MARS MASAI
MARSALA MASANIELLO
MARSDEN, WILLIAM MASAYA
MARSEILLES MASCAGNI, PIETRO
MARSH, ADAM MASCARA
MARSH, GEORGE PERKINS MASCARENE ISLANDS
MARSH, HERBERT MASCARON, JULES
MARSH, NARCISSUS MASCHERONI, LORENZO
MARSH, OTHNIEL CHARLES MASCOT
MARSH MASDEU, JUAN FRANCISCO
MARSHAL MASERU
MARSHALL, ALFRED MASHAM, ABIGAIL
MARSHALL, JOHN (American jurist) MASHAM, SAMUEL CUNLIFFE LISTER
MARSHALL, JOHN (British surgeon) MASHONA
MARSHALL, STEPHEN MASK
MARSHALL (Missouri, U.S.A.) MASKELYNE, NEVIL
MARSHALL (Texas, U.S.A.) MASOLINO DA PANICALE
MARSHALL ISLANDS MASON, FRANCIS
MARSHALLTOWN MASON, GEORGE
MARSHALSEA MASON, GEORGE HEMMING
MARSHBUCK MASON, JAMES MURRAY
MARSHFIELD MASON, SIR JOHN
MARSH GAS MASON, JOHN
MARSHMAN, JOSHUA MASON, JOHN YOUNG
MARSI MASON, SIR JOSIAH
MARSIGLI, LUIGI FERDINANDO MASON, LOWELL
MARSILIUS OF PADUA MASON, WILLIAM
MARSIVAN MASON AND DIXON LINE
MARS-LA-TOUR MASON CITY
MARSTON, JOHN MASONRY
MARSTON, PHILIP BOURKE MASPERO, GASTON CAMILLE CHARLES
MARSTON MOOR, BATTLE OF MASS
MARSUPIALIA MASSA
MARSUPIAL MOLE MASSACHUSETTS
MARSUS, DOMITIUS MASSACRE
MARSYAS MASSAGE
MARTABAN MASSAGETAE
MARTELLO TOWER MASSA MARITTIMA
MARTEN, HENRY MASSAWA
MARTEN MASSÉNA, ANDRÉ
MARTENS, FRÉDÉRIC FROMMHOLD DE MASSENBACH, CHRISTIAN KARL VON
MARTENS, GEORG FRIEDRICH VON MASSENET, JULES ÉMILE FRÉDÉRIC
MARTENSEN, HANS LASSEN MASSEREENE, JOHN CLOTWORTHY
MARTHA'S VINEYARD MASSEY, SIR EDWARD
MARTÍ, JUAN JOSÉ MASSEY, GERALD
MARTIAL MASSICUS, MONS
MARTIALIS, QUINTUS GARGILIUS MASSIF
MARTIAL LAW MASSILLON, JEAN BAPTISTE
MARTIGNAC, JEAN BAPTISTE GAY MASSILLON
MARTIGUES MASSIMO
MARTIN, ST MASSINGER, PHILIP
MARTIN (several popes) MASSINISSA
MARTIN, BON LOUIS HENRI MASSON, DAVID
MARTIN, CLAUD MASSON, LOUIS CLAUDE FRÉDÉRIC
MARTIN, FRANÇOIS XAVIER MAST
MARTIN, HOMER DODGE MASTABA
MARTIN, JOHN MASTER
MARTIN, LUTHER MASTER AND SERVANT
MARTIN, SIR THEODORE MASTER OF THE HORSE
MARTIN, WILLIAM MASTER OF THE ROLLS
MARTIN, SIR WILLIAM FANSHAWE MASTIC
MARTIN OF TROPPAU MASTIGOPHORA
MARTIN (bird) MASTODON
MARTINEAU, HARRIET MAS'UDI
MARTINEAU, JAMES MASULIPATAM
MARTINET MAT
MARTÍNEZ DE LA ROSA, DE PAULA MATABELE
MARTINI, GIOVANNI BATTISTA MATACHINES
MARTINI, SIMONE MATADOR
MARTINIQUE MATAMOROS
MARTINSBURG MATANZAS
MARTINS FERRY MATARÓ
MARTINUZZI, GEORGE MATCH
MARTIUS, CARL FRIEDRICH VON MATE (companion)
MARTOS, CHRISTINO MATÉ (shrub)
MARTOS MATERA
MARTYN, HENRY MATERIALISM
MARTYN, JOHN MATER MATUTA
MARTYR MATHEMATICS
MARTYROLOGY MATHER, COTTON
MARULLUS, MICHAEL TARCHANIOTA MATHER, INCREASE
MARUM, MARTIN VAN MATHER, RICHARD
MARUTS MATHERAN
MARVELL, ANDREW MATHESON, GEORGE
MARX, HEINRICH KARL MATHEW, THEOBALD
MARY (the mother of Jesus) MATHEWS, CHARLES
MARY (Magdalene) MATHEWS, THOMAS
MARY I. MATHY, KARL
MARY II. MATILDA (queen of England)
MARY QUEEN OF SCOTS MATILDA (countess of Tuscany)
MARY (duchess of Burgundy) MATINS
MARY (queen of France) MATLOCK
MARY OF LORRAINE MATOS FRAGOSO, JUAN DE
MARY OF MODENA MATRASS
MARY OF ORANGE MATRIARCHATE
MARYBOROUGH (Ireland) MATRIMONY
MARYBOROUGH (Queensland) MATRIX
