© Sierra College Astronomy Department1 Lecture 3b: A Sun-Centered System Nicolaus Copernicus (1473 – 1543) Copernicus, a contemporary of Columbus, worked

© Sierra College Astronomy Department© Sierra College Astronomy Department 11

Lecture 3b: A Sun-Centered SystemLecture 3b: A Sun-Centered System

Nicolaus Copernicus (1473 – 1543)Nicolaus Copernicus (1473 – 1543)

Copernicus, a contemporary of Copernicus, a contemporary of Columbus, worked 40 years on a Columbus, worked 40 years on a heliocentric (sun-centered) model heliocentric (sun-centered) model for two reasons:for two reasons: Ptolemy’s predicted positions for Ptolemy’s predicted positions for

celestial objects had become less celestial objects had become less accurate over time.accurate over time.

The Ptolemaic model was not The Ptolemaic model was not aesthetically pleasing enough.aesthetically pleasing enough.

D-8, Sun-centered

83 or Ptolemy’s System



The Copernican SystemThe Copernican System

His system revived many of the ideas of His system revived many of the ideas of the ancient Greek Aristarchus.the ancient Greek Aristarchus.

The Earth rotates under a stationary sky The Earth rotates under a stationary sky (which gives the same observations as a (which gives the same observations as a rotating celestial sphere and a stationary rotating celestial sphere and a stationary Earth).Earth).

The Earth revolves around a stationary The Earth revolves around a stationary Sun, which appears to move among the Sun, which appears to move among the background stars.background stars.




Motions of the PlanetsMotions of the Planets His model explains the generally west to His model explains the generally west to

east motion of the planets.east motion of the planets. Observed retrograde motion of planets Observed retrograde motion of planets

beyond Earth (such as Mars) is explained beyond Earth (such as Mars) is explained more simply and conclusively.more simply and conclusively.

Sidereal period vs. synodic period (see Chapter S1, p. 93-95)

Synodictrack

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Fig 1-25Real Retrograde

SynodicPlanet, p. 64




Copernicus had the Moon revolving around Copernicus had the Moon revolving around the Earth. All others circled the Sun.the Earth. All others circled the Sun.

The Sun’s apparent motion north and south The Sun’s apparent motion north and south of the equator is explained by having the of the equator is explained by having the Earth’s equator tilted with respect to the Earth’s equator tilted with respect to the planet’s orbit around the Sun.planet’s orbit around the Sun.

The tilt of Earth’s axis causes the ecliptic to The tilt of Earth’s axis causes the ecliptic to be sometimes above and sometimes below be sometimes above and sometimes below the celestial equator.the celestial equator.

tilt



Comparing The Two ModelsComparing The Two Models

1. Accuracy in Fitting the Data1. Accuracy in Fitting the Data A good model accurately fits all observed A good model accurately fits all observed

data.data. Copernicus’s model, Copernicus’s model, though more aesthetic though more aesthetic

than Ptolemy’s, still was than Ptolemy’s, still was no moreno more accurate accurate in predictingin predicting all observed planetary all observed planetary motions.motions.

Copernicus was forced to add small Copernicus was forced to add small epicycles of his own to improve accuracy.epicycles of his own to improve accuracy.




2. Predictive Power2. Predictive Power Using the Using the Astronomical Unit (AU)Astronomical Unit (AU) - the - the

average distance between Earth and Sun - average distance between Earth and Sun - Copernicus predicted with amazing accuracy Copernicus predicted with amazing accuracy the Sun-to-planet distances for the 5 planets the Sun-to-planet distances for the 5 planets visible from Earth in the 1500s.visible from Earth in the 1500s.




3. Aesthetics: Mercury and Venus3. Aesthetics: Mercury and Venus The Copernican model was more The Copernican model was more

aesthetic since it could explain the aesthetic since it could explain the motions of Mercury and Venus without motions of Mercury and Venus without resorting to special rules needed by the resorting to special rules needed by the Ptolemaic model.Ptolemaic model.

Copernicus offered a simpler explanation Copernicus offered a simpler explanation for retrograde motion that required no for retrograde motion that required no use of epicycles.use of epicycles.



Tycho Brahe (1546 – 1601)Tycho Brahe (1546 – 1601)

Tycho was born 3 years after Tycho was born 3 years after Copernicus died.Copernicus died.

Tycho built the largest and most Tycho built the largest and most accurate naked-eye instruments accurate naked-eye instruments yet constructed.yet constructed.

He could measure angles to within He could measure angles to within 0.1º, close to the limit the human 0.1º, close to the limit the human eye can observe.eye can observe.



