THE MINOR PLANETS.
The Lesser Members of our System--Bode's Law--The Vacant Region in
the Planetary System--The Research--The Discovery of Piazzi--Was
the small Body a Planet?--The Planet becomes Invisible--Gauss
undertakes the Search by Mathematics--The Planet Recovered--Further
Discoveries--Number of Minor Planets now known--The Region to be
Searched--The Construction of the Chart for the Search for Small
Planets--How a Minor Planet is Discovered--Physical Nature of the
Minor Planets--Small Gravitation on the Minor Planets--The Berlin
Computations--How the Minor Planets tell us the Distance of the
Sun--Accuracy of the Observations--How they may be
Multiplied--Victoria and Sappho--The most Perfect Method.
In our chapters on the Sun and Moon, on the Earth and Venus, and on
Mercury and Mars, we have been discussing the features and the movements
of globes of vast dimensions. The least of all these bodies is the moon,
but even that globe is 2,000 miles from one side to the other. In
approaching the subject of the minor planets we must be prepared to find
objects of dimensions quite inconsiderable in comparison with the great
spheres of our system. No doubt these minor planets are all of them some
few miles, and some of them a great many miles, in diameter. Were they
close to the earth they would be conspicuous, and even splendid,
objects; but as they are so distant they do not, even in our greatest
telescopes, become very remarkable, while to the unaided eye they are
almost all invisible.
In the diagram (p. 234) of the orbits of the various planets, it is
shown that a wide space exists between the orbit of Mars and that of
Jupiter. It was often surmised that this ample region must be tenanted
by some other planet. The presumption became much stronger when a
remarkable law was discovered which exhibited, with considerable
accuracy, the relative distances of the great planets of our system.
Take the series of numbers, 0, 3, 6, 12, 24, 48, 96, whereof each number
(except the second) is double of the number which precedes it. If we now
add four to each, we have the series 4, 7, 10, 16, 28, 52, 100. With the
exception of the fifth of these numbers (28), they are all sensibly
proportional to the distances of the various planets from the sun. In
fact, the distances are as follows:--Mercury, 3.9; Venus, 7.2; Earth,
10; Mars, 15.2; Jupiter, 52.9; Saturn, 95.4. Although we have no
physical reason to offer why this law--generally known as Bode's--should
be true, yet the fact that it is so nearly true in the case of all the
known planets tempts us to ask whether there may not also be a planet
revolving around the sun at the distance represented by 28.
So strongly was this felt at the end of the eighteenth century that some
energetic astronomers decided to make a united effort to search for the
unknown planet. It seemed certain that the planet could not be a large
one, as otherwise it must have been found long ago. If it should exist,
then means were required for discriminating between the planet and the
hosts of stars strewn along its path.
The search for the small planet was soon rewarded by a success which has
rendered the evening of the first day in the nineteenth century
memorable in astronomy. It was in the pure skies of Palermo that the
observatory was situated where the memorable discovery of the first
known minor planet was made by Piazzi. This laborious and accomplished
astronomer had organised an ingenious system of exploring the heavens
which was eminently calculated to discriminate a planet among the starry
host. On a certain night he would select a series of stars to the number
of fifty, more or less, according to circumstances. With his meridian
circle he determined the places of the chosen objects. The following
night, or, at all events, as soon as convenient, he re-observed the
whole fifty stars with the same instrument and in the same manner, and
the whole operation was afterwards repeated on two, or perhaps more,
nights. When the observations were compared together he was in
possession of some four or more places of each one of the stars on
different nights, and the whole series was complete. He was persevering
enough to carry on these observations for very many groups, and at
length he was rewarded by a success which amply compensated him for all
his toil.
It was on the 1st of January, 1801, that Piazzi commenced for the one
hundred and fifty-ninth time to observe a new series. Fifty stars this
night were viewed in his telescope, and their places were carefully
recorded. Of these objects the first twelve were undoubtedly stellar,
and so to all appearance was the thirteenth, a star of the eighth
magnitude in the constellation of Taurus. There was nothing to
distinguish the telescopic appearance of this object from all the others
which preceded or followed it. The following night Piazzi, according to
his custom, re-observed the whole fifty stars, and he did the same again
on the 3rd of January, and once again on the 4th. He then, as usual,
brought together the four places he had found for each of the several
bodies. When this was done it was at once seen that the thirteenth
object on the list was quite a different body from the remainder and
from all the other stars which he had ever observed before. The four
places of this mysterious object were all different; in other words, it
was in movement, and was therefore a planet.