MARYBOROUGH (Victoria, Australia) MATROSS
MARYLAND MATSUKATA
MARYPORT MATSYS, QUINTIN
MARZABOTTO MATTEAWAN
MASACCIO
MARS, in astronomy, the fourth planet in the order of distance from the
sun, and the next outside the earth. To the naked eye it appears as a
bright star of a decidedly reddish or lurid tint, which contrasts
strongly with the whiteness of Venus and Jupiter. At opposition it is
brighter than a first magnitude star, sometimes outshining even Sirius.
It is by virtue of its position the most favourably situated of all the
planets for observation from the earth. The eccentricity of its orbit,
0.0933, is greater than that of any other major planet except Mercury.
The result is that at an opposition near perihelion Mars is markedly
nearer to the earth than at an opposition near aphelion, the one
distance being about 35 million miles; the other 63 million. These
numbers express only the minimum distances at or near opposition, and
not the distance at other times. The time of revolution of Mars is
686.98 days. The mean interval between oppositions is 2 years 49½ days,
but, owing to the eccentricity of the orbit, the actual excess over two
years ranges from 36 days to more than 2½ months. Its period of rotation
is 24 h. 37 m. 22.66 s. (H. G. Bakhuyzen).
[Illustration: FIG. 1.--Orbits of Mars and the Earth, showing aspects of
the planet relative to the earth and sun.]
_Motions._--The accompanying diagram will convey a notion of the varied
aspects presented by the planet, of the cycles of change through which
they go, and of the order in which the oppositions follow each other.
The outer circle represents the orbit of Mars, the inner one that of the
earth. AE is the line of the equinoxes from which longitudes are
counted. The perihelion of Mars is in longitude 335° at the point [pi].
The ascending node [Omega] is in longitude 47°. The line of nodes makes
an angle of 74° with the major axis, so that Mars is south of the
ecliptic near perihelion, but north of it near aphelion. Around the
inner circle, representing the earth's orbit, are marked the months
during which the earth passes through the different parts of the orbit.
It will be seen that the distance of Mars at the time of any opposition
depends upon the month in which opposition occurs. The least possible
distance would occur in an opposition about the end of August, a little
before Mars reached the perihelion, because the eccentricity of the
earth's orbit throws our planet a little farther from the sun and nearer
the orbit of Mars in July than it does in August. The opposition of 1909
occurred on the 24th of September, at a point marked by the year near
the equinox, and the month and years of the oppositions following, up to
1941, are also shown in the same way. Tracing them around, it will be
seen that the points of opposition travel around the orbit in about 16
years, so that oppositions near perihelion, when Mars is therefore
nearest the earth, occur at intervals of 15 or 17 years.
