It was by the observations of a celebrated old astronomer, named Tycho
Brahe, that the true shape of a planet’s path came to be afterwards
determined. Tycho lived in days before telescopes were invented. He had
few of the excellent contrivances for measuring which we have in our
observatories. We shall take a look at this fine old astronomer, as he
sits amid his curious astronomical machines.
[Illustration: FIG. 56.--Tycho Brahe in his Observatory.]
He lived on an island near Copenhagen, and he has given us a picture
of himself (Fig. 56), as he is seated with his quaint apparatus, and
his assistants around him, busily engaged in observing the heavens.
You see the walls of his observatory are decorated with pictures; and
one of the great Danish hounds which the King of Denmark had presented
to him lies asleep at his feet. I do not think we should now encourage
big dogs in the observatory at night. Nor do modern astronomers put on
their velvet robes of state, as Tycho was said to have done when he
entered into the presence of the stars, as, by so doing, he showed his
respect for the heavens. Astronomers, nowadays, rather prefer to wear
some comfortable coat which shall keep out the cold, no matter what may
be its appearance from the picturesque point of view. In this wonderful
contrivance, you see Tycho Brahe did not use any actual telescope. He
observed through a small opening in the wall, and lest there should be
any mistake as to what is going on, you see he is pointing towards it,
and giving his three assistants their instructions. The most important
work is being done by the man on the right. He is engaged in making the
actual observation. But he has no aid from magnifying lenses. All he
can do is to slide a pointer up or down till it is just in line with
the planet or star as he sees it through the hole opposite.
On the circle a number of marks have been engraved, and there are
numbers placed opposite to the marks; it is by these that the position
of the object is to be ascertained. If the object is high, then the
pointer will be low; and if the object is low, then the pointer will
be high. The observer calls out the position when he has found it, and
there, you see, is a man ready with writing materials to take down
the observation. Notice also the other astronomer who is looking at
the clock. He gives the time, which must also be recorded accurately.
In fact, the entire process of finding the place of a heavenly body
consists in two observations--one from the circle and the other from
the clock; so that though Tycho had no telescope to aid his vision, yet
the principle on which his work was done was the same as that which we
use in our observatories at this moment.
You may think that such a concern would hardly be capable of producing
much reliable work. However, Tycho compensated in a great degree for
the imperfection of his instrument by the skill with which he used it.
He had a noble determination to do his very best. Perseverance will
accomplish wonders even with very imperfect means. A great astronomer
has said that a skilful observer ought to be able to make valuable
measurements with a common cart-wheel!
It was with instruments on the principle of that which I have here
shown that Tycho made his celebrated observations of Mars. Week
after week, month after month, year after year, did the patient old
astronomer track the planet through his capricious wanderings.
Before we try to explain anything, it is of course necessary to
ascertain, with all available accuracy, what the thing actually is.
Therefore, when we seek to explain the irregular movements of a planet,
the first thing to be done is to make a careful examination of the
nature of those irregularities. And this was what Tycho strove to do
with the best means at his disposal.
The full benefit of Tycho’s work was realized by Kepler when he
commenced to search out the kind of figure in which Mars was moving.
First he tried various circles, and then he sought, by placing the
centre in different positions, to see whether it would not be possible
to account thus for the irregularities of the wayward planet. It would
not do; the movement was not circular. This was thought very strange
in those days, for the circle was regarded as the only perfect curve,
and it was considered quite impossible for a planet to have any motion
except it were the most perfect. There was, however, no help for
it; so Kepler sagaciously tried the ellipse, which he considered to
be the most perfect curve next to the circle. He continued his long
calculations, until at last he succeeded in finding one particular
ellipse, placed in one particular position, which would just explain
the strange wanderings of our erratic neighbor. It was not alone
that the motion of the planet traced out an ellipse; it was further
discovered that the sun lies at one of the foci of the curve. If the
sun were anywhere else, the motion of the planet would have been
different from that which Tycho had found it to be.
You must know that this discovery is one of the very greatest that
have ever been made in the whole extent of human knowledge. After it
had been proved that the orbit of Mars was elliptic, it became plain
that the same path must be traced by every planet. There are very big
planets, and there are small ones; there are planets which move in
very large orbits, and there are planets whose paths are comparatively
small. In all cases the high road which the planet follows is
invariably an ellipse, and the sun is invariably to be found situated
at the focus. It is surely interesting to find that these beautiful
ellipses which we can draw so simply with a piece of twine and a pencil
should be also the very same figures which our great earth and all the
other bodies which revolve around the sun are ever compelled to follow.
