Transcript Chap. 12 Universal Gravitation


The idea that gravity extends throughout
the universe is credited to Sir Isaac
Newton

The apple is falling toward Earth

Reason: pulled by Earth’s gravity
Newton thought that the moon must be
falling around Earth
 The moon falls beneath the straight line it
would follow if no force acted on it

› See figure 12.1

He hypothesized that the moon was
simply a projectile circling Earth under
the attraction of gravity
The moon has a component of velocity
parallel to Earth’s surface
 The sideways or tangential velocity is
sufficient to ensure nearly circular motion
around Earth rather than into it
 If there’s no resistance to reduce its
speed, the moon will continue falling
around and around Earth indefinitely


Is the sideways
velocity-the
component of
velocity
perpendicular to
the pull of gravity

Newton’s theory confirms the
Copernican theory of the solar system

The Earth and the planets continually
“fall” around the sun in closed paths
Why don’t the planets crash into the
sun?
 They don’t because the planets have
tangential velocities

What would happen if the tangential
velocities of the planets were reduced to
zero?
 Their motion would be straight toward
the sun and they would indeed crash
into it

Newton discovered that gravity is
universal
 States that every object attracts every
other object with a force that is directly
proportional to the mass of each object
 F ~ m1 * m2
d2


m1 = the mass of one object

m2 = the mass of the other object

d = the distance between their center of
mass

The greater the masses, the greater the
force of attraction between them

The greater the distance between the
objects, the weaker the force of
attraction
G measures the strength of gravity
 G = 6.67x10-11 N*m2/kg2
 F = G * m1 * m2
d2
 The value of G tells us that the force of
gravity is a very weak force
 We sense gravitation only when masses
like that of Earth are involved


Between you and a classmate, it is too
weak to notice (but it’s there!)
› Weakest of the 4 fundamental forces
Between you and Earth it’s easy to
notice, it’s your weight
 Mass of Earth = 6x1024 kg


An apple weighs
1N at Earth’s
surface, weighs
only 0.25N when
located twice as
far because the
pull of gravity is
only ¼ as strong

3x as far, weighs
1/9

A physical quantity varies inversely as
another quantity is squared
The Earth is round, but why?
 Because of gravitation
 Since everything attracts everything else,
Earth had attracted itself together
before it became solid
 Any “corners” of Earth have been pulled
in so that Earth is a giant sphere

How is the gravitational force between a
pair of planets altered when the mass of
one of the planets is doubled?
 The force is doubled
 When both are doubled?
 The force is four times as great

When they are twice as far apart?
 The force is decreased to ¼ as much

When they are three times as far apart?
 The force is decreased to 1/9 as much

Ten times as far apart?
 The force is decreased to 1/100 as much