The axis of rotation of the planet is inclined between 23° and 24° to
the orbit, and the equator of the planet has the same inclination to the
plane of the orbit. The north pole is directed toward a point in
longitude 355°, in consequence of which the projection of the planet's
axis upon the plane of the ecliptic is nearly parallel to the line of
our equinoxes. This projection is shown by the dotted line SP-NP, which
corresponds closely to the line of the Martian solstices. It will be
seen that at a September opposition the north pole of the planet is
turned away from the sun, so that only the southern hemisphere is
presented to us, and only the south pole can be seen from the earth. The
Martian vernal equinox is near Q and the northern solstice near A. Here
at the point S.P. the northern hemisphere is turned toward the sun. It
will be seen that the aspect of the planet at opposition, especially the
hemisphere which is visible, varies with the month of opposition, the
general rule being that the northern hemisphere of the planet is
entirely seen only near aphelion oppositions, and therefore when
farthest from us, while the southern hemisphere is best seen near
perihelion oppositions. The distances of the planet from the sun at
aphelion and at perihelion are nearly in the ratio 6:5. The intensity of
the sun's radiation on the planet is as the inverse square of this
ratio. It is therefore more than 40% greater near perihelion than near
aphelion. It follows from all this that the southern hemisphere is
subjected to a more intense solar heat than the northern, and must
therefore have a warmer summer season. But the length of the seasons is
the inverse of this, the summer of the northern hemisphere being longer
and the heat of the southern hemisphere shorter in proportion.
_Surface Features._--The surface features of the planet will be better
understood by first considering what is known of its atmosphere and of
the temperature which probably prevails on its surface. One method of
detecting an atmosphere is through its absorption of the different rays
in the spectrum of the sunlight reflected from the planet. Several
observers have thought that they saw fairly distinct evidence of such
absorption when the planet was examined with the spectroscope. But the
observations were not conclusive; and with the view of setting the
question at rest if possible, W. W. Campbell at the Lick Observatory
instituted a very careful series of spectroscopic observations.[1] To
reduce the chances of error to a minimum the spectrum of Mars was
compared with that of the moon when the two bodies were near each other.
Not the slightest difference could be seen between any of the lines in
the two spectra. It being certain that the spectrum of the moon is not
affected by absorption, it followed that any absorption produced by the
atmosphere of Mars is below the limit of perception. It was considered
by Campbell that if the atmosphere of Mars were ¼ that of the earth in
density, the absorption would have been visible. Consequently the
atmosphere of Mars would be of a density less than ¼ that of the
earth.[2]
Closely related to the question of an atmosphere is that of possible
clouds above the surface of the planet, the existence of which, if real,
would necessarily imply an atmosphere of a density approaching the limit
set by Campbell's observations. The most favourable opportunity for
seeing clouds would be when they are formed above a region of the planet
upon which the sun is about to rise, or from which it has just been
setting. The cloud will then be illuminated by the sun's rays while the
surface below it is in darkness, and will appear to an observer on the
earth as a spot of light outside the terminator, or visible edge of the
illuminated part of the disk. It is noticeable that phenomena more or
less of this character, though by no means common, have been noted by
observers on several occasions. Among these have been the Mt Hamilton
and Lowell observers, and W. H. Pickering at Arequipa. Campbell has
shown that many of them may be accounted for by supposing the presence
of mountains not more than two miles in height, which may well exist on
the planet. While this hypothesis will serve to explain several of these
appearances, this can scarcely be said of a detached spot observed on
the evening of the 26th of May 1903, at the Lowell Observatory.[3] Dr
Slipher, who first saw it, was so struck by the appearance of the
projection from the terminator upon the dark side of the disk that he
called the other observers to witness it. Micrometric measures showed
that it was some 300 miles in length, and that its highest point stood
some 17 miles above the surface of the planet. That a cloud should be
formed at such a height in so rare an atmosphere seems difficult to
account for except on the principle that the rate of diminution of the
density of an atmosphere with its height is proportional to the
intensity of gravity, which is smaller on Mars than on the earth. The
colour was not white, but tawny, of the tint exhibited by a cloud of
dust. Percival Lowell therefore suggests that this and other appearances
of the same kind seen from time to time are probably dust clouds,
travelling over the desert, as they sometimes do on the earth, and
settling slowly again to the ground.
