7 Sep 2000ASTR103, Sec 3, GMU, Dr. Correll1 Ch 2--Gravitation/Planetary Motion.

7 Sep 2000 ASTR103, Sec 3, GMU, Dr. Correll 1

Ch 2--Gravitation/Planetary MotionCh 2--Gravitation/Planetary Motion

“Finally we shall place the Sun himself at the center of the Universe. All this is suggested by the systematic procession of events and the harmony of the whole Universe, if we only face the facts, as they say, with both eyes open.”

Nicolaus Copernicus


Greek CosmologyGreek Cosmology

• The Greek tradition of scholarship leaves a written record of their studies

• The Greeks developed a cosmology--a theory of the overall structure and evolution of the universe– incorporated mathematics– but was not truly scientific in that it was limited by an

absence of observational corroboration

• Nevertheless, their tradition became the dominant world view in Europe and the Middle East


Aristotle Aristotle (384-322 BCE)(384-322 BCE)

• Terrestrial and celestial realms different– Terrestrial realm is corruptible– Celestial realm begins at Moon’s orbit outward and is

incorruptible

• Terrestrial matter composed of four elements– Earth– Water– Air– Fire


Aristotelian Concepts of MotionAristotelian Concepts of Motion

• Natural motion - "like seeking like”– Earth and water go down– Air and fire up

• Forced or violent motion - “forces moving like away from like”– Example - throwing rock upward

EarthEarth

WaterWater

AirAir

FireFire

EarthEarth

Forced Forced motionmotion

Natural Natural motionmotion


Celestial MotionCelestial Motion

EarthEarth

MoonMoon

Sphere Sphere of Starsof Stars

Prime MoverPrime Mover

PlanetPlanet

Celestial Celestial realmrealm

Terrestrial Terrestrial realmrealm


Aristarchus Aristarchus (ca. 310 - ca. 230 B.C.)(ca. 310 - ca. 230 B.C.)

• On the Sizes and Distances of the Sun and Moon– Estimated Sun 20 times farther from Earth than Moon (closer to

400)

• Natural to put largest and only self-luminous body the Sun at center--minority opinion

• Explained– Daily movement of heavens by Earth’s rotation on its axis– Earth and planets revolve about Sun


Geocentric Becomes DominantGeocentric Becomes Dominant

• Geocentric became dominant - Ptolemaic system (2nd cent. CE)

• Geocentric cosmology dominates until Copernicus’ publishes his book in 1543 CE


Geocentric System OrderGeocentric System Order

EarthEarth

SunSun

MoonMoon

SaturnSaturn

JupiterJupiter

MarsMars

VenusVenus

MercuryMercury


Accounting for Retrograde MotionAccounting for Retrograde MotionRetrograde motion--change in direction of motion of a planet as seen against the fixed stars


Geocentric CosmologyGeocentric Cosmology

• Ptolemaic System used Cycles, Deferents and Epicycles to account for retrograde motion


Heliocentric CosmologyHeliocentric Cosmology

• Copernican model has a more “natural” explanation of retrograde motion--especially in hindsight


Which is better?Which is better?

• As observations of retrograde motion became more detailed, epicycles within epicycles were required, making a very complicated system

• Occam’s Razor (William of Occam, 14th Century)--Eliminate unnecessary hypothesis, or “keep it simple”

• But true test is observation…so here’s how it happened.


Nicolaus Copernicus Nicolaus Copernicus (1473-1543)(1473-1543)


Nicolaus CopernicusNicolaus Copernicus

• Studied mathematics, philosophy, astronomy, and astrology at University of Krakow in Poland

• Studied law and medicine at Universities of Bologna and Padua in Italy

• Elected Canon of Ecclesiastical Law by the Church

• 1543, published, On the Revolutions of the Heavenly Orbs


Nicolaus CopernicusNicolaus Copernicus

1543, published On the Revolutions of the Heavenly Orbs


Copernican Copernican SystemSystem

• Orbits perfect circles (incorrect!)

• Earth and Moon move on circles– Earth about Sun– Moon about Earth

• Planets move on epicycles, which move on deferents (fewer epicycles than Ptolemaic system)

• Predictive accuracy same as Ptolemaic system

EpicycleEpicycle

PlanetPlanet

DeferentDeferent

SunSun

EarthEarth

MoonMoon

SunSun


Arguments For Copernican SystemArguments For Copernican System

• Quantitative material in his book– Predictive accuracy of Ptolemaic/Copernican systems same

• Reduction of number of elements of Copernican system compared to Ptolemaic

• Problem: Earth not at the center means you have the possibility of seeing parallax in the position of planets as seen at different seasons on Earth– Parallax may not be observable because of immense

distances of sphere of stars


Arguments AgainstArguments Against

• Damage to Aristotelian science, which was more than just a physical system of world– Aristotelian science had become Church orthodoxy - an

article of faith

• Parallax not seen (should it be?)• Copernican system offered no observation which was

explainable only by it and not by Ptolemaic system…at the time


Most Important, though...Most Important, though...

