Astronomy 111 – Lecture 10 Galileo Galilei



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Astronomy 111 – Lecture 10

Galileo Galilei

And

Sir Isaac Newton



Galileo Galilei

  • Main Themes for today :

  • Important Discoveries with the telescope:

  • Moons of Jupiter

  • Phases of Venus

  • Craters & Mountains on the Moon

  • Sunspots

  • Confrontation with the Church

The First Modern Astronomer

  • Galileo Galilei (1564-1642)

  • Italian Contemporary of Kepler

  • First modern scientist (in many ways)

  • Gifted mathematician

  • Brilliant observer and experimenter

  • Preferred experimentation and measurement to philosophical rhetoric.

  • Staunch anti-Aristotelian

  • Often at odds with the scholarly establishment

The Aided Eye

  • The telescope was invented in 1608 by Dutch spectacle makers.

  • Tradition says by Hans Lipperhey (?)

  • Word spread fast:

  • In April 1609, one could obtain them in eyeglass shops in Paris.

  • First one reached Italy in August of 1609

  • Galileo learned about the telescope in 1609, but did not get a chance to see one.

  • Based on a description, and acquainted with lens making, he made his own.

  • Solved many technical problems, and came up with a design that produced good-quality images with a magnifying power of 20x.

a most beautiful & delightful sight

  • Galileo soon turned his telescope on the night sky.

  • In 1610, he published his telescopic observations in the Sidereus Nucius (The Starry Messenger).

  • Later observations published in letters, and in a longer work, The Assayer, in 1623.

a most beautiful & delightful sight

  • Among these observations were:

  • Craters and Mountains on the Moon

  • Sunspots & Solar Rotation

  • Moons of Jupiter

  • Phases of Venus

  • Galileo made other important observations

  • Milky Way is made of myriads of faint stars

  • odd shape of Saturn.

Fact 1 : About the Moon

  • Galileo found craters and mountains on the Moon:

  • Moon was not a smooth, perfect sphere as taught by the Aristotle and Ptolemy.

  • Surface was “... rough and uneven, and just like the surface of the Earth itself...”

  • Galileo was able to measure the heights of lunar mountains using their shadows.

  • Conclusion : The Moon was another world like the Earth.

Fact 2 : About the Sun

  • Galileo observed sunspots:

  • Bright surface of the Sun had dark spots that changed and moved across its surface.

  • Discerned solar rotation over time.

  • Sun was not a perfect body, and was in fact rotating.

  • Contemporaries also reported them (they appear in Chinese records as early as 28 BC, but nobody in the west had access to this knowledge).

  • Conclusion: The Sun imperfect, contrary to Aristotelian and Ptolemaic teachings. Further, if a huge object like the Sun were rotating, why not the Earth?

Fact 3 : About Jupiter

  • Galileo discovered 4 moons orbiting Jupiter

  • Jupiter appeared as a disk.

  • 4 points of light that followed it and moved in orbits around it.

  • Deduced that they were moons (We now call them the Galilean Satellites of Jupiter)

  • Conclusion: The Earth is not the only center of motion in the Universe.

  • There was a solar system in miniature around Jupiter for all to see!

Fact 4 : About Venus

  • Venus goes through phases like the Moon

  • Sequence of phases and changes in diameter proved conclusively that Venus orbits the Sun.

  • Ptolemaic theory predicts the opposite of what is observed with the telescope.

  • The Sun was also a center of Motion.

  • Profoundly damaging to the Ptolemaic system.

  • Didn’t prove the Copernican system (it was also consistent with the Tychonic system).

Galileo’s Impact

  • The impact was immediate and forceful:

  • Skeptics claimed that the telescope was lying (and Galileo, too) and entrenched.

  • Kepler was delighted, and soon got his own telescope, as did many others.

  • Many scholars began to take the Copernican system seriously.

  • The discoveries brought Galileo immediate fame throughout Europe.

  • With telescopes everyone could literally "see for themselves". More than all the profound philosophical speculations or obscure mathematical arguments, this was behind the tremendous impact of Galileo's observations.

  • These phenomena were observed facts of nature, and had to be confronted.

This Road leads to trouble…

  • Galileo knew he could hold his own on the ground of scholarly confrontation.

  • He was now by far the most famous scientist in Europe, and immensely influential.

  • This position led him to miscalculate his own influence, and to badly misjudge the influence of his enemies.

Galileo and the Church

  • 1616:

  • The Church officially declares that the heliocentric theory is “philosophically false and at least an erroneous belief.”

