12.1 - Newton’s law of gravitation
Newton’s law of gravitation: The attractive
force of gravity between two particles is
proportional to the product of their masses and
inversely proportional to the square of the
distance between them.
Newton’s law of gravitation states that there is a force between every pair of particles, of
any mass, in the universe. This force is called the gravitational force, and it causes
objects to attract one another. The force does not require direct contact. The Earth
attracts the Sun, and the Sun attracts the Earth, yet 1.5×10^11 meters of distance
separate the two.
The strength of the gravitational force increases with the masses of the objects, and
weakens proportionally to the square of the distance between them. Two masses exert
equal but opposite attractive forces on each other. The forces act on a line between the
two objects. The magnitude of the force is calculated using the equation on the right.
The symbol G in the equation is the gravitational constant.
It took Newton about 20 years and some false starts before he arrived at the
relationship between force, distance and mass. Later scientists established the value for
G, which equals 6.674 2×10í^11 N·m^2 /kg^2. This small value means that a large amount
of mass is required to exert a significant gravitational force.
The example problems on the right provide some sense of the magnitude of the
gravitational force. First, we calculate the gravitational force the Earth exerts on the
Moon (and the Moon exerts on the Earth). Although separated by a vast distance (on
average, their midpoints are separated by about 384,000,000 meters), the Earth and
the Moon are massive enough that the force between them is enormous: 1.98×10^20 N.
In the second example problem, we calculate the gravitational force between an 1100-
kg car and a 2200-kg truck parked 15 meters apart. The force is 0.00000072 N. When
you press a button on a telephone, you press with a force of about one newton,
1,400,000 times greater than this force.
Newton’s law of gravitation
Gravitational force
·Proportional to masses of bodies
·Inversely proportional to square of
distance