Tycho Brahe (1546 – 1601)Tycho Brahe (1546 – 1601)

Tycho opposed the heliocentric model because he could Tycho opposed the heliocentric model because he could not observe not observe stellar parallaxstellar parallax

Nearby stars would shift relative to faraway stars if the Nearby stars would shift relative to faraway stars if the earth were moving around the sunearth were moving around the sun

Since no parallax was observed (to observational limits), Since no parallax was observed (to observational limits), either the stars were over 7000 AU away or the earth did either the stars were over 7000 AU away or the earth did not move around the sunnot move around the sun

Tycho had thought he had measured angular sizes of the Tycho had thought he had measured angular sizes of the stars and this vast distance would have implied stars to stars and this vast distance would have implied stars to be several AU in size, so he concluded that Earth did not be several AU in size, so he concluded that Earth did not movemove

Proposed “compromise” model which had planets going Proposed “compromise” model which had planets going around Sun but Sun going around Eartharound Sun but Sun going around Earth

Parallax

Tychonicmodel



Johannes Kepler (1571 – 1630)Johannes Kepler (1571 – 1630)

In 1600, a year before Tycho died, Kepler In 1600, a year before Tycho died, Kepler accepted a position as Tycho’s assistant, accepted a position as Tycho’s assistant, working on models of planetary motion.working on models of planetary motion.

Tycho’s best data had been gathered for Mars.Tycho’s best data had been gathered for Mars. Based on circles and epicycles Kepler’s best Based on circles and epicycles Kepler’s best

model for Mars matched Tycho’s data to an model for Mars matched Tycho’s data to an accuracy of 0.13º (8 arcminutes).accuracy of 0.13º (8 arcminutes).

Yet, this error exceeded the error in Tycho’s measurements, which bothered Kepler.

Kepler’s persistence led him to abandon circles and try other shapes. The shape that worked for Mars and all other planets was the ellipse.



Johannes KeplerJohannes KeplerThe EllipseThe Ellipse The The ellipseellipse is a geometrical shape every point is a geometrical shape every point

of which is the same total distance from two of which is the same total distance from two fixed points (the fixed points (the focifoci, , one is called one is called focusfocus).).

EccentricityEccentricity is the distance between the foci is the distance between the foci divided by the longest distance across (major divided by the longest distance across (major axis).axis).

Astronomers refer to the Astronomers refer to the semi-major axissemi-major axis distancedistance and eccentricity.and eccentricity.

ellipse



Kepler’s First Two Laws of Planetary Kepler’s First Two Laws of Planetary MotionMotion

1st Law:1st Law: Each planet’s path around the Each planet’s path around the Sun is an ellipse, with the Sun at one focus Sun is an ellipse, with the Sun at one focus of the ellipse (the other focus is empty). of the ellipse (the other focus is empty). [Note: [Note: perihelionperihelion vs vs aphelionaphelion]]

2nd Law:2nd Law: A planet moves along its elliptical A planet moves along its elliptical path with a speed that changes in such a path with a speed that changes in such a way that a line from the planet to the Sun way that a line from the planet to the Sun sweeps out equal areas in equal intervals of sweeps out equal areas in equal intervals of time.time.

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1st Law

2nd Law



Kepler’s Third LawKepler’s Third Law

3rd Law:3rd Law: The ratio of the cube of a The ratio of the cube of a planet’s average distance planet’s average distance aa from the Sun from the Sun to the square of its orbital period to the square of its orbital period pp is the is the same for each planet: same for each planet: a³/p² = Ca³/p² = C

ExampleExample: Mars’s period is 1.88 year. Its : Mars’s period is 1.88 year. Its distance from the sun is calculated as:distance from the sun is calculated as:

aa³/(1.88 yr)² = 1 AU³/yr²³/(1.88 yr)² = 1 AU³/yr²

aa³ = 3.53 AU³³ = 3.53 AU³

aa = 1.52 AU = 1.52 AU Tablea3=p2



Kepler’s ContributionKepler’s Contribution

Kepler’s modification to the Copernican Kepler’s modification to the Copernican model brought it into conformity with the model brought it into conformity with the data. Finally, the heliocentric theory data. Finally, the heliocentric theory worked better than the old geocentric worked better than the old geocentric theory.theory.

Kepler’s breakthrough choice of ellipses Kepler’s breakthrough choice of ellipses to explain planetary motion was empirical to explain planetary motion was empirical - ellipses worked but he did not know - ellipses worked but he did not know why they worked.why they worked.


Lecture 3c: GalileoLecture 3c: Galileo

Galileo Galilei (1564 – 1642)Galileo Galilei (1564 – 1642)

Galileo was born in 1564 and Galileo was born in 1564 and was a contemporary of Kepler.was a contemporary of Kepler.