  • De Revolutionibus is officially banned.

  • Galileo was called to an audience with Cardinal Robert Bellarmine, who cautioned him verbally to stop teaching and defending the Copernican model in public.

An important ‘Dialogue’

  • 1624:

  • Galileo writes “A Dialogue on the Two Chief World Systems”, ably defending the Copernican system.

  • Seeks permission from Pope Urban VIII to publish it, but is rebuffed.

  • 1632:

  • Galileo’s dialogue is published in Florence, written in Italian (Tuscan), not Latin.

  • It was an instant success & widely acclaimed.

The Trial of Galileo

  • 1633:

  • Enemies of Galileo convinced Pope Urban VIII that a character in the Dialogue (Simplicio) who ineptly defends Ptolemy is a thinly veiled caricature of the Pope himself.

  • Galileo is summoned by the Roman Inquisition and a document is produced alleging that Bellarmine in 1616 specifically forbade him to discuss the Copernican system in any way

  • Modern scholarship has shown that this document is a forgery.

The Charges against Galileo

  • Galileo faced two charges:

  • Disobedience of Bellarmine’s 1616 order.

  • Misleading censors who published his book.

  • Publicly humiliated and threatened with torture, Galileo had no choice but to admit guilt, and “abjure, curse and detest the aforesaid errors and heresies...

Galileo under House Arrest

  • Galileo was placed under house arrest at his villa in Arcetri near Florence until his death in 1642.

  • Despite this, in 1636 he finished “The Two New Sciences” describing his earlier experiments in mechanics.

  • Published in Protestant Leyden in 1638.

  • Laid the foundations of classical physics.

And still, it moves !

  • Galileo spent his final 4 years in blindness, and died under house arrest, on January 8, 1642.

  • On Christmas Day of that same year, Isaac Newton was born in Woolsthorpe(England).

  • In 1992, 350 years later, Pope John Paul II officially declared Galileo innocent.



Isaac Newton’s ‘Principia’

  • Isaac Newton (1642-1727)

  • 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.

  • Graduated from Cambridge 1665




How the Plague comes into play

  • During Plague years 1665-1666, Cambridge closed and he went home to Woolsthorpe.

  • Spent two years in Woolsthorpe, during which he

  • Invented the integral and differential calculus.

  • Developed the binomial theorem.

  • Started fundamental work on optics.

  • Formulated his laws of motion & gravitation.

  • He published none of it until years later.

Being a Professor

  • In 1669 (at age 26!) he became the Lucasian Professor of Mathematics at Trinity College, Cambridge.

  • Settled into the life of a Cambridge don:

  • Continued fundamental work on optics (invented reflecting telescope).

  • Carried out a variety of experiments.

  • Was always unprepared for classes and hated to teach.

Newton’s ‘Principia’

  • 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

  • The result : Philosophiae Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy)

An important Book !

  • The Principia is one of the most important books in history:

  • 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, causal explanations of the nature of the physical world.

  • Unified all motions into three simple laws.

The 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.

Talking about motion

  • Some key terms explained :

  • All motion is composed of two parts:

  • 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 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.

  • Further, the acceleration will take place in the same direction as the applied force.

The mathematical expression

  • Expressed Mathematically:

  • a = F/m

  • Acceleration is proportional to force, and inversely proportional to mass.

  • F = ma

  • Force is mass times acceleration.

What, the heck, does that mean ?

  • Second law has two parts:

  • Quantifies 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.

  • Forces and accelerations have a direction:

  • Accelerations are in the same direction as the applied forces.

What is the relevance for our planetary motion problem ?

  • Planets are continually changing the speed and direction of their motion as they orbit the Sun.

  • Move along ellipses with the Sun at one focus.

  • Move fastest when at perihelion, slowest when at aphelion.

  • They are thus accelerating in response to a force.

  • What force?

  • Newton : The Force of Gravity !


The Third Law of Motion

  • For every force applied to a body, there is an equal and oppositely directed force exerted in response.

  • Or, as it is more commonly stated:

  • To every action there is an equal & opposite reaction.

Forces always come in pairs !

  • The third law brings together the first and second laws, which deal with single bodies.

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

  • If I set an apple on a table, it pushes down on the table with a force equal to its mass times the acceleration due to gravity.

  • To hold it stationary, the table must be exerting an equal and opposite upward force.

A tremendous improvement

  • Newton’s laws of motion provide a complete, quantitative explanation of the motions of objects.

  • 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. Everything explained with the same set of self-consistent rules.



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