Great Astronomers - Robert Stawell Ball (the little red hen ebook .TXT) 📗

would happen

at a thousand miles, or at hundreds of thousands of miles. No

doubt the intensity of the attraction becomes weaker with every

increase in the altitude, but that action would still exist to

some extent, however lofty might be the elevation which had been

attained.

 

It then occurred to Newton, that though the moon is at a distance

of two hundred and forty thousand miles from the earth, yet the

attractive power of the earth must extend to the moon. He was

particularly led to think of the moon in this connection, not only

because the moon is so much closer to the earth than are any other

celestial bodies, but also because the moon is an appendage to the

earth, always revolving around it. The moon is certainly

attracted to the earth, and yet the moon does not fall down; how

is this to be accounted for? The explanation was to be found in

the character of the moon’s present motion. If the moon were left

for a moment at rest, there can be no doubt that the attraction of

the earth would begin to draw the lunar globe in towards our globe.

In the course of a few days our satellite would come down on the

earth with a most fearful crash. This catastrophe is averted by

the circumstance that the moon has a movement of revolution around

the earth. Newton was able to calculate from the known laws of

mechanics, which he had himself been mainly instrumental in

discovering, what the attractive power of the earth must be, so

that the moon shall move precisely as we find it to move. It then

appeared that the very power which makes an apple fall at the

earth’s surface is the power which guides the moon in its orbit.

 

[PLATE: SIR ISAAC NEWTON’S TELESCOPE.]

 

Once this step had been taken, the whole scheme of the universe

might almost be said to have become unrolled before the eye of the

philosopher. It was natural to suppose that just as the moon

was guided and controlled by the attraction of the earth, so the

earth itself, in the course of its great annual progress, should

be guided and controlled by the supreme attractive power of the

sun. If this were so with regard to the earth, then it would be

impossible to doubt that in the same way the movements of the

planets could be explained to be consequences of solar attraction.

 

It was at this point that the great laws of Kepler became

especially significant. Kepler had shown how each of the planets

revolves in an ellipse around the sun, which is situated on one of

the foci. This discovery had been arrived at from the

interpretation of observations. Kepler had himself assigned no

reason why the orbit of a planet should be an ellipse rather than

any other of the infinite number of closed curves which might be

traced around the sun. Kepler had also shown, and here again he

was merely deducing the results from observation, that when the

movements of two planets were compared together, the squares of

the periodic times in which each planet revolved were proportional

to the cubes of their mean distances from the sun. This also

Kepler merely knew to be true as a fact, he gave no demonstration of

the reason why nature should have adopted this particular relation

between the distance and the periodic time rather than any other.

Then, too, there was the law by which Kepler with unparalleled

ingenuity, explained the way in which the velocity of a planet

varies at the different points of its track, when he showed how

the line drawn from the sun to the planet described equal areas

around the sun in equal times. These were the materials with

which Newton set to work. He proposed to infer from these the

actual laws regulating the force by which the sun guides the

planets. Here it was that his sublime mathematical genius came

into play. Step by step Newton advanced until he had completely

accounted for all the phenomena.

 

In the first place, he showed that as the planet describes equal

areas in equal times about the sun, the attractive force which the

sun exerts upon it must necessarily be directed in a straight line

towards the sun itself. He also demonstrated the converse truth,

that whatever be the nature of the force which emanated from a

sun, yet so long as that force was directed through the sun’s

centre, any body which revolved around it must describe equal

areas in equal times, and this it must do, whatever be the actual

character of the law according to which the intensity of the force

varies at different parts of the planet’s journey. Thus the first

advance was taken in the exposition of the scheme of the universe.

 

The next step was to determine the law according to which the

force thus proved to reside in the sun varied with the distance of

the planet. Newton presently showed by a most superb effort of

mathematical reasoning, that if the orbit of a planet were an

ellipse and if the sun were at one of the foci of that ellipse,

the intensity of the attractive force must vary inversely as the

square of the planet’s distance. If the law had any other

expression than the inverse square of the distance, then the orbit

which the planet must follow would not be an ellipse; or if

an ellipse, it would, at all events, not have the sun in the

focus. Hence he was able to show from Kepler’s laws alone that

the force which guided the planets was an attractive power

emanating from the sun, and that the intensity of this attractive

power varied with the inverse square of the distance between the

two bodies.