Copernicus’ idea was the watershed event that started a revolution in thought. It even gave a new meaning to the word “revolution”!

The Copernican revolution forever displaced the earth and its humble inhabitants from the center of the universe!


Tycho Brahe Tycho Brahe (1546-1601)(1546-1601)


Tycho BraheTycho Brahe

• Extensive naked-eye observations which were basis for acceptance of heliocentric cosmology– Observations accurate to 1 minute of arc - best

naked-eye– Published his own cosmology

• Planets orbit Sun• Sun and Moon orbit Earth


Tycho BraheTycho Brahe

• Parallax measurements of supernova in 1572


Johannes Kepler Johannes Kepler (1571-1630)(1571-1630)

…and his three laws


Johannes KeplerJohannes Kepler

• Convinced that mathematical relations existed that could make sense of planetary motion– Acquired and analyzed Brahe's observations of planets– 1609, New Astronomy, contains first two laws of planetary motion– 1619, The Harmonies of the World, contains third law

• Extended laws derived from basically Mars to all planets, regarded laws as universal--very imaginative step

• His big idea--orbits are ellipses, not circles!



• First Law--The orbit of a planet about the Sun is an ellipse with the Sun at one focus



Semi-major axis

Semi-minor axis

"a"


Johannes KeplerJohannes Kepler• Second Law--A line joining a planet and the Sun sweeps

out equal areas in equal intervals of time



• Third Law--The square of a planet’s sidereal period around the Sun is directly proportional to the cube of the length of its orbit’s semimajor axis

» Where P is the period in years

» and a is the semimajor axis in AU of elliptical orbit

32 aP




Galileo Galilei Galileo Galilei (1564-1642)(1564-1642)


Galileo GalileiGalileo Galilei

• 1632, The Dialogues of Galileo Galilei on the Two Principal Systems of the World: The Ptolemaic and Copernican– Powerful enemies convinced Pope that Galileo had cast

Ptolemaic system in unfavorable light

• 1633, book banned and Galileo publicly humiliated before papal tribunal– Forced to recant Copernican views

• Last 9 years of life spent in Arcetri under house arrest


Galileo GalileiGalileo Galilei

• Galileo’s dispute with Church often recited as classic example of “war between theology and science”– mostly true, but there were also conflicts of

personalities--priests and scientists are human, too!


Galileo’s Astronomical ObservationsGalileo’s Astronomical Observations

• Devised telescope in 1609 having heard of its invention in Holland

• Discoveries and observations with telescope– Jupiter's four large satellites– Craters and mountains on Moon– Phases of Venus– Milky Way composed of individual stars– Observes sunspots (not new)

• 1609, published discoveries in Starry Messenger


Galileo’s Astronomical ObservationsGalileo’s Astronomical Observations


Method of Experimental ScienceMethod of Experimental Science

• Galileo establishes standard for doing experimental science with Starry Messenger– Design experiment– Build equipment– Take and analyze data– Publish results


Modern Concepts of MotionModern Concepts of Motion

• Body in motion will continue indefinitely at same speed and in same direction (law of inertia)

• Force is responsible for change in body’s motion

External External ForceForce


Falling BodiesFalling Bodies

• Falling body one of most common experience, but also one of most mysterious of experiences

• In free fall in vacuum, all objects--of whatever weight, size, or constitution--fall given distance in same interval of time

• Free fall is uniformly accelerated motion, i.e., gains equal increments of speed in equal times

• Earth exerts influence on body in free fall or rolling down an inclined plane - gravity (not new to scientific discussion)


Falling Bodies Falling Bodies (cont)(cont)

Surface of EarthSurface of Earth

Massive Massive BodyBody

Less Less Massive Massive BodyBody

Strike Strike TogetherTogether

1.5 m1.5 m

1.23 m1.23 m

0.78 m0.78 m

0.44 m0.44 m

0.20 m0.20 m

0.05 m0.05 m

0.5 s0.5 s

0.4 s0.4 s

0.3 s0.3 s

0.2 s0.2 s

0.1 s0.1 sTimeTime DistanceDistance


Galileo’s ContributionGalileo’s Contribution

• Galileo brings together strands of medieval thought regarding space, time, and motion– 1632, published Dialogues on the Two Great World

Systems– 1638, published Discourses and Mathematical

Demonstrations Concerning Two New Sciences Pertaining to Mechanics and Local Motion


Isaac Newton Isaac Newton (1642-1727)(1642-1727)


Isaac Newton (1642-1727)Isaac Newton (1642-1727)

• Educated at Trinity College, Cambridge University– Entered in 1661 to study mathematics

• Years of 1665 and 1666 were Plague years with university closed – Newton spent 1665-66 on family farm

• 1687, published Mathematical Principles of Natural Philosophy– Instant success revealing Newton's genius

• 1704, published Opticks


Newton's PrincipiaNewton's Principia



• A most impressive work– Lays out essential physical concepts and laws– Develops a new mathematical formulation of theory– Application to many long-standing problems

• Planetary motion• Lunar motion• Tides• Etc.