Kepler also made another great discovery in connection with the same
subject. If the planet moved in a circle with the sun in the centre,
then there would be very good reason to expect that it would always
move at the same speed, for there would be no reason why it should go
faster at one place than at another. In fact, the planet would then be
revolving always at the same distance from the sun, and every part of
its path would be exactly like every other part. But when we consider
that the motion is performed in an ellipse, so that the planet is
curving round more rapidly at the extremities of its path than in the
other parts where the curvature is less perceptible, we have no reason
to expect that the speed shall remain the same all round.
We know that the engine-driver of a railway train always has to slacken
speed when he is going round a sharp curve. If he did not do so, his
train would be very likely to run off the line, and a dreadful accident
would follow. The engine-driver is well aware that the conditions of
pace are dependent on the curvature of his line. The planet finds that
it, too, must pay attention to the curves; but the extraordinary
point is that the planet acts exactly in the opposite way to the
engine-driver. The planet puts on its highest pace at one of the most
critical curves in the whole journey. There are two specially sharp
curves in the planet’s path. These are, of course, the two extremities
of the ellipse which it follows. The cautious engine-driver would, of
course, creep round these with equal care, and no doubt the planet
goes slowly enough about that end of the ellipse which is farthest
from the sun. There its pace is slower than anywhere else; but from
that moment onwards the planet steadily applies itself to getting
up more and more speed. As it traverses the comparatively straight
portion of the celestial road, the pace is ever accelerating until the
sharp curve near the sun is being approached; then the velocity gets
more and more alarming, until at last, in utter defiance of all rules
of engine-driving, the planet rushes round one of the worst parts of
the orbit at the highest possible speed. And yet no accident happens,
though the planet has no nicely laid lines to keep it on the track.
If lines are necessary to save a railway train from destruction, how
can we possibly escape when we have no similar assistance to keep us
from flying away from the sun and off into infinite space? Kepler
has taught us to measure the changes in the speed of the body with
precision. He has shown that the planet must, at every point of its
long journey, possess exactly the right speed; otherwise everything
would go wrong. I dare say you have seen, at different points along
a line of railway, boards put up here and there, with notices like,
“Ten miles an hour.” These words are, of course, an intimation to the
engine-driver that he is not to vary from the speed thus stated. Kepler
has given us a law which is equivalent to a large number of caution
boards, fixed all round the planet’s path, indicating the safe speed
for the journey at every stage. It is fortunate for us that the planet
is careful to observe these regulations. If the earth were to leave
her track, the consequences would be far worse than those of the most
frightful railway accident that ever happened. Whichever side we took
would be almost equally disastrous. If we went inwards we should plunge
into the sun, and if we went outwards we should be frozen by cold.
We owe our safety to the care with which the speed of the earth is
prescribed. When near the sun, the earth is pulled inwards with
exceptionally strong attraction. We are often told that when a strong
temptation seizes us, the wisest thing that we can do is to run away
as hard as possible. This is just what the laws of dynamics cause the
earth to do at this critical time. She puts on her very best pace, and
only slackens when she has got well away from the danger.
The peril that we are exposed to when the earth is at the other end
of the orbit is of an opposite character. We are then a long way
from the sun, and the pull which it can exercise upon the earth is
correspondingly lessened. Care is then required lest we should escape
altogether from the sun’s warmth and his guidance. We must therefore
give time to the sun to exercise his power, so as to enable the earth
to be recalled; accordingly we move as slowly as possible until the
sun conquers the earth’s disposition to fly off, and we begin to return.
You may remember that when we were speaking about the moon, I showed
you how a body might revolve around the earth in a circle under the
influence of an attraction towards the earth’s centre. So long as the
path is really a circle, then the power with which the earth is drawing
the body remains the same. In a precisely similar way, a body could
revolve around the sun in a circle, in which case also the attraction
of the sun will remain the same all round. But now we have a very much
more difficult case to consider. If the body does not always remain at
the same distance, the power of the sun will not be the same at the
different places. Whenever the object is near the sun, the attraction
will be greater than when it is farther off. For example, when the
distance between the two bodies is doubled, then the pull is reduced to
the fourth part of what it was before.