Transcript Newton`s Law of Universal Gravitation

Newton’s Law of Universal Gravitation
 According to the Greeks, objects have a built-in desire to
fall. They fall until they reach a lowest energy point.
Here they are very stable.
 According to Galileo and Newton, a force called gravity
exists. It is an attractive force between the Earth and
other objects or between any two objects.
 Newton studied the motion of the planets and the moon.
He wondered what kept the moon in its orbit around the
Earth and what kept the Earth in orbit around the sun.
 The idea that gravity extends throughout the universe is
credited to Newton who is said to have thought of it
when an apple fell on his head.
The Falling Moon
 Newton compared the falling apple to the falling moon.
 Remember that a projectile will move in a straight line unless
acted upon by a force. Here the force is gravitational
attraction of Earth. This is a centripetal force so the object is
accelerated to the center of the Earth. The moon follows the
straight line path but is pulled down as it travels over.
 The moon falls in the sense that it falls below the straight line
path that inertia would carry it on if no forces were acting on
it.
 He used a cannonball example to prove his point. In his
thought experiment, he fires the cannonball with everincreasing velocity. The cannonball eventually would have
tangential velocity sufficient to carry it around the earth.
The Falling Moon
 Newton tested his hypothesis by reasoning that the mass
of an object should not affect how far it falls.
 How far an object falls should only relate to its distance
from Earth’s center.
 In fact, it is related to the square of the distance from
Earth’s center.
 The moon accelerates to the Earth at about 1/3600 g.
 Even though this acceleration is very small, remember
that the force of Earth-on-moon and moon-on-Earth.
The Falling Earth
 Why does the earth not crash into the sun? HINT: Does the
Earth move? What does it have?
 Which attraction is greater, the sun for the earth or the earth
for the sun? HINT: One of Newton’s laws addresses this.
 If there is an attraction for all objects, why do we not feel
gravitated towards large buildings and other massive objects?
HINT: Are we very massive compared to the Earth?
Newton’s Law of Universal Gravitation
 Newton’s Law states that every object attracts every
other object with a force that is directly proportional to
the mass of each object.
 He also deduced that the force decreases as the square of
the distance between the objects increases.
 F = Gm1m2/d2, where G is the universal gravitation
constant, 6.67 x 10-11Nm2/kg2. m1 is the mass of one
object and m2 is the mass of a second object. d is the
distance between their centers.
 The gravitation constant was measured by Henry
Cavendish.
Khan Academy on Universal Gravitation
 http://www.khanacademy.org/science/physics/mechanics/
v/introduction-to-newton-s-law-of-gravitation
 http://www.khanacademy.org/science/physics/mechanics/
v/gravitation--part-2
 http://www.khanacademy.org/science/physics/mechanics/
v/viewing-g-as-the-value-of-earth-s-gravitational-field-nearthe-surface
Newton’s Law of Universal
Gravitation
 The force between you and any object is usually very small.
The force of attraction between you and the earth is _____.
 Your weight depends on your distance from the center of the
earth. The closer you are to the center, the smaller will be
your weight. This is due to the change in the mass and radius
of the planet.
 What happens to the Fg if
 The mass of the planet doubles?
 The mass of you doubles?
 The distance between you and the center of the planet doubles?
 The distance between you and the center of the planet cuts in half?
 Your mass doubles and the planet’s radius cuts in half?
 Cavendish went so far as to mass the earth. Its mass is 5.98 x
1024kg.
Newton’s Law of Universal Gravitation
 The distance that an object is from the center of the Earth
affects its acceleration due to gravity. Earth’s radius is 6.38 x
106m. That is the average radius. If one is on a mountain that
is very high, its height must be taken into consideration.
 That means that you must add the radius of the Earth to the
distance an object is above the surface.
 If you are 2 Earth radii high, then your distance is 3 Earth
radii.
Gravitational Interactions
 A force field exerts a force on objects in its vicinity. That
means that technically an object interacts with the field
exhibited by an object and not the object itself.
 A field is represented by field lines. Where the lines are
closer together, the field is stronger. They extend in all
directions.
 A gravitational field for a planet is represented by vectors
which point to the center of mass. Remember gravity is only
attractive.
Weight and Weightlessness
 Suppose you weighed in an elevator.
 What would be your weight if the elevator accelerated
downward?
 What would be your weight if the elevator accelerated upward?
 What would be your weight if the elevator was not accelerating?
 What would be your weight if the elevator cable broke and the
elevator fell freely?
 Weight then is the force that you exert against a support.
 Weightlessness then becomes the absence of a supporting
force.
History
 Tycho Brahe spent his life accurately predicting astronomical
events.
 He believed that the Earth was the center of the universe.
 His protege’ Johannes Kepler believed that the sun was the
center of the universe. He formulated 3 laws based on his
observations of the motions of the planets.
Kepler’s Laws
 First Law: The paths of the planets are ellipses with the
center of the sun at one focus.
 Second Law: An imaginary line from the sun to a planet
sweeps out equal areas in equal time intervals. Thus
planets move fastest when they are closest to the sun.
 Third Law: The ratio of the squares of the periods of
any two planets revolving about the sun is equal to the
ratio of the cubes of their average distances from the sun.
T12/ T22 = r13/ r23