_Temperature._--Up to a recent time all that could be said of the
probable temperature of Mars was that, being more distant from the sun
than the earth, and having a rarer atmosphere, it had a general mean
temperature probably below that of the earth. Greater precision can now
be given to this theoretical conclusion by recent determination of the
law of radiation of heat by bodies at different temperatures. Regarding
it as fairly well established that at ordinary temperatures the
radiation varies directly as the fourth power of the absolute
temperature, it is possible when the "solar constant" is known to
compute the temperature of a non-coloured body at the distance of Mars
which presents every part of its surface in rapid succession to the
sun's rays in the absence of atmosphere only. This has been elaborately
done for the major planets by J. H. Poynting,[4] who computes that the
mean temperature of Mars is far below the freezing point of water. On
the other hand an investigation made by Lowell in 1907,[5] taking into
account the effect of the rare atmosphere on the heat lost by
reflection, and of several other factors in the problem hitherto
overlooked, led him to the conclusion that the mean temperature is about
48° Fahr.[6] But the temperature may rise much above the mean on those
regions of the surface exposed to a nearly vertical noon-day sun. The
diurnal changes of temperature, being diminished by an atmosphere, must
be greater on Mars than on the earth, so that the vicissitudes of
temperature are there very great, but cannot be exactly determined,
because they must depend upon the conductivity and thermal capacity of
the matter composing the surface of the planet. What we can say with
confidence is that, during the Martian winter of between eight and
twelve of our months, the regions around either pole must fall to a
temperature nearer the absolute zero than any known on this planet. In
fact the climatic conditions in all but the equatorial regions are
probably of the same nature as those which prevail on the tops of our
highest mountains, except that the cold is more intense.[7]
Having these preliminary considerations in mind, we may now study the
features presented to our view by the surface of the planet. These have
a permanence and invariability which markedly differentiate them from
the ever varying surfaces of Jupiter and Saturn, and show that what we
see is a solid surface, like that of our earth. They were observed and
delineated by the leading astronomers of the 16th century, especially
Huygens, Cassini and Hooke. These observers could only distinguish the
different regions upon the planet as bright or dark. Reasoning as they
did in the case of the moon, it was naturally supposed that the brighter
regions were land and the darker ones seas. The observers of our time
find that the darker regions have a slightly blue-green aspect, which
might suggest the idea of water, but are variegated in a way to show
that they must be composed of a solid crust, like the brighter regions.
The latter have a decidedly warm red or ochre tint, which gives the
characteristic colour to the planet as seen by the naked eye. The
regions in equatorial and middle latitudes, which are those best seen
from our planet, show a surface of which the general aspect is not
dissimilar to that which would be presented by the deserts of our earth
when seen from the moon. With each improvement in the telescope the
numerous drawings of the planet show more definiteness and certainty in
details. About 1830 a fairly good map was made by W. Beer and J. H.
Mädler, a work which has been repeated by a number of observers since
that time. The volume of literature on the subject, illustrated by
drawings and maps, has become so great that it is impossible here to
present even an abstract of it; and it would not be practicable, even
were it instructive, to enter upon any detailed description of Martian
topography. A few great and well-marked features were depicted by the
earliest observers, who saw them so plainly that they may be recognized
by their drawings at the present time. There is also a general agreement
among nearly all observers with good instruments as to the general
features of the planet, but even in the latest drawings there is a
marked divergence as to the minuter details. This is especially true of
the boundaries of the more ill-defined regions, and of the faint and
difficult markings of various kinds which are very numerous on every
part of the planet. There is not even a close agreement between the
drawings by the same observer at different oppositions; but this may be
largely due to seasonal and other changes.