A few days' observation sufficed to show how this little body,
afterwards called Ceres, revolved around the sun, and how it circulated
in that vacant path intermediate between the path of Mars and the path
of Jupiter. Great, indeed, was the interest aroused by this discovery
and the influence which it has exercised on the progress of astronomy.
The majestic planets of our system had now to admit a much more humble
object to a share of the benefits dispensed by the sun.
After Piazzi had obtained a few further observations, the season for
observing this part of the heavens passed away, and the new planet of
course ceased to be visible. In a few months, no doubt, the same part of
the sky would again be above the horizon after dark, and the stars would
of course be seen as before. The planet, however, was moving, and would
continue to move, and by the time the next season had arrived it would
have passed off into some distant region, and would be again confounded
with the stars which it so closely resembled. How, then, was the planet
to be pursued through its period of invisibility and identified when it
again came within reach of observation?
This difficulty attracted the attention of astronomers, and they sought
for some method by which the place of the planet could be recovered so
as to prevent Piazzi's discovery from falling into oblivion. A young
German mathematician, whose name was Gauss, opened his distinguished
career by a successful attempt to solve this problem. A planet, as we
have shown, describes an ellipse around the sun, and the sun lies at a
focus of that curve. It can be demonstrated that when three positions of
a planet are known, then the ellipse in which the planet moves is
completely determined. Piazzi had on each occasion measured the place
which it then occupied. This information was available to Gauss, and the
problem which he had to solve may be thus stated. Knowing the place of
the planet on three nights, it is required, without any further
observations, to tell what the place of the planet will be on a special
occasion some months in the future. Mathematical calculations, based on
the laws of Kepler, will enable this problem to be solved, and Gauss
succeeded in solving it. Gauss demonstrated that though the telescope of
the astronomer was unable to detect the wanderer during its season of
invisibility, yet the pen of the mathematician could follow it with
unfailing certainty. When, therefore, the progress of the seasons
permitted the observations to be renewed, the search was recommenced.
The telescope was directed to the point which Gauss's calculations
indicated, and there was the little Ceres. Ever since its re-discovery,
the planet has been so completely bound in the toils of mathematical
reasoning that its place every night of the year can be indicated with a
fidelity approaching to that attainable in observing the moon or the
great planets of our system.
The discovery of one minor planet was quickly followed by similar
successes, so that within seven years Pallas, Juno, and Vesta were added
to the solar system. The orbits of all these bodies lie in the region
between the orbit of Mars and of Jupiter, and for many years it seems to
have been thought that our planetary system was now complete. Forty
years later systematic research was again commenced. Planet after planet
was added to the list; gradually the discoveries became a stream of
increasing volume, until in 1897 the total number reached about 430.
Their distribution in the solar system is somewhat as represented in
Fig. 55. By the improvement of astronomical telescopes, and by the
devotion with which certain astronomers have applied themselves to this
interesting research, a special method of observing has been created for
the distinct purpose of searching out these little objects.
It is known that the paths in which all the great planets move through
the heavens coincide very nearly with the path which the sun appears to
follow among the stars, and which is known as the ecliptic. It is
natural to assume that the small planets also move in the same great
highway, which leads them through all the signs of the zodiac in
succession. Some of the small planets, no doubt, deviate rather widely
from the track of the sun, but the great majority are approximately near
it. This consideration at once simplifies the search for new planets. A
certain zone extending around the heavens is to be examined, but there
is in general little advantage in pushing the research into other parts
of the sky.
The next step is to construct a map containing all the stars in this
region. This is a task of very great labour; the stars visible in the
large telescopes are so numerous that many tens of thousands, perhaps we
should say hundreds of thousands, are included in the region so narrowly
limited. The fact is that many of the minor planets now known are
objects of extreme minuteness; they can only be seen with very powerful
telescopes, and for their detection it is necessary to use charts on
which even the faintest stars have been depicted. Many astronomers have
concurred in the labour of producing these charts; among them may be
mentioned Palisa, of Vienna, who by means of his charts has found
eighty-three minor planets, and the late Professor Peters, of Clinton,
New York, who in a similar way found forty-nine of these bodies.
