The path of the earth lies between the orbits of the planets Venus and
Mars. It is natural for us to endeavor to learn what we can about our
neighbors. We ought to know something, at all events, as to the people
who live next door to us on each side. I have, however, already said
that we cannot observe very much upon Venus. The case is very different
with respect to Mars. He is a planet which we are fortunately enabled
to study minutely, and he is full of interest when we examine him
through a good telescope.
The right season for observing Mars must, of course, be awaited, as he
is not always visible. Such seasons recur about every two years, and
then for months together Mars will be a brilliant object in the skies
every night. Nor has Mars necessarily to be sought in the early morn or
immediately after sunset, in the manner we have already described for
Venus and Mercury. At the time Mars is at his best he comes into the
highest position at midnight, and he can generally be seen for hours
before, and be followed for hours subsequently. You may, however, find
some difficulty in recognizing him. You probably would not at first be
able to distinguish Mars from a fixed star. No doubt this planet is a
ruddy object, but some stars are also ruddy, and this is at the best a
very insecure characteristic for identification. I cannot give you any
more general directions, except that you should get your papa to point
out Mars to you the next time it is visible. It is just conceivable
that papa himself might not know how to find Mars. If so, the sooner he
gets a set of star maps and begins to teach himself and to teach you,
the better it will be for you both.
Mars, though apparently so like a star, differs in some essential
points from any star in the sky. The stars proper are all fixed in the
constellations, and they never change their relative positions. The
groups which form the Great Bear or the Belt of Orion do not alter,
they are just the same now as they were centuries ago. But the case is
very different with a planet such as Mars. The very word planet means a
_wanderer_, and it is justly applied, because Mars, instead of staying
permanently in any one constellation, goes constantly roaming from one
group to the other. He is a very restless body; sometimes he pays his
respects to the heavenly Twins, and is found near Castor and Pollux in
Gemini, then he goes off and has a brief sojourn with the Bull, but it
looks as if that fierce animal got tired of his company and hunted
him off to the Lion. His quarters then become still more critical.
Sometimes it looks as if he desired to seek for peace beneath the
waters, and so he visits Aquarius, while at other times he is found in
dangerous proximity to the claws of the Crab.
Mars cannot even make up his mind to run steadily round the heavens in
one direction; sometimes he will bolt off rapidly, then pause for a
while, and turn back again; then the original impulse will return, and
he will resume his journey in the direction he at first intended. It
is no wonder that I am not able to give you very explicit directions
as to how you may secure a sight of a truant whose wanderings are
apparently so uncertain. Yet there is a definite order underlying all
his movements. Astronomers, who make it their business to study the
movements of Mars, can follow him on his way; they know exactly where
he is now, and where he will be every night for years and years to
come. The people who make the almanacs come to the astronomers and get
hints from them as to what Mars intends to do, so that the almanacs
announce the positions in which the planet will be found with as much
regularity as if he was in the habit of behaving with the orderly
propriety of the sun or the moon.
We must not lay all the blame on Mars for the eccentricities of his
movements. Our earth is to a very large extent responsible. What we
think to be Mars’ vagaries are often to be explained by the fact that
we ourselves on the earth are rapidly shifting about and altering our
point of view.
[Illustration: FIG. 52.--How the Tree seems to move about.]
I was driving down a pretty country road with a little girl three years
old beside me, when I was addressed with the little remark, “Look at
the tree going about in the field.” Now, you or I, with our longer
experience of the world around us, know that it is not the custom of
trees to take themselves up and walk about the fields. But this was
what this little girl saw, or rather what she thought she saw; and very
often what we do see is something very different from what we think we
see. We think we see Mars performing all these extraordinary movements,
as the little girl thought she saw the tree moving about. But just as
that little girl, when she grew to be a big girl, found that what she
thought was a tree walking across the field must really have some quite
different explanation, so we, too, find that what Mars seems to do is
one thing, and what Mars actually does is quite another thing.
Let us see what the little girl noticed. She was looking at the tree,
and first she saw it on one side of the house, and then she saw it on
the opposite side (Fig. 52). If it had been a cow instead of a tree, of
course the natural supposition would have been that the cow had walked.
Our little friend may, perhaps, have thought it unusual for a tree to
walk, but still she saw the undoubted fact that the tree had shifted to
the other side of the house, and therefore, perhaps, remembering what
the cow could do, she said the tree had moved.
[Illustration: FIG. 53.--A Specimen of the Track of Mars.]
The little girl did not stop to reflect that she herself had entirely
changed her position, and hence arose the surprising phenomenon of a
tree that could move about. You will understand this, at once, from the
two positions of the car here shown. In the first position, as the girl
looks at the tree, the dotted line shows the direction of her glance,
and the other dotted line shows how the apparent places of the tree and
the house have altered. It is her change of place that has accomplished
the transformation. Observe also that the tree appeared to her to move
in the direction opposite to that in which she is going.
Mars generally appears to move round among the stars from west to east.
In fact, if we were viewing him from the sun he would always seem to
move in this manner. But at certain seasons our earth is moving very
fast past Mars, and this will make him appear to move in the opposite
direction. This apparent motion is sometimes so much in excess of his
real motion, that it may give us an entirely incorrect idea of what the
planet is actually doing.
