixed star.
Occasionally, at the time of inferior conjunction, Venus passes
directly across the sun's disk. The last of these _transits_ of
Venus occurred in 1874, and the next will occur in 1882. It will
then be over a hundred years before another will occur.

Suppose two observers, _A_ and _B_ (Fig. 158), near the poles of the
earth at the time of a transit of Venus. The observer at _A_ would
see Venus crossing the sun at _V_{2}_, and the one at _B_ would see
it crossing at _V_{1}_. Any observation made upon Venus, which would
give the distance and direction of Venus from the centre of the sun,
as seen from each station, would enable us to calculate the angular
distance between the two chords described across the sun. This, of
course, would give the displacement of Venus on the sun's disk. This
method was first employed at the last transits of Venus which
occurred before 1874; namely, those of 1761 and 1769.

There are three methods of observation employed to ascertain the
apparent direction and distance of Venus from the centre of the sun,
called respectively the _contact method_, the _micrometric method_,
and the _photographic method_.

(_a_) In the _contact_ method, the observation consists in noting
the exact time when Venus crosses the sun's limb. To ascertain this
it is necessary to observe the exact time of external and internal
contact. This observation, though apparently simple, is really very
difficult. With reference to this method Professor Young says,--

"The difficulties depend in part upon the imperfections of optical
instruments and the human eye, partly upon the essential nature of
light leading to what is known as diffraction, and partly upon the
action of the planet's atmosphere. The two first-named causes
produce what is called irradiation, and operate to make the apparent
diameter of the planet, as seen on the solar disk, smaller than it
really is; smaller, too, by an amount which varies with the size of
the telescope, the perfection of its lenses, and the tint and
brightness of the sun's image. The edge of the planet's image is
also rendered slightly hazy and indistinct.

"The planet's atmosphere also causes its disk to be surrounded by a
narrow ring of light, which becomes visible long before the planet
touches the sun, and, at the moment of internal contact, produces an
appearance, of which the accompanying figure is intended to give an
idea, though on an exaggerated scale. The planet moves so slowly as
to occupy more than twenty minutes in crossing the sun's limb; so
that even if the planet's edge were perfectly sharp and definite,
and the sun's limb undistorted, it would be very difficult to
determine the precise second at which contact occurs. But, as things
are, observers with precisely similar telescopes, and side by side,
often differ from each other five or six seconds; and, where the
telescopes are not similar, the differences and uncertainties are
much greater.... Astronomers, therefore, at present are pretty much
agreed that such observations can be of little value in removing the
remaining uncertainty of the parallax, and are disposed to put more
reliance upon the micrometric and photographic methods, which are
free from these peculiar difficulties, though, of course, beset with
others, which, however, it is hoped will prove less formidable."

(_b_) Of the _micrometric_ method, as employed at the last transit,
Professor Young speaks as follows:--

"The micrometric method requires the use of a heliometer,--an
instrument common only in Germany, and requiring much skill and
practice in its use in order to obtain with it accurate measures. At
the late transit, a single English party, two or three of the
Russian parties, and all five of the German, were equipped with
these instruments; and at some of the stations extensive series of
measures were made. None of the results, however, have appeared as
yet; so that it is impossible to say how greatly, if at all, this
method will have the advantage in precision over the contact
observations."

(_c_) The following observations, with reference to the
_photographic_ method, are also taken from Professor Young:--

"The Americans and French placed their main reliance upon the
photographic method, while the English and Germans also provided for
its use to a certain extent. The great advantage of this method is,
that it makes it possible to perform the necessary measurements
(upon whose accuracy every thing depends) at leisure after the
transit, without hurry, and with all possible precautions. The
field-work consists merely in obtaining as many and as good pictures
as possible. A principal objection to the method lies in the
difficulty of obtaining good pictures, i.e., pictures free from
distortion, and so distinct and sharp as to bear high magnifying
power in the microscopic apparatus used for their measurement. The
most serious difficulty, however, is involved in the accurate
determination of the scale of the picture; that is, of the number of
seconds of arc corresponding to a linear inch upon the plate.
Besides this, we must know the exact Greenwich time at which each
picture is taken, and it is also extremely desirable that the
_orientation_ of the picture should be accurately determined; that
is, the north and south, the east and west points of the solar image
on the finished plate. There has been a good deal of anxiety lest
the image, however accurate and sharp when first produced, should
alter, in course of time, through the contraction of the collodion
film on the glass plate; but the experiments of Rutherfurd, Huggins,
and Paschen, seem to show that this danger is imaginary.... The
Americans placed the photographic telescope exactly in line with a
meridian instrument, and so determined, with the extremest
precision, the direction in which it was pointed. Knowing this and
the time at which any picture was taken, it becomes possible, with
the help of the plumb-line image, to determine precisely the
orientation of the picture,--an advantage possessed by the American
pictures alone, and making their value nearly twice as great as
otherwise it would have been.

"The figure below is a representation of one of the American
photographs reduced about one-half. _V_ is the image of Venus,
which, on the actual plate, is about a seventh of an inch in
diameter; _aa'_ is the image of the plumb-line. The centre of the
reticle is marked with a cross."

The English photographs proved to be of little value, and the
results of the measurements and calculations upon the American
pictures have not yet been published. There is a growing
apprehension that no photographic method can be relied upon.

The most recent determinations by various methods indicate that the sun's distance is such that his parallax is about eighty-eight seconds. This would make the linear value of a second at the surface of the sun about four hundred and fifty miles.