The most striking feature, and one which shows the greatest resemblance
to a familiar terrestrial process, is that when either polar region
comes into view after being turned nearly a year away from the sun, it
is found to be covered with a white cap. This gradually contracts in
extent as the sun shines upon it during the remaining half of the
Martian year, sometimes nearly disappearing. That this change is due to
the precipitation of watery vapour in the form of ice, snow or frost
during the winter, and its melting or evaporation when exposed to the
sun's rays, is so obvious a conclusion that it has never been seriously
questioned. It has indeed been suggested that the deposit may be frozen
carbonic acid. While we cannot pronounce this out of the question, the
probabilities seem in favour of the deposit being due to the
precipitation of aqueous vapour in a frozen form. At a temperature of
-50° C., which is far above what we can suppose to prevail in the polar
regions during the winter, the tension of aqueous vapour is 0.034 mm. On
the other hand Faraday found the tension of carbonic acid to be still an
entire atmosphere at as low a temperature as -80° C. Numerically exact
statements are impossible owing to our want of knowledge of the actual
temperature, which must depend partly upon air currents between the
equator and the poles of Mars. It can, however, be said, in a general
way, that a proportion of aqueous vapour in the rare atmosphere of Mars,
far smaller than that which prevails on the earth, would suffice to
explain the observed formation and disappearances of the polar caps.
Since every improvement in the telescope and in the conditions of
observation must enable modern observers to see all that their
predecessors did and yet more, we shall confine our statements to the
latest results. These may be derived from the work of Professor Lowell
of Boston, who in 1894 founded an observatory at Flagstaff, Arizona,
7250 ft. above sea-level, and supplied it with a 24´´ telescope, of
which the main purpose was the study of Mars. This work has been
continued with such care and assiduity that its results must take
precedence of all others in everything that relates to our present
subject.[8]
Among the more probable conclusions to be drawn from Lowell's
observations, the following are of most interest. The darker areas are
all seamed by lines and dots darker than themselves, which are permanent
in position, so that there can be no bodies of water on the planet. On
the other hand, their colour, blue-green, is that of vegetation. This
fades out as vegetation would at certain seasons to faint blue-green,
but in some places to a tawny brown. Each hemisphere undergoes these
changes in its turn, the changes being opposite in opposite
hemispheres. The changes in the dark areas follow some time after the
melting of the polar caps. The aspect of these areas suggests old sea
bottoms, and when on the terminator appear as depressions, though this
may be only apparent and due to the dark colour. The smoothness and soft
outline of the terminator shows that there are no mountains on Mars
comparable with ours, but that the surface is surprisingly flat. White
spots are occasionally visible in the tropical and temperate regions,
which are perhaps due to the condensation of frost or snow, or to saline
exudation such as seasonally occurs in India (Lowell). Moreover in
winter the temperate zones are more or less covered by a whitish veil,
which may be either hoar frost or cloud. A spring haze seems to surround
the north polar cap during its most extensive melting; otherwise the
Martian sky is quite clear, like that of a dry desert land. When either
polar cap is melting it is bordered by a bluish area, which Lowell
attributes to the water produced by the melting. But the obliquity at
which the sun's rays strike the surface as the cap is melting away is so
great that it would seem to preclude the possibility of a temperature
high enough to melt the snow into water. Under the low barometric
pressure prevailing on the planet, snow would evaporate under the
influence of the sun's rays without changing into water. It is also
contended that what looks like such a bluish border may be formed around
a bright area by the secondary aberration of a refracting telescope.[9]
The modern studies of Mars which have aroused so much public interest
began with the work of Schiaparelli in 1877. Accepting the term "ocean,"
used by the older observers, to designate the widely extended darker
regions on the planet, and holding that they were really bodies of
water, he found that they were connected by comparatively narrow
streaks. (Schiaparelli considered them really water until after the
Lowell observations.) In accordance with the adopted system of
nomenclature, he termed these streaks _canale_, a word of which the
proper rendering into English would be _channels_. But the word was
actually translated into both English and French as canal, thus
connoting artificiality in the supposed waterways, which were attributed
to the inhabitants of the planet. The fact that they were many miles in
breadth, and that it was therefore absurd to call them canals, did not
prevent this term from being so extensively used that it is now scarcely
possible to do away with it. A second series of observations was made by
Schiaparelli at the opposition of 1879, when the planet was farther
away, but was better situated as to altitude above the horizon. He now
found a number of additional channels, which were much finer than those
he had previously drawn. The great interest attaching to their seemingly
artificial character gave an impetus to telescopic study of the planet
which has continued to the present time. New canals were added,
especially at the Lowell Observatory, until the entire number listed in
1908 amounted to more than 585. The general character of this complex
system of lines is described by Lowell as a network covering the whole
face of the planet, light and dark regions alike, and connecting at
either end with the respective polar caps there. At their junctions are
small dark pinheads of spots. The lines vary in size between themselves,
but each maintains its own width throughout. But the more difficult of
these objects are only seen occasionally and are variable in
definiteness. Of two canals equally well situated for seeing, only one
may be visible at one time and only the other at other times. If this
variability of aspect among different canals is true as they are seen
from the Lowell Observatory, we find it true to a much greater extent
when we compare descriptions by different observers. At Flagstaff, the
most favourably situated of all the points of observation, they are seen
as fine sharp lines, sometimes as well marked as if drawn with a pencil.
