How Newton Unified the Motions How Newton Unified the Motions of the Moon, Sun, and Applesof the Moon, Sun, and Apples

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Heliocentric Model of Copernicus

Review of Renaissance Review of Renaissance

Galileo

Saw Venus go through phases like the moon

Saw objects orbiting Jupiter

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Makes the first measurements of how quickly objects pick up speed as they fall – finds all objects fall at the same rate regardless of size or how heavy they are

The first measurement of gravity. Although he doesn't call it that.

How long does it take the ball to fall ½ way down the ramp?

About ¾ of the total time it takes to fall all the way to the bottom:

Using ratios he discovers d = 1/2at2

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He also studied horizontal motion and the concept of forces acting to move objects or stop them moving. He surmised that without something to change the motion of an object it should keep going.

NewtonNewton

Born in 1642, the same year Galileo died.

He died in 1727, at the age of 85.

Newton discovered the origin of color.

He used his knowledge of optics to invent the first reflecting telescope - a major breakthrough because this will eventually allow larger, more sensitive telescopes to be built.

NewtonNewton

Discovered the nature of gravity as an attractive force.

Created a unified view of force and motion in which motion in the heavens, and on Earth, the known universe at the time could be explained by the same few rules.

Before he's through, he invents calculus as the mathematical language necessary to understand how gravity works.

CalculusCalculus

For example, how do I compute the area of a circle.

Using calculus you take a line of some radius and rotate it around 3600 or 2 radians.

In calculus this operation looks like this :

Language should evolve so that communication becomes more efficient; i.e. the above graphic shows how to derive the area of a circle in using the least amount of characters and symbols

Principia (1687)Principia (1687)

Provided a detailed explanation of the laws of gravity and motion, particularly as they applied to astronomy.

Principia is still considered by many to be the greatest scientific book ever written. It contains the fundamentals for all of modern science.

So What did he do?So What did he do?

Remember Galileo was studying laws of motion, the concepts of inertia, and forces. But he did not formalize all of them.

Newton takes what Galileo did and expands on it until he has a new mathematical model of forces. We call this Newton's laws of motion.

First Some DefinitionsFirst Some DefinitionsNewton describes the concepts of

Momentum which equals mass times velocity.

p = m v

The law of the conservation of momentum. The total momentum of a system is conserved. Meaning for example you can transfer momentum between objects in a collision the total amount of momentum stays the same.

Force causes changes in momentum.

Newton's 1Newton's 1stst Law Law

The momentum law :

A body remains at rest or moves in a straight line of constant velocity as long as no external forces acts on it

Newton's 2nd LawNewton's 2nd Law

The force law :

A body acted on by a force will accelerate such that force equals mass times acceleration

F = m a

More accurately, a force is the time rate of change of the momentum.

Resistance

Impulse

Newton's 3rd LawNewton's 3rd Law

Law of Reaction :

For every action there is an equal and opposite reaction.

Means whenever one thing exerts a force on another, an equal amount of force is exerted back on it.

GravityGravity

Things near the earth fall to the ground unless something holds them up.

Earth's gravity pulls any object toward it - even without touching it.

It is also the force that holds the Universe together: planets to stars, stars to galaxies, galaxies to each other.

Universal GravityUniversal Gravity

ALL objects attract each other with a force of gravitational attraction.

GravityGravity

Newton also showed when we deal with spherical bodies, the force of gravity acts as if all the mass is concentrated at the center of the spheres

Makes math much easier for us now

But he had to develop modern calculus to do this

GravityGravity

The force of gravity between you and the Earth acts as though all the mass of the Earth is concentrated at a point at its center and all your mass is concentrated at your center of mass

In this case, masses are said to be Point Masses

A Concern for NewtonA Concern for Newton

How come the Moon doesn't fall into the Earth?

Or the Earth into the Sun...

An orbit is the balance between inertial (Newton's First Law) and gravitational forces (Newton's second law).

That is, the earth is continually falling toward the sun, but inertia also wants the earth to keep moving in a straight line. When these two forces are in balance a stable orbit results:

A Stable OrbitA Stable Orbit

Well, Is the Universe Stable?Well, Is the Universe Stable?

Is gravity there at large distances?

If so, How is it the universe avoids collapsing in on itself?

Are there orbits in the Universe?

It seems to me that if the matter of our sun and planets and all the matter of the Universe were evenly scattered throughout all of the heavens, and every particle had and innate gravity towards all the rest … some of it would convene into one mass and some into another so as to make an infinite number of great masses, scattered at great distances from one another throughout all that infinite space.

Newton's ConvincedNewton's Convinced

NewtonNewton

Newton was the integrator, the unifier, the organizer, of all the scientific knowledge available at the time. He established a solid platform on which all modern science could be built.

For centuries, Newton's physics was accepted without major changes because it explained so many different phenomena, could be used to predict many physical events (such as the return of Halley's comet), was mathematically sound, and had many practical applications.