 

These circumstances being known, it was then easy to show that the

last of Kepler’s three laws must necessarily follow. If a number

of planets were revolving around the sun, then supposing the

materials of all these bodies were equally affected by

gravitation, it can be demonstrated that the square of the

periodic time in which each planet completes its orbit is

proportional to the cube of the greatest diameter in that orbit.

 

[PLATE: SIR ISAAC NEWTON’S ASTROLABE.]

 

These superb discoveries were, however, but the starting point

from which Newton entered on a series of researches, which

disclosed many of the profoundest secrets in the scheme of

celestial mechanics. His natural insight showed that not only

large masses like the sun and the earth, and the moon, attract

each other, but that every particle in the universe must attract

every other particle with a force which varies inversely as the

square of the distance between them. If, for example, the two

particles were placed twice as far apart, then the intensity of

the force which sought to bring them together would be reduced to

one-fourth. If two particles, originally ten miles asunder,

attracted each other with a certain force, then, when the distance

was reduced to one mile, the intensity of the attraction between

the two particles would be increased one-hundred-fold. This

fertile principle extends throughout the whole of nature. In some

cases, however, the calculation of its effect upon the actual

problems of nature would be hardly possible, were it not for

another discovery which Newton’s genius enabled him to accomplish.

In the case of two globes like the earth and the moon, we must

remember that we are dealing not with particles, but with two

mighty masses of matter, each composed of innumerable myriads of

particles. Every particle in the earth does attract every

particle in the moon with a force which varies inversely as the

square of their distance. The calculation of such attractions is

rendered feasible by the following principle. Assuming that the

earth consists of materials symmetrically arranged in shells

of varying densities, we may then, in calculating its attraction,

regard the whole mass of the globe as concentrated at its centre.

Similarly we may regard the moon as concentrated at the centre of

its mass. In this way the earth and the moon can both be regarded

as particles in point of size, each particle having, however, the

entire mass of the corresponding globe. The attraction of one

particle for another is a much more simple matter to investigate

than the attraction of the myriad different points of the earth

upon the myriad different points of the moon.

 

Many great discoveries now crowded in upon Newton. He first of

all gave the explanation of the tides that ebb and flow around

our shores. Even in the earliest times the tides had been shown

to be related to the moon. It was noticed that the tides were

specially high during full moon or during new moon, and this

circumstance obviously pointed to the existence of some connection

between the moon and these movements of the water, though as to

what that connection was no one had any accurate conception until

Newton announced the law of gravitation. Newton then made

it plain that the rise and fall of the water was simply a

consequence of the attractive power which the moon exerted

upon the oceans lying upon our globe. He showed also that

to a certain extent the sun produces tides, and he was able

to explain how it was that when the sun and the moon both

conspire, the joint result was to produce especially high

tides, which we call “spring tides”; whereas if the solar

tide was low, while the lunar tide was high, then we had the

phenomenon of “neap” tides.

 

But perhaps the most signal of Newton’s applications of the

law of gravitation was connected with certain irregularities

in the movements of the moon. In its orbit round the earth

our satellite is, of course, mainly guided by the great

attraction of our globe. If there were no other body in the

universe, then the centre of the moon must necessarily perform an

ellipse, and the centre of the earth would lie in the focus of

that ellipse. Nature, however, does not allow the movements to

possess the simplicity which this arrangement would imply, for the

sun is present as a source of disturbance. The sun attracts the

moon, and the sun attracts the earth, but in different degrees,

and the consequence is that the moon’s movement with regard to the

earth is seriously affected by the influence of the sun. It is

not allowed to move exactly in an ellipse, nor is the earth

exactly in the focus. How great was Newton’s achievement in the

solution of this problem will be appreciated if we realise that he

not only had to determine from the law of gravitation the nature

of the disturbance of the moon, but he had actually to construct

the mathematical tools by which alone such calculations could be

effected.

 

The resources of Newton’s genius seemed, however, to prove

equal to almost any demand that could be made upon it. He saw

that each planet must disturb the other, and in that way he was

able to render a satisfactory account of certain phenomena which

had perplexed all preceding investigators. That mysterious

movement by which the pole of the earth sways about among the

stars had been long an unsolved enigma, but Newton showed that the

moon grasped with its attraction the protuberant mass at the

equatorial regions of the earth, and thus tilted the earth’s

axis in a way that accounted for the phenomenon which had been

known but had never been explained for two thousand years. All

these discoveries were brought together in that immortal work,

Newton’s Principia.”

 

Down to the year 1687, when the “Principia” was published, Newton

had lived the life of a recluse at Cambridge, being entirely

occupied with those transcendent researches