• Provides a standard for doing scientific investigations (along with Opticks in 1704)

• Establishes for all times mathematics not only as language of physics (and all science) but as a means of knowing


Newton’s LawsNewton’s LawsNewton’s Laws of Motion:

1 Bodies move in uniform (straight line) motion unless acted on by a force

2 Acceleration proportional to force, inversely proportional to mass

F is forcea is acceleration

m is mass

3 To every action there is an equal and opposite reaction

Newton’s Law of Gravity:– Mutual gravitational attraction is

proportional to both masses, inversely proportional to distance squared

• F is force• G is gravitational constant• m is mass of each body• r12 is separation

m

Fa

212

21

r

mGmF


Law of GravityLaw of Gravity

• Always attractive, never repulsive• Based on concept of "action-at-a-distance”

– Ability of one body to influence motion of second body without physical contact

• For two spheres, r12 is distance between centers, not surfaces– One can think of spherical bodies attracting each other as if

they were mathematical points

mm11

mm22

rr1212

FF1212

FF2121


Newtonian MechanicsNewtonian Mechanics

Newton's theories of motion and gravitation reigned for over 200 years accurately described all known phenomenon until late 1800s

precession of perihelion of mercury different than predicted

new theory of light and electomagnetism has some philosophical problems


Geometries of SpaceGeometries of Space

• Euclidean space - space of our experience– Euclid, Aristotle, Galileo, Newton

• Non-Euclidean space - understood from mathematical arguments, not practical experience– Einstein, and others


General RelativityGeneral Relativity

• 1916, general relativity devised by Einstein

…gravity as curvature!

7 Sep 2000 ASTR103, Sec 3, GMU, Dr. Correll

General Relativity - BasicsGeneral Relativity - Basics

• General relativity - alternative theory of gravity– Not action-at-a-distance Newtonian force field – Newtonian gravity may be replaced by accelerations

arising from curvature of spacetime produced by matter

– Bodies always follow shortest available path (geodesic)

in response to local structure of curved spacetime


Two-Dimensional Spacetime CurvatureTwo-Dimensional Spacetime Curvature

Curvature of 2-dimensional Curvature of 2-dimensional space due to large mass starspace due to large mass star

Curvature of 2-dimensional Curvature of 2-dimensional space due to small mass starspace due to small mass star


Cast of CharactersCast of CharactersPlato Circa 400 BC,

GreeceIdeal form: eg—uniformcircular motion

N/A

Aristotle Circa 350 BC,Greece

Celestial spheres, naturalmotions & violent motions

N/A

Ptolemy 140 AD, Alexandria Capstone of Greekthought—geocentric model:Heavenly spheres with cycleand epicycles to account forretrograde motion of planets

Mathematical Syntaxis,or better know as TheAlmagest (thanks to theArabs)

Copernicus 1507 AD, Poland Heliocentric model…nodiscriminating obsevationaldata, however.

De RevolutionibusOrbium Coelestium, orThe Revolution of theHeavenly Orbs

Galileo Circa 1600, Italy First telescope observations:(make your own list)Physics of motion--acceleration of gravity

Siderial Messenger andDialogue Concerning theTwo Chief WorldSystems

Tycho Brahe Circa 1600, Denmark 20 years of data on star andplanet positions

N/A

Kepler Circa 1600, Germany Keplers’ Laws Mystery of the UniverseNewton 1643-1727, Great

BritainNewtons three laws ofmotion and law of gravity

Principia

Einstein 1879-1955, Germany(later the USA)

Theory of Relativity: Gravityas curvature of spacetime

Journal publications


Some CalculationsSome Calculations

• Kepler’s Laws:1 Orbits of planets are

ellipses with the sun at one focus

2 A line from a planet to the sun sweeps over equal area in equal time

3 Orbital period squared is proportional to it’s averaged distance from the sun cubed

• P2 = ka3








Some Calculations Some Calculations (cont)(cont)

Newton’s Laws of Motion:1 Bodies move in uniform

(straight line) motion unless acted on by a force

2 Acceleration proportional to force, inversely proportional to mass

a = F/m

3 To every action there is an equal and opposite reaction

Newton’s Law of Gravity:– Mutual gravitational

attraction is proportional to both masses, inversely proportional to distance squared

F = GMm/r2












……until next timeuntil next time

A time to embrace, and a time to refrain from embracing;

a time to seek, and a time to lose;

a time to keep, and a time to cast away;

a time to rend, and a time to sew;

a time to keep silence, and a time to speak;

a time to love, and a time to hate;

a time for war, and a time for peace.

--Ecclesiastes 3:6-9

Date post:	26-Dec-2015
Category:	Documents
Upload:	owen-watkins
View:	215 times
Download:	1 times

7 Sep 2000ASTR103, Sec 3, GMU, Dr. Correll1 Ch 2--Gravitation/Planetary Motion.

Documents