But other observers see them with varying degrees of breadth and
diffuseness.
One remarkable feature of these objects is their occasional
"gemination," some of the canals appearing as if doubled. This was
first noticed by Schiaparelli, and has been confirmed, so far as
observations can confirm it, by other observers. Different explanations
of this phenomenon have been suggested, but the descriptions of it are
not sufficiently definite to render any explanation worthy of entire
confidence possible. Indeed the more cautious astronomers, who have not
specially devoted themselves to the particular phenomena, reserve a
doubt as to how far the apparent phenomena of the finer canals are real,
and what the markings which give rise to their appearance might prove to
be if a better and nearer view of the planet than is now possible could
be obtained. Of the reality of the better marked ones there can be no
doubt, as they have been seen repeatedly by many observers, including
those at the Lick Observatory, and have actually been photographed at
the Lowell Observatory. The doubt is therefore confined to the vast
network of lines so fine that they never certainly have been seen
elsewhere than at Flagstaff. The difficulty of pronouncing upon their
reality arises from the fact that we have to do mainly with objects not
plainly visible (or, as Lowell contends, not plainly visible elsewhere).
The question therefore becomes one of psychological optics rather than
of astronomy. When the question is considered from this point of view it
is found that combinations of light and shaded areas very different from
continuous lines, will, under certain conditions, be interpreted by the
eye as such lines; and when such is the case, long practice by an
observer, however carefully conducted, may confirm him in this
interpretation. To give a single example of the principles involved; it
is found by experiment that if, through a long line so fine as to
approach the limit of visibility, segments not too near each other, or
so short that they would not be visible by themselves, be taken out,
their absence from the line will not be noticed, and the latter will
still seem continuous.[10] In other words we do not change the aspect of
the line by taking away from it a part which by itself would be
invisible. This act of the eye, in interpreting a discontinuous series
of very faint patches as a continuous line, is not, properly speaking,
an optical illusion, but rather a habit. The arguments for the reality
of all the phenomena associated with the canals, while cogent, have not
sufficed to bring about a general consensus of opinion among critics
beyond the limit already mentioned.
Accepting the view that the dark lines on Mars are objectively real and
continuous, and are features as definite in reality as they appear in
the telescope, Professor Lowell has put forth an explanation of
sufficient interest to be mentioned here. His first proposition is that
lines frequently thousands of miles long, each following closely a great
circle, must be the product of design rather than of natural causes. His
explanation is that they indicate the existence of irrigating canals
which carry the water produced annually by the melting of the polar
snows to every part of the planet. The actual canals are too minute to
be visible to us. What we really see as dark lines are broad strips of
vegetation, produced by artificial cultivation extending along each
border of the irrigating streams. On the other hand, in the view of his
critics, the quantity of ice or snow which the sun's rays could melt
around the poles of Mars, the rate of flow and evaporation as the water
is carried toward the equator, and several other of the conditions
involved, require investigation before the theory can be
established.[11]
The accompanying illustrations of Mars and its canals are those of
Lowell, and represent the planet as seen by the Flagstaff observers.
[Illustration: FIG. 2.]
