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of the dots are stars. Although they look as ïf they are packed solid toward the
center, that is due to the fallibility of our instruments. Actually, the distances
between even the centermost stars are very great and they very rarely collide.
There are more stars in the Interior than farther out, and as we move outward
there are fewer and fewer. It is obvious that there is an attraction among these
stars. It is clear that gravitation exists at these enormous dimensions, perhaps
100,000 times the size of the solar system. Let us now go further, and look at an
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Fig. 7-9. A galaxy.
cntire galaz, shown in Fìg. 7-9. 'The shape of this galaxy indicates an obvious
tendency for its matter to agglomerate. OÝ course we cannot prove that the
law here is precisely Inverse square, only that there ¡s still an attraction, at this
enormous dimension, that holds the whole thing together. One may say, “Well,
that is all very clever but why is it not Just a ball?” Because it is sp#mn#ng and
has angular rmnormmnentưm which it cannot give up as it contracts; it must contract
mostly in a plane. (Incidentally, if you are looking for a good problem, the
exact details of how the arms are formed and what determines the shapes of
these galaxies has not been worked out.) It is, however, clear that the shape of
the galaxy is due to gravitation even though the complexities of its structure
have not yet allowed us to analyze it completely. In a galaxy we have a scale
of perhaps 50,000 to 100,000 light years. The earth's distance from the sun 1s
8 light mưnutes, so you can see how large these dimensions are.
Gravity appears to exist at even bigger dimensions, as indicated by Fig. 7-10,
which shows many “little” things clustered together. This is a clusfer oƒ galazies,
Just like a star cluster. Thus galaxies attract each other at such distances that
they too are agglomerated into clusters. Perhaps gravitation exists even OVer
distances of tens oƒ mmillions of light years; so far as we now know, gravity seems
to go out forever inversely as the square of the distanee.
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Fig. 7-10. A cluster of galaxies.
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Fig. 7-11. An interstellar dust cloud.
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Fig. 7-12. The formation of new stars?
Not only can we understand the nebulae, but from the law of gravitation we
can even get some ideas about the origin of the stars. If we have a big cloud of
dust and gas, as indicated in Eig. 7-11, the gravitational attractions of the pieces
of dust for one another might make them form little lumps. Barely visible in the
figure are “little” black spots which may be the beginning of the accumulations
of dust and gases which, due to their gravitation, begin to form stars. Whether
we have ever seen a star form or not is still debatable. Figure 7-12 shows the one
piece of evidence which suggests that we have. At the left is a picture oŸ a region
of gas with some stars in it taken in 1947, and at the right is another picture,
taken only 7 years later, which shows two new bright spots. Has gas accumulated,
has gravity acted hard enough and collected it into a ball big enough that the
stellar nuclear reaction starts in the interior and turns ¡it into a star? Perhaps,
and perhaps not. Ït is unreasonable that in only seven years we should be so
lucky as to see a star change itself into visible form; it is much less probable that
we should see #of
7-6 Cavendish°s experiment
Gravitation, therefore, extends over enormous distances. But ï1f there is a
force bebween ønw pair of objects, we ought to be able to measure the force
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bebween our own objects. Instead of having to watch the stars go around each
other, why can we not take a ball of lead and a marble and watch the marble go
toward the ball of lead? 'Phe difficulty of this experiment when done in such a
simple manner is the very weakness or delicacy of the force. It must be done with
extreme care, which means covering the apparatus to keep the air out, making
sure it is not electrically charged, and so on; then the force can be measured.
lt was first measured by Cavendish with an apparatus which is schematically
indicated in Eig. 7-13. 'This ñrst demonstrated the direct force bebween ©wo large,
fñxed balls of lead and two smaller balls of lead on the ends of an arm supported
by a very fñne fñber, called a torsion fber. By measuring how much the fñber
gets twisted, one can measure the strength of the force, verify that it is inversely
proportional to the square of the distance, and determine how strong it is. Thus,
one may accurately determine the coefficient G in the formula
AII the masses and distances are known. You say, “We knew it already for
the earth” Yes, but we did not know the rmass of the earth. By knowing G
from this experiment and by knowing how strongly the earth attracts, we can
indirectly learn how great is the mass of the earthl "This experiment has been
called “weighing the earth” by some people, and it can be used to determine the
coefficient G of the gravity law. 'This is the only way in which the mass of the
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Fig. 7-13. A simplified diagram of the apparatus used by Cavendish to
verify the law of universal gravitation for small objects and to measure
the gravitational constant G.
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earth can be determined. Πturns out to be
6.670 x 10~!! newton - m”/kgŸ.
Tt is hard to exaggerate the importance of the efect on the history of sclence
produced by this great success of the theory of gravitation. Compare the confusion,
the lack of confidence, the ineomplete knowledge that prevailed in the earlier ages,
when there were endless debates and paradoxes, with the clarity and simplicity
of this law—this fact that all the moons and planets and stars have such a sữmnpÏle
ruïe to govern them, and further that man could understønd it and deduce how
the planets should movel "This is the reason for the success of the sciences in
following years, for it gave hope that the other phenomena of the world might
also have such beautifully simple laws.
7-7 What is gravity?
But is this such a simple law? What about the machinery ofit? All we have