[Illustration: Fig. 55.--The Zone of Minor Planets between Mars and
Jupiter.]
The astronomer about to seek for a new planet directs his telescope
towards that part of the sun's path which is on the meridian at
midnight; there, if anywhere, lies the chance of success, because that
is the region in which such a body is nearer to the earth than at any
other part of its course. He steadfastly compares his chart with the
heavens, and usually finds the stars in the heavens and the stars in the
chart to correspond; but sometimes it will happen that a point in the
heavens is missing from the chart. His attention is at once arrested; he
follows the object with care, and if it moves it is a planet. Still he
cannot be sure that he has really made a discovery; he has found a
planet, no doubt, but it may be one of the large number already known.
To clear up this point he must undertake a further, and sometimes a very
laborious, enquiry; he must search the Berlin Year-Book and other
ephemerides of such planets and see whether it is possible for one of
them to have been in the position on the night in question. If he can
ascertain that no previously discovered body could have been there, he
is then entitled to announce to his brother astronomers the discovery of
a new member of the solar system. It seems certain that all the more
important of the minor planets have been long since discovered. The
recent additions to the list are generally extremely minute objects,
beyond the powers of small telescopes.
Since 1891 the method of searching for minor planets which we have just
described has been almost abandoned in favour of a process greatly
superior. It has been found feasible to employ photography for making
charts of the heavens. A photographic plate is exposed in the telescope
to a certain region of the sky sufficiently long to enable very faint
telescopic stars to imprint their images. Care has to be taken that the
clock which moves the camera shall keep pace most accurately with the
rotation of the earth, so that fixed stars appear on the plate as sharp
points. If, on developing the plate, a star is found to have left a
trail, it is evident that this star must during the time of exposure
(generally some hours) have had an independent motion of its own; in
other words, it must be a planet. For greater security a second picture
is generally taken of the same region after a short interval. If the
place occupied by the trail on the first plate is now vacant, while on
the second plate a new trail appears in a line with the first one, there
remains no possible doubt that we have genuine indications of a planet,
and that we have not been led astray by some impurity on the plate or by
a few minute stars which happened to lie very closely together. Wolf,
of Heidelberg, and following in his footsteps Charlois, of Nice, have in
this manner discovered a great number of new minor planets, while they
have also recovered a good many of those which had been lost sight of
owing to an insufficiency of observations.
On the 13th of August, 1898, Herr G. Witt, of the observatory of Urania
in Berlin, discovered a new asteroid by the photographic method. This
object was at first regarded merely as forming an addition of no special
importance to the 432 asteroids whose discovery had preceded it. It
received, as usual, a provisional designation in accordance with a
simple alphabetical device. This temporary label affixed to Witt's
asteroid was "D Q." But the formal naming of the asteroid has now
superseded this label. Herr Witt has given to his asteroid the name of
"Eros." This has been duly accepted by astronomers, and thus for all
time the planet is to be known.
The feature which makes the discovery of Eros one of the most remarkable
incidents in recent astronomy is that on those rare occasions when this
asteroid comes nearest to the earth it is closer to the earth than the
planet Mars can ever be. Closer than the planet Venus can ever be.
Closer than any other known asteroid can ever be. Thus we assign to Eros
the exceptional position of being our nearest planetary neighbour in the
whole host of heaven. Under certain circumstances it will have a
distance from the earth not exceeding one-seventh of the mean distance
of the sun.
Of the physical composition of the asteroids and of the character of
their surfaces we are entirely ignorant. It may be, for anything we can
tell, that these planets are globes like our earth in miniature,
diversified by continents and by oceans. If there be life on such
bodies, which are often only a few miles in diameter, that life must be
something totally different from anything with which we are familiar.
Setting aside every other difficulty arising from the possible absence
of water and from the great improbability of finding there an atmosphere
of a density and a composition suitable for respiration, gravitation
itself would prohibit organic beings adapted for this earth from
residing on a minor planet.
