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direction in space, but again øøw from the center of the earth. The net result is
that we get £ưo tidal bulges.
7-5 Universal gravitation
'What else can we understand when we understand gravity? Everyone knows
the earth is round. Why is the earth round? That is easy; it is due to gravitation.
The earth can be understood to be round merely because everything attracts
everything else and so it has attracted itself together as far as it can! If we go
even further, the earth is not ezøcflu a sphere because it is rotating, and this
brings in centrifugal efects which tend to oppose gravity near the equator. ÏI§
turns out that the earth should be elliptical, and we even get the right shape for
the ellipse. We can thus deduce that the sun, the moon, and the earth should be
(nearly) spheres, Just from the law of gravitation.
'What else can you do with the law of gravitation? If we look at the moons
of Jupiter we can understand everything about the way they move around that
planet. Incidentally, there was once a certain dificulty with the moons oŸ Jupiter
that is worth remarking on. 'Phese satellites were studied very carefully by
Roemer, who noticed that the moons sometimes seemed to be ahead of schedule,
and sometimes behind. (One can ñnd their schedules by waiting a very long tỉme
and fnding out how long ïÈ takes on the average for the moons to go around.)
Now they were øhead when Jupiter was particularly close to the earth and they
were 0ch¿nd when Jupiter was ƒfarther from the earth. This would have been
a very diffcult thing to explain according to the law of gravitation—it would
have been, in fact, the death of this wonderful theory If there were no other
explanation. If a law does not work even in ønwe pÌace where it ought to, it 1s
Just wrong. But the reason for this discrepancy was very simple and beautiful: ït
takes a little while to see the moons of Jupiter because of the time it takes light
to travel from Jupiter to the earth. When Jupiter is closer to the earth the time
1s a little less, and when ït is farther from the earth, the time is more. This is why
mmoons appear to be, on the average, a little ahead or a little behind, depending
--- Trang 148 ---
on whether they are closer to or farther om the earth. 'This phenomenon showed
that light does not travel instantaneously, and furnished the first estimate of the
speed of light. This was done in 1656.
T all of the planets push and pull on each other, the force which controls,
let us say, Jupiter in going around the sun is not just the force from the sun;
there is also a pull from, say, Saturn. This force is not really strong, since the
sun is much more massive than Saturn, but there is søzne pull, so the orbit
of Jupiter should not be a perfect ellipse, and it is not; it is slightly of, and
“wobbles” around the correct elliptical orbit. Such a motion 1s a little more
complicated. Attempts were made to analyze the motions of Jupiter, Saturn,
and Uranus on the basis of the law of gravitation. 'Phe efects of each of these
planets on each other were calculated to see whether or not the tiny deviations
and irregularities in these motions could be completely understood from this
one law. Lo and behold, for Jupiter and Saturn, all was well, but Ủranus was
“weïrd.” behaved in a very peculiar manner. It was not travelling in an exact
ellipse, but that was understandable, because of the attractions of Jupiter and
Saturn. But even ïf allowance were made for these attractions, Dranus si was
not going right, so the laws of gravitation were in danger of beïng overturned,
a possibility that could not be ruled out. Two men, Adams and Le Verrier, in
England and FErance, independently, arrived at another possibility: perhaps there
1s another planet, dark and invisible, which men had not seen. This planet, N,
could pull on Dranus. They calculated where such a planet would have to be in
order to cause the observed perturbations. They sent messages to the respective
observatories, saying, “Gentlemen, point your telescope to such and such a place,
and you will see a new planet.” It often depends on with whom you are working
as to whether they pay any attention to you or not. They did pay attention to
Le Verrier; they looked, and there planet W wasl "The other observatory then
also looked very quickly in the next few days and saw it too.
This discovery shows that Newton”s laws are absolutely right in the solar
system; but do they extend beyond the relatively small distances of the nearest
planets? 'The first test lies in the question, do s#ars attract cach other as well as
planets? We have defnite evidence that they do in the double stars. Figure 7-6
shows a double star—Ewo stars very close together (there is also a third star in
the picture so that we will know that the photograph was not turned). "The stars
are also shown as they appeared several years later. We see that, relative to the
“ñxed” star, the axis of the pair has rotated, i.e., the bwo stars are going around
each other. Do they rotate according to NÑewton's laws? Careful measurements
--- Trang 149 ---
Fig. 7-6. A double-star system.
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Fig. 7-7. Orbit of Sirnus B with respect to Sirius A.
--- Trang 150 ---
of the relative positions of one such double star system are shown in Fig. 7-7.
There we see a beautiful ellipse, the measures starting in 1862 and going all the
way around to 1904 (by now it must have gone around once more). Ðverything
coincides with Newton?s laws, except that the sbar Sirius Á is no at the ƒocus.
'Why should that be? Because the plane of the ellipse is not in the “plane of the
sky.” We are not looking at right angles to the orbit plane, and when an ellipse is
viewed at a tilt, it remains an ellipse but the focus is no longer at the same place.
Thus we can analyze double stars, moving about each other, according to the
requirements of the gravitational law.
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Fig. 7-8. A globular star cluster.
That the law of gravitation is true at even bigger distances is indicated in
Hig. 7-8. lÝ one cannot see gravitation acting here, he has no soul. 'This fgure
shows one of the most beautiful things in the sky—a globular star cluster. AII