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Discussion Questions
A. If you hold an apple in your hand, does the apple exert a gravitational force
on the earth. Is it much weaker than the earth’s gravitational force on the
apple. Why doesn’t the earth seem to accelerate upward when you drop the
apple.
B. When astronauts travel from the earth to the moon, how does the gravita-
tional force on them change as they progress.
C. How would the gravity in the first-floor lobby of a massive skyscraper
compare with the gravity in an open field outside of the city.
D. In a few billion years, the sun will start undergoing changes that will
eventually result in its puffing up into a red giant star. (Near the beginning of
this process, the earth’s oceans will boil off, and by the end, the sun will
probably swallow the earth completely.) As the sun’s surface starts to get
closer and close to the earth, how will the earth’s orbit be affected.
10.5Weighing the Earth
Let’s look more closely at the application of Newton’s law of gravity to
objects on the earth’s surface. Since the earth’s gravitational force is the
same as if its mass was all concentrated at its center, the force on a falling
object of mass m is given by
F=G M
earth
m / r
earth
2
.
The object’s acceleration equals F/m, so the object’s mass cancels out and we
get the same acceleration for all falling objects, as we knew we should:
g = G M
earth
/ r
earth
2
.
Newton knew neither the mass of the earth nor a numerical value for
the constant G. But if someone could measure G, then it would be possible
for the first time in history to determine the mass of the earth! The only
way to measure G is to measure the gravitational force between two objects
of known mass, but that’s an exceedingly difficult task, because the force
between any two objects of ordinary size is extremely small. The English
physicist Henry Cavendish was the first to succeed, using the apparatus
shown in the diagrams. The two larger balls were lead spheres 8 inches in
diameter, and each one attracted the small ball near it. The two small balls
hung from the ends of a horizontal rod, which itself hung by a thin thread.
The frame from which the larger balls hung could be rotated by hand about
a vertical axis, so that for instance the large ball on the right would pull its
Cavendish’s apparatus viewed from
the side, and a simplified version
viewed from above. The two large balls
are fixed in place, but the rod from
which the two small balls hang is free
to twist under the influence of the
gravitational forces.
Section 10.5Weighing the Earth