Let us attempt to illustrate this point, and suppose that we take the
case of a minor planet eight miles in diameter, or, in round numbers,
one-thousandth part of the diameter of the earth. If we further suppose
that the materials of the planet are of the same nature as the
substances in the earth, it is easy to prove that the gravity on the
surface of the planet will be only one-thousandth part of the gravity of
the earth. It follows that the weight of an object on the earth would be
reduced to the thousandth part if that object were transferred to the
planet. This would not be disclosed by an ordinary weighing scales,
where the weights are to be placed in one pan and the body to be weighed
in the other. Tested in this way, a body would, of course, weigh
precisely the same anywhere; for if the gravitation of the body is
altered, so is also in equal proportion the gravitation of the
counterpoising weights. But, weighed with a spring balance, the change
would be at once evident, and the effort with which a weight could be
raised would be reduced to one-thousandth part. A load of one thousand
pounds could be lifted from the surface of the planet by the same effort
which would lift one pound on the earth; the effects which this would
produce are very remarkable.
In our description of the moon it was mentioned (p. 103) that we can
calculate the velocity with which it would be necessary to discharge a
projectile so that it would never again fall back on the globe from
which it was expelled. We applied this reasoning to explain why the moon
has apparently altogether lost any atmosphere it might have once
possessed.
If we assume for the sake of illustration that the densities of all
planets are identical, then the law which expresses the critical
velocity for each planet can be readily stated. It is, in fact, simply
proportional to the diameter of the globe in question. Thus, for a minor
planet whose diameter was one-thousandth part of that of the earth, or
about eight miles, the critical velocity would be the thousandth part of
six miles a second--that is, about thirty feet per second. This is a low
velocity compared with ordinary standards. A child easily tosses a ball
up fifteen or sixteen feet high, yet to carry it up this height it must
be projected with a velocity of thirty feet per second. A child,
standing upon a planet eight miles in diameter, throws his ball
vertically upwards; up and up the ball will soar to an amazing
elevation. If the original velocity were less than thirty feet per
second, the ball would at length cease to move, would begin to turn, and
fall with a gradually accelerating pace, until at length it regained the
surface with a speed equal to that with which it had been projected. If
the original velocity had been as much as, or more than, thirty feet per
second, then the ball would soar up and up never to return. In a future
chapter it will be necessary to refer again to this subject.
A few of the minor planets appear in powerful telescopes as discs with
appreciable dimensions, and they have even been measured with the
micrometer. In this way Professor Barnard, late of the Lick Observatory,
determined the following values for the diameters of the four first
discovered minor planets:--
Ceres 485 miles.
Pallas 304 miles.
Juno 118 miles.
Vesta 243 miles.
The value for Juno is, however, very uncertain, and by far the greater
number of the minor planets are very much smaller than the figures here
given would indicate. It is possible by a certain calculation to form an
estimate of the aggregate mass of all the minor planets, inasmuch as
observations disclose to us the extent of their united disturbing
influences on the motion of Mars. In this manner Le Verrier concluded
that the collected mass of the small planets must be about equal to
one-fourth of the mass of the earth. Harzer, repeating the enquiry in an
improved manner, deduced a collected mass one-sixth of that of the
earth. There can be no doubt that the total mass of all the minor
planets at present known is not more than a very small fraction of the
amount to which these calculations point. We therefore conclude that
there must be a vast number of minor planets which have not yet been
recognised in the observatory. These unknown planets must be extremely
minute.
The orbits of this group of bodies differ in remarkable characteristics
from those of the larger planets. Some of them are inclined at angles of
30 deg. to the plane of the earth's orbit, the inclinations of the great
planets being not more than a few degrees. Some of the orbits of the
minor planets are also greatly elongated ellipses, while, of course, the
orbits of the large planets do not much depart from the circular form.
The periods of revolution of these small objects round the sun range
from three years to nearly nine years.
A great increase in the number of minor planets has rewarded the zeal of
those astronomers who have devoted their labours to this subject. Their
success has entailed a vast amount of labour on the computers of the
"Berlin Year-Book." That useful work occupies in this respect a position
which has not been taken by our own "Nautical Almanac," nor by the
similar publications of other countries. A skilful band of computers
make it their duty to provide for the "Berlin Year-Book" detailed
information as to the movements of the minor planets. As soon as a few
complete observations have been obtained, the little object passes into
the secure grasp of the mathematician; he is able to predict its career
for years to come, and the announcements with respect to all the known
minor planets are to be found in the annual volumes of the work referred
to.
