Astronomy 161:
An Introduction to Solar System Astronomy Prof. Richard Pogge, MTWThF 9:30 |

Newton's Synthesis

**1st Law of Motion**:- Objects in motion remain in motion unless acted upon by an
outside force.
**2nd Law of Motion**:- Acceleration is proportional to the force & inversely
proportional to the mass (F=ma)
**3rd Law of Motion**:- To every action there is an equal an opposite reaction.

Isaac Newton was born in Woolsthorpe in rural England on Christmas Day of 1642 (Old Style, England had not yet adopted the Gregorian Calendar).

- 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 never married). He was always fearful that others would steal from him.

He Graduated from Cambridge in 1665 at the age of 23.

Spent two years in Woolsthorpe, during which

- Invented the integral and differential calculus.
- Developed the binomial theorem.
- Started fundamental work on optics.
- Formulated his laws of motion & gravitation.

All this in his early 20s. He was publish none of it until many years later.

- Settled into the life of a Cambridge don.
- Continued fundamental work on optics (including inventing a novel reflecting telescope that is the prototype of all modern large telescopes).
- Carried out a variety of experiments in optics and alchemy.
- Was always unprepared for classes and hated to teach.

It took Newton about 3 years to reproduce his earlier work.

Halley paid the publication expenses out of his own pocket, after wheedling, cajoling, and flattering Newton into finishing it.

The results were published by the Royal Society of London in 1687
as the *Philosophiae Naturalis Principia Mathematica
*(Mathematical Principles of Natural Philosophy).

- Laid the foundations of modern physics.
- Completely 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.

Every body will stay in a state of rest oruniform motion in a straight lineunless that state is changed by forces impressed upon it.

Often called the "Law of Inertia".

- Inertia is the property of matter that it resists having its state of motion changed.

- Speed (how fast is it going)
- Direction (where is it going)

The combination is called the VELOCITY:

- Velocity = how
**fast**, and in what**direction**.

Change in motion is **acceleration**

- Measures how fast the
*velocity*changes. - Change can be in speed, or direction, or both!

The size of anaccelerationis directly proportional to theforceapplied, and inversely proportional to themassof the body. Further, the acceleration will take place in thesame directionas the applied force.

Expressed Mathematically:

## a = F/m

**In Words:**Acceleration is proportional to the applied force and inversely proportional to the mass.

## F = ma

**In Words:**Force is the mass times the acceleration

- F = force applied to a body
- m = mass of the body (e.g., in kilograms)
- a = acceleration the body experiences in response to the force applied

1) Quantifies the idea of a force in terms of its effects on a massive body.

- Forces produce accelerations.
- The
*more*mass a body has, the*less*it will be accelerated by a given force.

2) Forces and accelerations have a **direction**:

- Accelerations are be in the
*same*direction as the applied forces.

- Move along ellipses with the Sun at one focus.
- Move the fastest when at perihelion (closest to the Sun)
- Move the slowest when at aphelion (furthest from the Sun)

Why does the speed and direction change?

- They are thus
*accelerating*in response to an applied*force*.

What force?

*The Force of Gravity*.

For every force applied to a body, there is anequal and oppositely directedforce exerted in response.

This is commonly stated more simply as:

To every action there is an equal & opposite reaction.

Unifies them in the case of the interaction between two (or more) bodies via forces.

- If I set an apple on this table, it pushes down on the table with a force equal to its mass times the acceleration due to gravity.
- To hold it stationary (unmoving), the table must be
exerting an equal and opposite
*upward*force.

- They are simple, easily stated in either words or mathematics.
*Universal Physical Laws*that apply to*all*moving objects, on the Earth or in the heavens.- They unify phenomena by explaining everyting with the same set of self-consistent rules.

Independently invented by Newton & Leibnitz, Calculus is the mathematics of change:

- Language for describing the change in the velocity of a moving object with time.
- Sets geometry into motion.

The Calculus provides a powerful framework within which we can explore the motion of objects, from the fall of an apple, to the orbit of the planets about the Sun.

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Updated: 2006 October 4

Copyright © Richard W. Pogge, All Rights Reserved.