AFTER NEWTON
We have said that practically all the motions in the solar system have
been accounted for by the Newtonian law of gravitation. It will be of
interest to inquire into the instances that lead to qualification of
this absolute statement.
One relates to the planet Mercury, whose orbit or path round the sun is
the most elliptical of all the planetary orbits. This will be explained
a little later.
The moon has given the mathematical astronomers more trouble than any
other of the celestial bodies, for one reason because it is nearest to
us and very minute deviations in its motion are therefore detectible.
Halley it was who ascertained two centuries ago that the moon's motion
round the earth was not uniform, but subject to a slight acceleration
which greatly puzzled Lagrange and Laplace, because they had proved
exactly this sort of thing to be impossible, unless indeed the body in
question should be acted on by some other force than gravitation. But
Laplace finally traced the cause to the secular or very slow reduction
in the eccentricity of the earth's own orbit. The sun's action on the
moon was indeed progressively changing from century to century in such
manner as to accelerate the moon's own motion in its orbit round the
earth.
Adams, the eminent English astronomer, revised the calculations of
Laplace, and found the effect in question only half as great as Laplace
had done; and for years a great mathematical battle was on between the
greatest of astronomical experts in this field of research. Adams, in
conjunction with Delaunay, the greatest of the French mathematicians a
half century ago, won the battle in so far as the mathematical
calculations were concerned; but the moon continues to the present day
her slight and perplexing deviation, as if perhaps our standard
time-keeper, the earth, by its rotation round its axis, were itself
subject to variation. Although many investigations have been made of the
uniformity of the earth's rotation, no such irregularity has been
detected, and this unexplained variation of the moon's motion is one of
the unsolved problems of the gravitational astronomer of to-day.
But we are passing over the most impressive of all the earlier
researches of Lagrange and Laplace, which concerned the exceedingly slow
changes, technically called the secular variations of the elements of
the planetary orbits. These elements are geometrical relations which
indicate the form of the orbit, the size of the orbit, and its position
in space; and it was found that none of these relations or quantities
are constant in amount or direction, but that all, with but one
exception, are subject to very slow, or secular, change, or oscillation.
This question assumed an alarming significance at an early day,
particularly as it affected the eccentricity of the earth's orbit round
the sun. Should it be possible for this element to go on increasing for
indefinite ages, clearly the earth's orbit would become more and more
elliptical, and the sun would come nearer and nearer at perihelion, and
the earth would drift farther and farther from the sun at aphelion,
until the extremes of temperature would bring all forms of life on the
earth to an end. The refined and powerful analysis of Lagrange, however,
soon allayed the fears of humanity by accounting for these slow
progressive changes as merely part of the regular system of mere
oscillations, in entire accord with the operation of the law of
gravitation; and extending throughout the entire planetary system.
Indeed, the periods of these oscillations were so vast that none of them
were shorter than 50,000 years, while they ranged up to two million
years in length--"great clocks of eternity which beat ages as ours beat
seconds."
About a century ago, an eminent lecturer on astronomy told his audience
that the problem of weighing the planets might readily be one that would
seem wholly impossible to solve. To measure their sizes and distances
might well be done, but actually to ascertain how many tons they
weigh--never!
Yet if a planet is fortunate enough to have one satellite or more, the
astronomer's method of weighing the planet is exceedingly simple; and
all the major planets have satellites except the two interior ones,
Mercury and Venus. As the satellite travels round its primary, just as
the moon does round the earth, two elements of its orbit need to be
ascertained, and only two. First, the mean distance of the satellite
from its primary, and second the time of revolution round it.
Now it is simply a case of applying Kepler's third law. First take the
cube of the satellite's distance and divide it by the square of the
time of revolution. Similarly take the cube of the planet's distance
from the sun and divide by the square of the planet's time of revolution
round him. The proportion, then, of the first quotient to the second
shows the relation of the mass (that is the weight) of the planet to
that of the sun. In the case of Jupiter, we should find it to be 1,050,
in that of Saturn 3,500, and so on.
The range of planetary masses, in fact, is very curious, and is
doubtless of much significance in the cosmogony, with which we deal
later. If we consider the sun and his eight planets, the mass or weight
of each of the nine bodies far exceeds the combined mass of all the
others which are lighter than itself.
