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