Newton thought that a force must act on the Moon because,
since it moves in a curved (almost, but not quite) circular path,
it is accelerating. After all, the direction of its
velocity is constantly changing, and acceleration is the rate
velocity changes. An acceleration requires a net force (2nd
The Moon (and every other Earth satellite) is in free fall
toward the Earth, but it is a projectile whose tangential
velocity keeps it from getting closer to the Earth. In the
same time that the Moon falls a centimeter, the Earth curves a
centimeter out from under it!
In order for a scientific hypothesis to advance to the status
of a scientific theory, it must be thoroughly and extensively
Since Fgrav = GMm/r2, the gravitational force is directly proportional to G. The small size of the gravitational constant G tells you that
the gravitational force is actually quite weak compared to
other known forces like the electric, magnetic, and nuclear
You need to know: (1) your mass, (2) the Earth's
mass, and (3) the radius of the Earth in order to
determine the gravitational force on you, which is your
The gravitational force is an inverse-square-law force - the
strength of the force decreases with the square of the
distance between objects. In other words, twice the distance
means one-fourth of the force, three times the distance means
one-ninth of the force, etc.
(a) If you were five times farther from the center of the
Earth than you are now, your weight would be 1/25 ( =
1/52) of your current weight.
(b) If you were ten times farther from the center of the Earth
than you are now, your weight would be 1/100 (=
1/102) of your current weight.
Ch 12 Plug & Chug Answers:
(Note that this is the same result you would get from w = mg.)
(Comparing the answers for this question and the last one, notice that the gravitational force that the Sun exerts on the Moon is about 100 times as much as the gravitational force that the Earth exerts on the Moon. Why, then, does the Moon orbit the Earth and not the Sun? )
Ch 12 Think & Explain Answers:
No, this label is not cause for alarm! The same thing
can be said about every object in the universe -
The same amount of force. The forces "Earth pulls Moon" and
"Moon pulls Earth" are a Newton's 3rd Law action/reaction
500 N toward the center of the Earth. This gravitational force
is the force we commonly call her weight.
If the gravitational force of the Sun on the planets suddenly
disappeared, they would move off with the velocity that they had
at that instant (Newton's 1st Law). So, they would move in a
straight line tangent to their orbit, at constant speed.
(a) Yes, if the Moon were twice as massive, the gravitational
force of the Earth on the Moon would be twice as much, since the
gravitational force is proportional to both masses involved.
(b) Yes, the gravitational force that the Moon exerts on the Earth
would double also (according to Newton's Third Law).
A rocket going from the Earth to the Moon would require more
fuel. Since the Earth has more mass than the Moon, the Earth will
exert a larger gravitational force on the rocket than the Moon
would (things weigh less on the Moon). This means that the rocket
would have to exert a larger force to balance its weight leaving
the Earth than leaving the Moon. Since the rocket exerts a larger
force leaving the Earth, it must do more work to leave the Earth,
which takes more energy (in the form of chemical potential energy
stored in the rocket fuel).
Gravitational forces on a galaxy near the "edge" of
the Universe. (Not all forces are shown.)
Net force on a galaxy near the "edge" of the
The observation that the expansion of the Universe is slowing down
is consistent with the law of gravity. Every object in the
Universe attracts every other object in the Universe with a
gravitational force. The diagram on the left above shows some of
the gravitational forces on a galaxy near the "edge" of the
universe. Looking at the diagram you can see that all of the
forces on this galaxy point "inward", since all gravitational
forces are attractive. This means that the net force on this
galaxy points "inward" toward the "center" of the Universe, as
shown in the diagram at right above. So, if the galaxy is moving
away from the "center" of the Universe (an expanding universe),
then the net force on the galaxy will act to slow the galaxy down,
and the expansion of the Universe should be slowing down.
However, recent observations (since the publication of your text)
seem to indicate that the expansion of the Universe is in fact NOT
slowing down - in fact, the Universe seems to be accelerating.
This is contrary to the behavior that the law of gravity predicts
as described above. This is an area of very heated and intense
research and discussion at the moment. If the Universe's expansion
is really speeding up, then there has to be some
previously-undetected force that is driving it. What could that
Ch 12 Think & Solve Answers
If the Earth's diameter doubled and its mass also doubled, your weight would be half as much as now. Your weight is the gravitational force between you and the Earth. Doubling the mass of the Earth would double your weight, since gravitational force is directly proportional to mass, but doubling the radius (which doubles if the diameter doubles) would decrease your weight by a factor of 1/4, since gravitational force is inversely proportional to the square of the radius. Mathematically:
If you were twice as far from the center of the Earth as you are now, your weight would be 1/4 of its current value (See #32).