To illustrate: suppose we take as our unit of weight the one-billionth
part of the sun's weight; then the planets in the order of their masses
will be Mercury, Mars, Venus, Earth, Uranus, Neptune, Saturn, and
Jupiter. According to their relative masses, then, Mercury being a
five-millionth part the weight of the sun will be represented by 200;
similarly Venus, a four hundred and twenty-five thousandth part by
2,350, and so on. Then we have
Mercury 200
Mars 340
------
Sum of weights of Mercury and Mars 540
Venus 2,350
------
Sum of weights of Mercury, Mars, and Venus 2,890
The Earth 3,060
------
Sum of weights of four inner planets 5,950
Uranus 44,250
------
Sum of weights of five planets 50,200
Neptune 51,600
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Sum of weights of six planets 101,800
Saturn 285,580
---------
Sum of weights of seven planets 387,380
Jupiter 954,300
---------
Sum of weights of all the planets 1,341,680
Mass or weight of the sun 1,000,000,000
Curious and interesting it is that Saturn is nearly three times as heavy
as the six lighter planets taken together, Jupiter between two and three
times heavier than all the other planets combined, while the sun's mass
is 750 times that of all the great planets of his system rolled into
one.
All the foregoing masses, except those of Mercury and Venus, are pretty
accurately known because they were found by the satellite method just
indicated. Mercury's mass is found by its disturbing effects on Encke's
comet whenever it approaches very near. The mass of Venus is ascertained
by the perturbations in the orbital motion of the earth. In such cases
the Newtonian law of gravitation forms the basis of the intricate and
tedious calculations necessary to find out the mass by this indirect
method.
Its inferiority to the satellite method was strikingly shown at the
Observatory in Washington soon after the satellites of Mars were
discovered in 1877. The inaccurate mass of that planet, as previously
known by months of computation based upon years and years of
observation, was immediately discarded in favor of the new mass derived
from the distance and period of the outer satellite by only a few
minutes' calculation.
In weighing the planets, astronomers always use the sun as the unit.
What then is the sun's own weight? Obviously the law of gravitation
answers this question, if we compare the sun's attraction with the
earth's at equal distances. First we conceive of the sun's mass as if
all compressed into a globe the size of the earth, and calculate how far
a body at the surface of this globe would fall in one second. The
relation of this number to 16.1 feet, the distance a body falls in one
second on the actual earth, is about 330,000, which is therefore the
number of times the sun's weight exceeds that of the earth.
A word may be added regarding the force of gravitation and what it
really is. As a matter of fact Newton did not concern himself in the
least with this inquiry, and says so very definitely. What he did was to
discover the law according to which gravitation acts everywhere
throughout the solar system. And although many physicists have
endeavored to find out what gravitation really is, its cause is not yet
known. In some manner as yet mysterious it acts instantaneously over
distances great and small alike, and no substance has been found which,
if we interpose it between two bodies, has in any degree the effect of
interrupting their gravitational tendency toward each other.
While the Newtonian law of gravitation has been accepted as true because
it explained and accounted for all the motions of the heavenly bodies,
even including such motions of the stars as have been subjected to
observation, astronomers have for a long time recognized that quite
possibly the law might not be absolutely exact in a mathematical sense,
and that deviations from it would surely make their appearance in time.
A crude instance of this was suggested about a century ago, when the
planet Uranus was found to be deviating from the path marked out for it
by Bouvard's tables based on the Newtonian law; and the theory was
advocated by many astronomers that this law, while operant at the medium
distances from the sun where the planets within Jupiter and Saturn
travel, could not be expected to hold absolutely true at the vast
distance of Uranus and beyond. The discovery of Neptune in 1846,
however, put an end to all such speculation, and has universally been
regarded as an extraordinary verification of the law, as indeed it is.
When, however, Le Verrier investigated the orbit of Mercury he found an
excess of motion in the perihelion point of the planet's orbit which
neither he nor subsequent investigators have been able to account for by
Newtonian gravitation, pure and simple. If Newton's theory is absolutely
true, the excess motion of Mercury's perihelion remains a mystery.
