Astronomy 171
Solar System Astronomy
Prof. Paul Martini

Lecture 16: Newton

Key Ideas

First Law of Motion:: Objects in motion remain in motion unless acted upon by an outside force
Second Law of Motion:: Acceleration is proportional to the force and inversely proportional to the mass (F = m a)
Third Law of Motion:: To every action there is an equal an opposite reaction

Isaac Newton (1642 - 1727)

Born in Woolsthorpe in rural England: Mother was a widow who remarried after he was born; Raised by his maternal grandmother; Grew up a solitary boy, quite unfit as a farmer
Quiet, irascible, and solitary as an adult. He was always fearful that others would steal his work from him
Graduated from Cambridge in 1665

The Plague Years

An outbreak of Bubonic Plague closed Cambridge in 1665 and 1666, so Newton went home to Woolsthorpe
During these years, Newton:: Invented the integral and differential calculus; Developed the binomial theorem; Started fundamental work on optics; Formulated his laws of motion and gravitation
But, he published none of it until years later

Lucasian Professor

In 1669, at age 26, he became the second Lucasian Professor of Mathematics at Trinity College, Cambridge
He settled into the life of a Cambridge don:: Continued fundamental work on optics (invented a reflecting telescope); Carried out a variety of experiments in optics and alchemy; Was always unprepared for classes and hated to teach

Principia Mathematica

In 1684, Newton was prevailed upon by Edmond Halley to publish his work on motion and gravitation.: Newton took 3 years to reproduce his work; Halley paid the publication expenses out of his own pocket after wheedling, cajoling, and flattering Newton into finishing it in 1687.
This book was entitled Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy)

Newton's Synthesis

The Principia is one of the most important books in history: Laid the foundations of modern physics; Swept away the last vestiges of the Aristotelian view of the world; Replaced older, empirical descriptions with quantifiable, physical explanations of the nature of the World.
Unified all motions into three simple laws

First Law of Motion

Every body will stay in a state of rest or uniform motion in a straight line unless that state is changed by forces impressed upon it
Often called the Law of Inertia: Property of matter that it resists having its state of motion changed

Speed versus Velocity

All motion is composed of two parts:: Speed: how fast it is moving; Direction: where it is going
The combination is called Velocity: Velocity is both how fast something is moving and in what direction
Change in velocity is acceleration: Measures how fast the velocity changes; Can be due to a change in speed, change in direction, or both

Second Law of Motion

The size of an acceleration is directly proportional to the force applied, and inversely proportional to the mass of the body
The resulting acceleration is in the same direction as the applied force
Expressed mathematically:: a = F/m; Acceleration is proportional to force and inversely proportional to mass
This may also be written as F = m a: Force is equal to mass times acceleration

Force, Mass, and Acceleration

Second law has two parts:
1. Quantifies a force in terms of its effects on a massive body: Forces produce accelerations; The more mass a body has, the less it can be accelerated by a given force
2. Forces and accelerations have directions: Acceleration is in the same direction as the applied force

Application to Planetary Motion

Planets are continually changing the speed and direction as they orbit the Sun: Move along ellipses with the Sun at one focus; Move fastest at perihelion (greatest force); Move slowest at aphelion (least force)
Why does the speed and direction change?: They are accelerating in response to an applied force
What force?: The Force of Gravity

Third Law of Motion

For every force applied to a body, there is an equal and oppositely directed force exerted in response
This can also be expressed as:: "To every action there is an equal and opposite reaction"

A Complete Description

Newton's Laws of Motion provide a complete, quantitative explanation of the motions of objects: They are simple and easily stated in either words or mathematics; They are Universal Physical Laws applicable to all objects on the Earth or in the heavens; They unify phenomena, explaining all motions with the same set of self-consistent rules

The Mathematics of Change

The full statement of the laws required the invention of a new mathematical language: Calculus: Independently invented by Newton and Leibnitz
Calculus is the mathematics of change: Gives us a way to descibe the change in the velocity of a moving object with time; Calculus sets geometry into motion
Provides a framework for exploring motion

See A Note about Graphics to learn why some of the graphics shown in the lectures are not reproduced with these notes.