Thus, notwithstanding that Mars is moving one way, he may appear to us
who dwell on the earth to be going in the opposite way. This illusion
only happens for a short time, just when we are passing Mars, as we
do every two years. The effect on the planet is to make the path he
pursues at this time something like that shown in Fig. 53. The planet
is nearest to us at the time he is moving in this loop. He is then
to be seen at his best in the telescope, so that it is especially
interesting to watch Mars through this critical part of his career.
I want to show you how to make a little calculation which will explain
the law by which the seasons when we can see Mars best will follow
each other. The period he requires for a voyage round the sun is not
quite two years, for that would be 730 days, and Mars only takes 687
days for his journey. It is, however, true that 1-15/17 years is very
nearly the period of Mars. Hence, every 32 years Mars will complete 17
rounds. From this we shall be able to see how long it will take after
the earth once passes Mars before they pass again. I shall suppose
there is a circular course, around which two boys start together to
run a race. One of these boys is such a good runner that he will get
quite round in 17 minutes; but the other boy can hardly run more than
half as quickly, for he will require 32 minutes to complete one circle.
Here then is the question. Suppose the two boys to start together: how
long will it be before the faster runner gains one complete circuit on
the other? By the time the good runner (A) has completed one circuit,
the bad runner (B) has only got a little more than halfway. When A
has completed his second circuit, he has, of course, run for twice
17 minutes--that is, for 34 minutes. This is two minutes longer than
the time B requires to get round once; therefore B is only ahead by
a distance which A could cover in about one minute; but B will have
advanced during this minute a distance for which A will require another
half-minute, during which B covers a distance for which A will need a
further quarter, and so on. But all these intervals--one minute, half
a minute, a quarter of a minute, one-eighth, one-sixteenth, and so
on--added together amount to two minutes, and hence it follows that B
will not be overtaken until about two minutes after A has completed his
second round--that is, in 36 minutes altogether.
We can pass from this illustration to the case of the planet Mars
and the earth. The orbit of the earth is traversed in a year, and
therefore, after the earth has once passed Mars, which is then, as
astronomers would say, in _opposition_, about two years and the eighth
of a year--that is, two years and six or seven weeks--will elapse
before Mars is again favorably placed. You will thus see that we need
not expect to observe Mars under the best conditions every year.
Besides, the distance of the planet from the earth at opposition
varies so greatly that some oppositions are more favorable than others.
The time has come when I must tell you something about the shapes
of the paths in which the earth and the other planets perform their
great journeys round the sun. Perhaps you will think that I am going
to contradict some of the things that I have told you before. I have
often represented the orbits of the planets as circles, and now I am
going to tell you that this is not correct. The fact is that the paths
are nearly circles; but, still, there is some departure from the exact
circular shape. Mars, in particular, moves in a path which is more
different from a circle than the path of the earth, and consequently it
is appropriate to introduce this subject when we are engaged about Mars.
[Illustration: FIG. 54.--How to draw an Ellipse.]
We must first take another lesson in drawing, and the appliances I
want you to use for the purpose are very simple. You must have a smooth
board and some tacks or drawing-pins, besides paper, pencil, and twine.
[Illustration: FIG. 55.--Specimens of Ellipses.]
We first lay a sheet of paper on the board, and then put in two tacks
through the paper and into the board. It does not much matter where
we put them in. Next we take a piece of twine and tie the two ends
together so as to form a loop, which we pass round the two tacks
(Fig. 54). In the loop I place the pencil, and then you see I move it
round, taking care to keep the twine stretched. Thus I produce a pretty
curve, which we call the ellipse. I must ask all of you to practise
this experiment. Try with different lengths of string, and try using
different distances between the tacks. Here are some sketches of two
shapes of ellipse and a parabola (Fig. 55). Elliptic curves can be made
almost circles by putting the two tacks close together, or they can be
made very long in comparison with their width. They are all pretty and
graceful figures, and are often useful for ornamental work. The ellipse
is a pretty shape for beds of flowers in a grass-plot.
The importance of the ellipse to astronomers is greater than that of
any other geometrical figure. In fact, all the planets, as they perform
their long and unceasing journeys round the sun, move in ellipses; and
though it is true that these ellipses are very nearly circles, yet the
difference is quite appreciable.
It is also important to observe that the sun is not in the centre
of the ellipse which the planet describes. The sun is nearer to one
end than to the other. And the actual position of the sun must be
particularly noted. Suppose that some mighty giant were preparing to
draw an exact path for the earth, or for Mars, of course he would
want to have millions of miles of string for producing a big enough
curve, and one of the nails that he used would have to be driven right
into the sun. The following is the astronomer’s more accurate method
of stating the facts. He calls each of the points represented by the
tacks around which the string is looped a _focus_ of the ellipse; the
two points together are said to be the _foci_; and as the planet is
describing its orbit, the position of the sun will lie exactly at one
of the foci.
The ellipse is a curve that nature is very fond of reproducing. From
an electric light, a brilliant beam will diverge. If you hold a globe
in the beam, and let the shadow fall on a sheet of paper, it forms an
ellipse. If you hold the sheet squarely, the shadow is a circle; but as
you incline it, you obtain a beautiful oval, and by gradually altering
the position, you can get a greatly elongated curve. Indeed, you can
thus produce an ellipse of almost any form. The electric light is not
indispensable for this purpose; any ordinary bright lamp with a small
flame will answer, and by taking different sized balls and putting them
in various positions, you can make many ellipses, great and small.