Only one theory has been advanced to account for this discrepancy, and
that is the Einstein theory of gravitation. This ingenious speculation
was first propounded in comprehensive form nearly fifteen years ago, and
its author has developed from it mathematical formulae which appear to
yield results even more precise than those based on the Newtonian
theory.
In expressing the difference between the law of gravitation and his own
conception, Einstein says: "Imagine the earth removed, and in its place
suspended a box as big as a moon or a whole house and inside a man
naturally floating in the center, there being no force whatever pulling
him. Imagine, further, this box being, by a rope or other contrivance,
suddenly jerked to one side, which is scientifically termed 'difform
motion,' as opposed to 'uniform motion.' The person would then naturally
reach bottom on the opposite side. The result would consequently be the
same as if he obeyed Newton's law of gravitation, while, in fact, there
is no gravitation exerted whatever, which proves that difform motion
will in every case produce the same effects as gravitation.... The term
relativity refers to time and space. According to Galileo and Newton,
time and space were absolute entities, and the moving systems of the
universe were dependent on this absolute time and space. On this
conception was built the science of mechanics. The resulting formulas
sufficed for all motions of a slow nature; it was found, however, that
they would not conform to the rapid motions apparent in
electrodynamics.... Briefly the theory of special relativity discards
absolute time and space, and makes them in every instance relative to
moving systems. By this theory all phenomena in electrodynamics, as well
as mechanics, hitherto irreducible by the old formulae, were
satisfactorily explained."
Natural phenomena, then, involving gravitation and inertia, as in the
planetary motions, and electro-magnetic phenomena, including the motion
of light, are to be regarded as interrelated, and not independent of one
another. And the Einstein theory would appear to have received a
striking verification in both these fields. On this theory the
Newtonian dynamics fails when the velocities concerned are a near
approach to that of light. The Newtonian theory, then, is not to be
considered as wrong, but in the light of a first approximation. Applying
the new theory to the case of the motion of Mercury's perihelion, it is
found to account for the excess quite exactly.
On the electro-magnetic side, including also the motion of light, a
total eclipse of the sun affords an especially favorable occasion for
applying the critical test, whether a huge mass like the sun would or
would not deflect toward itself the rays of light from stars passing
close to the edge of its disk, or limb. A total eclipse of exceptional
duration occurred on May 29, 1919, and the two eclipse parties sent out
by the Royal Society of London and the Royal Astronomical Society were
equipped especially with apparatus for making this test. Their stations
were one on the east coast of Brazil and the other on the west coast of
Africa.
Accurate calculation beforehand showed just where the sun would be among
the stars at the time of the eclipse; so that star plates of this region
were taken in England before the expeditions went out. Then, during the
total eclipse, the same regions were photographed with the eclipsed sun
and the corona projected against them. To make doubly sure, the stars
were a third time photographed some weeks after the eclipse, when the
sun had moved away from that particular region.
Measuring up the three sets of plates, it was found that an appreciable
deflection of the light of the stars nearest alongside the sun actually
exists; and the amount of it is such as to afford a fair though not
absolutely exact verification of the theory. The observed deflection
may of course be due to other causes, but the English astronomers
generally regard the near verification as a triumph for the Einstein
theory. Astronomers are already beginning preparations for a repetition
of the eclipse programme with all possible refinement of observation,
when the next total eclipse of the sun occurs, September 20, 1922,
visible in Australia and the islands of the Indian Ocean.
A third test of the theory is perhaps more critical than either of the
others, and this necessitates a displacement of spectral lines in a
gravitational field toward the red end of the spectrum; but the experts
who have so far made measures for detecting such displacement disagree
as to its actual existence. The work of St. John at Mt. Wilson is
unfavorable to the theory, as is that of Evershed of Kodiakanal, who has
made repeated tests on the spectrum of Venus, as well as in the cyanogen
bands of the sun.
The enthusiastic advocates of the Einstein theory hold that, as Newton
proved the three laws of Kepler to be special cases of his general law,
so the "universal relativity theory" will enable eventually the
Newtonian law to be deduced from the Einstein theory. "This is the way
we go on in science, as in everything else," wrote Sir George Airy,
Astronomer Royal; "we have to make out that something is true; then we
find out under certain circumstances that it is not quite true; and then
we have to consider and find out how the departure can be explained."
Meanwhile, the prudent person keeps the open mind.