The growth of discovery has been so rapid that the necessary labour for
the preparation of such predictions is now enormous. It must be
confessed that many of the minor planets are very faint and otherwise
devoid of interest, so that astronomers are sometimes tempted to concur
with the suggestion that a portion of the astronomical labour now
devoted to the computation of the paths of these bodies might be more
profitably applied. For this it would be only necessary to cast adrift
all the less interesting members of the host, and allow them to pursue
their paths unwatched by the telescope, or by the still more ceaseless
tables of the mathematical computer.
The sun, which controls the mighty orbs of our system, does not disdain
to guide, with equal care, the tiny globes which form the minor planets.
At certain times some of them approach near enough to the earth to merit
the attention of those astronomers who are specially interested in
determining the dimensions of the solar system. The observations are of
such a nature that they can be made with considerable precision; they
can also be multiplied to any extent that may be desired. Some of these
little bodies have consequently a great astronomical future, inasmuch as
they seem destined to indicate the true distance from the earth to the
sun more accurately than Venus or than Mars. The smallest of these
planets will not answer for this purpose; they can only be seen in
powerful telescopes, and they do not admit of being measured with the
necessary accuracy. It is also obvious that the planets to be chosen for
observation must come as near the earth as possible. In favourable
circumstances, some of the minor planets will approach the earth to a
distance which is about three-quarters of the distance of the sun. These
various conditions limit the number of bodies available for this purpose
to about a dozen, of which one or two will usually be suitably placed
each year.
For the determination of the sun's distance this method by the minor
planets offers unquestionable advantages. The orb itself is a minute
star-like point in the telescope, and the measures are made from it to
the stars which are seen near it. A few words will, perhaps, be
necessary at this place as to the nature of the observations referred
to. When we speak of the measures from the planet to the star, we do not
refer to what would be perhaps the most ordinary acceptation of the
expression. We do _not_ mean the actual measurement of the number of
miles in a straight line between the planet and the star. This element,
even if attainable, could only be the result of a protracted series of
observations of a nature which will be explained later on when we come
to speak of the distances of the stars. The measures now referred to are
of a more simple character; they are merely to ascertain the apparent
distance of the objects expressed in angular measure. This angular
measurement is of a wholly different character from the linear
measurement, and the two methods may, indeed, lead to results that would
at first seem paradoxical.
We may take, as an illustration, the case of the group of stars forming
the Pleiades, and those which form the Great Bear. The latter is a large
group, the former is a small one. But why do we think the words large
and small rightly applied here? Each pair of stars of the Great Bear
makes a large angle with the eye. Each pair of stars in the Pleiades
makes a small angle, and it is these angles which are the direct object
of astronomical measurement. We speak of the distance of two stars,
meaning thereby the angle which is bounded by the two lines from the eye
to the two stars. This is what our instruments are able to measure, and
it is to be observed that no reference to linear magnitude is implied.
Indeed, if we are to mention actual dimensions, it is quite possible,
for anything we can tell, that the Pleiades may form a much larger group
than the Great Bear, and that the apparent superiority of the latter is
merely due to its being closer to us. The most accurate of these angular
measures are obtained when two stars, or two star-like points, are so
close together as to enable them to be included in one field of view of
the telescope. There are special forms of apparatus which enable the
astronomer in this case to give to his observations a precision
unattainable in the measurement of objects less definitely marked, or at
a greater apparent distance. The determination of the distance of the
small star-like planet from a star is therefore characterised by great
accuracy.
But there is another and, perhaps, a weightier argument in favour of the
determination of the scale of the solar system by this process. The real
strength of the minor planet method rests hardly so much on the
individual accuracy of the observations, as on the fact that from the
nature of the method a considerable number of repetitions can be
concentrated on the result. It will, of course, be understood that when
we speak of the accuracy of an observation, it is not to be presumed
that it can ever be entirely free from error. Errors always exist, and
though they may be small, yet if the quantity to be measured is minute,
an error of intrinsic insignificance may amount to an appreciable
fraction of the whole. The one way by which their effect can be subdued
is by taking the mean of a large number of observations. This is the
real source of the value of the minor planet method. We have not to wait
for the occurrence of rare events like the transit of Venus. Each year
will witness the approach of some one or more minor planets sufficiently
close to the earth to render the method applicable. The varied
circumstances attending each planet, and the great variety of the
observations which may be made upon it, will further conduce to
eliminate error.
