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something which is going around ïn a cirele. Therefore two obJects, one heavy
and one light, goïng around a larger object in the same cirele at the same speed
because of gravity, will stay together because to go in a circle reguzres a Íforce
which is stronger for a bigger mass. That is, the gravity is stronger Íor a given
mass in 7us( the right proportion so that the ©wo objects will go around together.
TỶ one object were inside the other it would sa inside; it is a perfect balance.
'Therefore, Gagarin or Titov would fñnd things “weightless” inside a space ship; 1Ý
they happened to let go of a piece of chalk, for example, it would go around the
earth in exactly the same way as the whole space ship, and so it would appear
to remain suspended before them in space. Ït is very interesting that this Íorce
1s eœøctu proportional to the mass with great precision, because 1Ý it were not
exactly proportional there would be some effect by which inertia and weight
would difer. The absence of such an efect has been checked with great accuracy
by an experiment done fñrst by Eötvös in 1909 and more recently by Dicke. Eor
all substances tried, the masses and weights are exactly proportional within 1
part in 1,000,000,000, or less. This is a remarkable experiment.
7-8 Gravity and relativity
Another topic deserving discussion is Einstein's modification of Newton°s law
OŸ gravitation. In spite of all the excitement it created, Newton's law of gravitation
is not correctl It§ was modifed by Einstein to take into account the theory of
relativity. According to NÑewton, the gravitational efect is instantaneous, that
1s, IŸ we were to move a mass, we would at onece feel a new force because of the
new position of that mass; by such means we could send signals at infinite speed.
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Binstein advanced arguments which suggest that we cannot send signals ƒaster
than the specd oƒ light, so the law oŸ gravitation must be wrong. By correcting
1t to ©ake the delays into account, we have a new law, called Einstein's law of
gravitation. One feature of this new law which is quite easy to understand is this:
In the Einstein relativity theory, anything which has energy has mass—mass in
the sense that it is attracted gravitationally. Even light, which has an energy,
has a “mass.” When a light beam, which has energy ¡n it, comes past the sun
there is an attraction on i% by the sun. 'Phus the light does not go straight, but is
defected. During the eclipse of the sun, for example, the stars which are around
the sun should appear displaced from where they would be ïif the sun were not
there, and this has been observed.
Finally, let us compare gravitation with other theories. In recent years we have
discovered that all mass is made of tiny particles and that there are several kinds
of interactions, such as nuclear forces, etc. None of these nuclear or electrical
forces has yet been found to explain gravitation. 'The quantum-mechanical aspects
Of nature have not yet been carried over to gravitation. When the scale is sO
small that we need the quantum efects, the gravitational efects are so weak
that the need for a quantum theory of gravitation has not yet developed. Ôn
the other hand, for consistency in our physical theories it would be important to
see whether Newton's law modified to Einstein”s law can be further modifed to
be consistent with the uncertainty principle. 'Phis last modification has not yet
been completed.
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JMoffort
8-1 Description of motion
In order to fnd the laws governing the various changes that take place in
bodies as time goes on, we must be able to đescribe the changes and have some
way to record them. 'Phe simplest change to observe in a body is the apparent
change in its position with time, which we call motion. Let us consider some solid
object with a permanent mark, which we shall call a point, that we can observe.
We shall discuss the motion of the little marker, which might be the radiator cap
of an automobile or the center of a falling baill, and shall try to describe the fact
that it moves and how it moves.
These examples may sound trivial, bu many subtleties enter into the descrip-
tion of change. Some changes are more difficult to describe than the motion of a
point on a solid object, for example the speed of drift of a cloud that is drifting
very slowly, but rapidly forming or evaporating, or the change of a womans mind.
W© do not know a simple way to analyze a change of mind, but since the cloud
can be represented or described by many molecules, perhaps we can describe the
motion of the cloud in principle by describing the motion of all its individual
molecules. Likewise, perhaps even the changes in the mind may have a parallel
in changes of the atoms inside the brain, but we have no such knowledge yet.
At any rate, that is why we begin with the motion of points; perhaps we
should think of them as atom, but it is probably better to be more rough in
the beginning and simply to think of some kind of small obJects—smaill, that
1s, compared with the distance moved. For instance, in describing the motion
of a car that is going a hundred miles, we do not have to distinguish bebween
the front and the back of the car. To be sure, there are slight diferences, but
for rough purposes we say “the car,” and likewise it does not matter that our
points are not absolute points; for our present purposes it is not necessary to be
extremely precise. Also, while we take a first look at this subjecb we are goïng
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Table 8-1 E- 25000
# (min) | s (ft) # 2oooo
0 0 D
1 1200 ụ 15000
2 4000 3
3 9000 ụị 10000
4 9500 š
b) 9600 b 5000
6 13000 5
7 18000 2A4 6 8 q0
§ 23500 TIME IN MINUTES
9 24000 Fig. 8-1. Graph of distance versus time for the car.
to forget about the three dimensions of the world. We shall just concentrate
on moving in one direction, as in a car on one road. We shall return to three
dimensions after we see how to describe motion in one dimension. Ñow, you may
say, ““This ¡is all some kind of trivia,” and indeed it is. How can we describe such a
one-dimensional motion——let us say, of a car? Nothing could be simpler. Among
many possible ways, one would be the following. To determine the position of
the car at diferent times, we measure its distance from the starting point and
record all the observations. In 'Table S-1, s represents the distance of the car, In
feet, from the starting point, and # represents the time in minutes. 'Phe first line
in the table represents zero distance and zero time—the car has not started yet.
After one minute it has started and has gone 1200 feet. Then in two minutes, it
goes farther——notice that it picked up more distance in the second minute——1§