Download Universal Gravitation

Universal Gravitation
Universal Gravitation
• Gravity…
• Makes things such as leaves and rain fall
• It made the Earth round
• Builds up the pressures that kindle every star to
shine
• But… What is Gravity?
Universal Gravitation
• GRAVITY
• Albert Einstein
• Discovered that gravity arises from the “warping”
of space and time
• The way in which masses communicate with each
other
• Every mass in the universe reaches out to attract
every other one, and every mass feels an attraction
from every other one
Universal Gravitation
• The Falling Apple
• Issac Newton
• Credited for the idea that gravity extends
throughout the universe
• According to the popular legend
• Idea of gravity occurred to Newton while he was
sitting underneath an apple tree on his mother’s
farm
The Falling Apple
• Newton
• Understood the concept of inertia developed
earlier by Galileo
• Without an outside force, moving objects
continue to move at constant speed in a straight
line
• Force is necessary for an object to undergo a
change in speed or direction
The Falling Apple
• The Falling Apple, Newton observed, triggered
what was to become one of the most far-reaching
generalizations of the human mind
• Newton saw the apple fall or perhaps felt it hit his
head (Story unclear)
• Perhaps he looked up through the apple tree
branches and noticed the moon
• Newton was probably puzzled by the fact that the
moon does not follow a straight-line path, but instead
circles the Earth
• He knew circular motion is accelerated motion, which
requires a force
• But what was this force?
The Falling Apple
• Newton had the insight to see that the moon
is falling toward the earth, just as the apple is
• He reasoned that the moon is falling for the
same reason the apple is
• ** They are both pulled by Earth’s GRAVITY
The Falling Moon
• Newton compared the falling apple with the
falling moon
• He realized if the moon did not fall, it would
move off in a straight line and leave its orbit
• The moon must be falling around the earth
• He hypothesized that the moon was simply a
projectile circling the earth under the attraction of
gravity  falling toward the earth but with a great
enough tangential velocity to avoid hitting the
earth
Gravitational Force
• Earth and many of the other planets in our
solar system travel in nearly circular paths
around the sun
• A centripetal force is keeping them in orbit
• This centripetal force that holds the planets in
orbit is the same force that pulls an apple
towards the ground  GRAVITATIONAL FORCE
• One of Newton’s greatest discoveries
Orbiting Objects are in
Free Fall
• Newton developed a Thought Experiment
• Consider a cannon sitting on a high mountaintop
• The path of each cannonball is a parabola
• The horizontal distance that each cannonball covers
increases as the cannonball’s initial speed increases
• Newton realized  if the initial speed of the cannonball was great
enough, the curvature of Earth will cause the cannonball to
continue falling without ever landing
** In other words, it would orbit
Earth
Orbiting Objects are in
Free Fall
• The gravitational force
between the cannonball and
Earth = Centripetal force that
keeps the cannonball in orbit
• Satellites stay in orbit for the
same reason
• Similarly, a gravitational
attraction between Earth and
our sun keeps Earth in its
orbit around the sun
Newton’s Law of
Gravitation
• The attractive force of gravity between 2 particles
is proportional to the product of their masses and
inversely proportional to the square of the
distance between them
• Gravitational Force
Fg = G (m1m2 / r2)
Fg = Gravitational Force (Newtons)
G = Constant of universal gravitation
(G = 6.67 x 10-11 N x m2/ kg2)
m1 = Mass of object 1 (kg)
m2 = mass of object 2 (kg)
r2 = (Distance between the centers of the spherical masses (m)2
Gravitational Force
• Gravitational Force
• Exists between any two masses, regardless of
size
• Always attracts objects to one another
• The force that the moon exerts on Earth is equal
and opposite to the force that Earth exerts on the
moon  Newton’s Third Law of Motion
Gravitational Force
• If gravitational force acts between all masses, why
doesn’t Earth accelerate up toward a falling apple?
• In fact, it does!
• But, Earth’s acceleration is so tiny  you cannot
detect it
• Because Earth’s mass is so large and acceleration is
inversely proportional to mass, the Earth’s acceleration
is negligible
• The apple has a much smaller mass and thus a much
greater acceleration