_Satellites and Pole of Mars._--At the opposition of Mars which occurred
in August 1877 the planet was unusually near the earth. Asaph Hall, then
in charge of the 26´´ telescope at the Naval Observatory in Washington,
took advantage of this favourable circumstance to make a careful search
for a visible satellite of the planet. On the night of the 11th of
August he found a faint object near the planet. Cloudy weather
intervened, and the object was not again seen until the 16th, when it
was found to be moving with the planet, leaving no doubt as to its being
a satellite. On the night following an inner satellite much nearer the
planet was observed. This discovery, apart from its intrinsic interest,
is also noteworthy as the first of a series of discoveries of satellites
of the outer planets. The satellites of Mars are difficult to observe,
on account not merely of their faintness, but of their proximity to the
planet, the light of which is so bright as to nearly blot out that of
the satellite. Intrinsically the inner satellite is brighter than the
outer one, but for the reason just mentioned it is more difficult to
observe. The names given them by Hall were Deimos for the outer
satellite and Phobos for the inner one, derived from the mythological
horses that drew the chariot of the god Mars. A remarkable feature of
the orbit of Phobos is that it is so near the planet as to perform a
revolution in less than one-third that of the diurnal rotation of Mars.
The result is that to an inhabitant of Mars this satellite would rise in
the west and set in the east, making two apparent diurnal revolutions
every day. The period of Deimos is only six days greater than that of a
Martian day; consequently its apparent motion around the planet would be
so slow that more than two days elapse between rising and setting, and
again between setting and rising.
[Illustration: FIG. 3.]
Owing to the minuteness of these bodies it is impossible to make any
measures of their diameters. These can be inferred only from their
brightness. Assuming them to be of the same colour as Mars, Lowell
estimates them to be about ten miles for Deimos and somewhat more for
Phobos. But these estimates are uncertain, not only from the somewhat
hypothetical character of the data on which they rest, but from the
difficulty of accurately estimating the brightness of such an object in
the glare of the planet.
A long and careful series of observations was made upon these bodies by
other observers. Later, especially at the very favourable oppositions of
1892 and 1894, observations were made by Hermann Struve at Poulkova, who
subjected all the observations up to 1898 to a very careful discussion.
He showed that the inclination of the planes of the orbits to the
equator of the planet is quite small, thus making it certain that these
two planes can never wander far from each other. In the following
statement of the numerical elements of the entire system, Struve's
results are given for the satellites, while those of Lowell are adopted
for the position of the plane of the equator.
The relations of the several planes can be best conceived by considering
the points at which lines perpendicular to them, or their poles, meet
the celestial sphere. By theory, the pole of the orbital plane of each
satellite revolves round the pole of a certain fixed plane, differing
less from the plane of the equator of Mars the nearer the satellite is
to Mars. Lowell from a combination of his own observations with those
of Schiaparelli, Lohse and Cerulli, found for the pole of the axis of
rotation of Mars[12]:--
R.A. = 317.5°; Dec. = +54.5°; Epoch, 1905.
Tilt[13] of Martian Equator to Martian ecliptic, 23°. 59´. Hermann
Struve, from the observations of the satellites, found theoretically the
following positions of this pole, and of those of the fixed planes of
the satellite orbits for 1900:--
Pole of Mars: R.A. = 317.25° Dec. = 52.63°
Pole of fixed plane for Phobos = 317.24° = 52.64°
Pole of fixed plane for Deimos = 316.20° = 53.37°
Lowell's position of the pole is that now adopted by the British
Nautical Almanac.
The actual positions of the poles of the satellite--orbits revolve
around these poles of the two fixed planes in circles. Putting N for the
right-ascensions of their nodes on the plane of the terrestrial equator,
and J for their angular distance from the north terrestrial pole, N, and
J, for the corresponding poles of the fixed planes, and t for the time
in years after 1900, Struve's results are:--
Deimos.
N1 = 46°.12´ + 0.463´ t; J =36°.42´ - 0.24´ t
(N - N1) sin J = 97.6´ sin (356.8° - 6.375° t)
J - J1 = 97.6 cos (356.8° - 6.375° t)
Phobos.
N1 = 47° 14.3´ + 0.46´ t; J1 = 37° 21.9´ - 0.24´ t
(N - N1) sin J = 53.1´ sin (257°.1´ - 158.0° t)
J - J1 = 53.1´ cos (257°1´ - 158.0 t)