As the planet pursues its course through the sky, which is everywhere
studded over with countless myriads of minute stars, it is evident that
this body, itself so like a star, will always have some stars in its
immediate neighbourhood. As the movements of the planet are well known,
we can foretell where it will be on each night that it is to be
observed. It is thus possible to prearrange with observers in
widely-different parts of the earth as to the observations to be made on
each particular night.
An attempt has been made, on the suggestion of Dr. Gill, to carry out
this method on a scale commensurate with its importance. The planets
Iris, Victoria, and Sappho happened, in the years 1888 and 1889, to
approach so close to the earth that arrangements were made for
simultaneous measurements in both the northern and the southern
hemispheres. A scheme was completely drawn up many months before the
observations were to commence. Each observer who participated in the
work was thus advised beforehand of the stars which were to be employed
each night. Viewed from any part of the earth, from the Cape of Good
Hope or from Great Britain, the positions of the stars remain absolutely
unchanged. Their distance is so stupendous that a change of place on the
earth displaces them to no appreciable extent. But the case is different
with a minor planet. It is hardly one-millionth part of the distance of
the stars, and the displacement of the planet when viewed from the Cape
and when viewed from Europe is a measurable quantity.
The magnitude we are seeking is to be elicited by comparison between the
measurements made in the northern hemisphere with those made in the
southern. The observations in the two localities must be as nearly
simultaneous as possible, due allowance being made for the motion of the
planet in whatever interval may have elapsed. Although every precaution
is taken to eliminate the errors of each observation, yet the fact
remains that we compare the measures made by observers in the northern
hemisphere with those made by different observers, using of course
different instruments, thousands of miles away. But in this respect we
are at no greater disadvantage than in observing the transit of Venus.
It is, however, possible to obviate even this objection, and thus to
give the minor planet method a supremacy over its rival which cannot be
disputed. The difficulty would be overcome if we could arrange that an
astronomer, after making a set of observations on a fine night in the
northern hemisphere, should be instantly transferred, instruments and
all, to the southern station, and there repeat the observations. An
equivalent transformation can be effected without any miraculous agency,
and in it we have undoubtedly the most perfect mode of measuring the
sun's distance with which we are acquainted. This method has already
been applied with success by Dr. Gill in the case of Juno, and there are
other members of the host of minor planets still more favourably
circumstanced.
Consider, for instance, a minor planet, which sometimes approaches to
within 70,000,000 miles of the earth. When the opposition is drawing
near, a skilled observer is to be placed at some suitable station near
the equator. The instrument he is to use should be that marvellous piece
of mechanical and optical skill known as the heliometer.[20] It can be
used to measure the angular distance between objects too far apart for
the filar micrometer. The measurements are to be made in the evening as
soon as the planet has risen high enough to enable it to be seen
distinctly. The observer and the observatory are then to be transferred
to the other side of the earth. How is this to be done? Say, rather, how
we could prevent it from being done. Is not the earth rotating on its
axis, so that in the course of a few hours the observatory on the
equator is carried bodily round for thousands of miles? As the morning
approaches the observations are to be repeated. The planet is found to
have changed its place very considerably with regard to the stars. This
is partly due to its own motion, but it is also largely due to the
parallactic displacement arising from the rotation of the earth, which
may amount to so much as twenty seconds. The measures on a single night
with the heliometer should not have a mean error greater than one-fifth
of a second, and we might reasonably expect that observations could be
secured on about twenty-five nights during the opposition. Four such
groups might be expected to give the sun's distance without any
uncertainty greater than the thousandth part of the total amount. The
chief difficulty of the process arises from the movement of the planet
during the interval which divides the evening from the morning
observations. This drawback can be avoided by diligent and repeated
measurements of the place of the planet with respect to the stars among
which it passes.
In the monumental piece of work which issued in 1897 from the Cape
Observatory, under the direction of Dr. Gill, the final results from the
observations of Iris, Victoria, and Sappho have been obtained. From this
it appears that the angle which the earth's equatorial radius subtends
at the centre of the sun when at its mean distance has the value
8".802. If we employ the best value of the earth's equatorial radius we
obtain 92,870,000 miles as the mean distance of the centre of the sun
from the centre of the earth. This is probably the most accurate
determination of the scale of the solar system which has yet been made.