Galileo built his first telescope Galileo built his first telescope in 1609, shortly after hearing in 1609, shortly after hearing about telescopes being about telescopes being constructed in the Netherlands.constructed in the Netherlands.

Galileo was the first person to Galileo was the first person to use a telescope to study the use a telescope to study the sky sky (and publish the results!).(and publish the results!).

poor Thomas Harriot (1560-1621)poor Thomas Harriot (1560-1621)



Galileo Galilei and the TelescopeGalileo Galilei and the Telescope

Galileo made 6 important observationsGalileo made 6 important observations:: Mountains and valleys on the MoonMountains and valleys on the Moon Sunspots Sunspots More stars than can be More stars than can be observed observed

with the naked eye with the naked eye Four moons of JupiterFour moons of Jupiter Complete cycle of phases of Complete cycle of phases of

VenusVenus The nature of EarthshineThe nature of Earthshine


The Moon


11-Sep-2006 13-Sep-2006

http://umbra.nascom.nasa.gov/images/latest.html


Aldebaran

Pleiades

Stars seen with just your eyes

TAURUS


Aldebaran

Pleiades

More seen stars through telescope than with just your eye

TAURUS


Earthshine




The Moon, the Sun, and the StarsThe Moon, the Sun, and the Stars Though Galileo’s first three observations Though Galileo’s first three observations

do not disprove the geocentric theory, do not disprove the geocentric theory, they cast doubt on the the assumption of they cast doubt on the the assumption of perfection in the heavens.perfection in the heavens.

The existence of stars too dim to be The existence of stars too dim to be seen with the naked eye also cast doubt seen with the naked eye also cast doubt on the literal interpretation of some Bible on the literal interpretation of some Bible passages.passages.




Satellites of JupiterSatellites of Jupiterhttp://http://www.webpersonal.net/parabolix/castro/satgali.en.htmlwww.webpersonal.net/parabolix/castro/satgali.en.html

In 1610 Galileo discovered that Jupiter had four In 1610 Galileo discovered that Jupiter had four satellites of its own, now known as the satellites of its own, now known as the Galilean Galilean moonsmoons of Jupiter. of Jupiter.

Jupiter and its orbiting moons contradicted the Jupiter and its orbiting moons contradicted the Ptolemaic notions that the Earth is the center of Ptolemaic notions that the Earth is the center of all things and if the Earth moved it would leave all things and if the Earth moved it would leave behind the Moon.behind the Moon.

Galileo Jup




The Phases of VenusThe Phases of Venus Galileo observed that Venus goes through Galileo observed that Venus goes through

a full set of phases: a full set of phases: full, gibbous, full, gibbous, quarter, crescentquarter, crescent..

Venus’s full set of phases can be Venus’s full set of phases can be explained by the heliocentric theory.explained by the heliocentric theory.

The Ptolemaic theory predicts that Venus The Ptolemaic theory predicts that Venus will always appear in a crescent phase, will always appear in a crescent phase, which is not borne out by the which is not borne out by the observations.observations.

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The Starry MessengerThe Starry Messenger ( (Sidereus NunciusSidereus Nuncius, 1610), 1610)First telescopic discoveriesFirst telescopic discoveries

Letters on SunspotsLetters on Sunspots (1613)(1613)Correspondence with German amateurCorrespondence with German amateurRealized the general nature of sunspotsRealized the general nature of sunspots

Letter to the Grand Duchess CristinaLetter to the Grand Duchess Cristina (1615)(1615)The Bible and ScienceThe Bible and Science

The AssayerThe Assayer (1623)(1623)Opinions on Comets (dismissed as atmospheric [!])Opinions on Comets (dismissed as atmospheric [!])


Galileo Galilei’s Major WorksGalileo Galilei’s Major Works


The Dialogue Concerning the Two Chief World The Dialogue Concerning the Two Chief World SystemsSystems (1632)(1632)Discourse between three characters (Salviati, Discourse between three characters (Salviati,

Sagredo, Simplicio) about the geocentric and Sagredo, Simplicio) about the geocentric and heliocentric theories of the universeheliocentric theories of the universe

Led to his condemnationLed to his condemnationThis wasn’t his first controversy …This wasn’t his first controversy …


Galileo Galilei’s Major WorksGalileo Galilei’s Major Works



Galileo Galilei’s ControversyGalileo Galilei’s Controversy

SunspotsSunspots (1613) irked some Jesuits (1613) irked some Jesuits Copernicus’ book banned by Catholic ChurchCopernicus’ book banned by Catholic Church

Led to decree of 1616 about the heliocentric universeLed to decree of 1616 about the heliocentric universe Jesuit Orazio Grassi wrote book about Comets in 1619Jesuit Orazio Grassi wrote book about Comets in 1619

Had correct view of extraterrestrial nature of cometsHad correct view of extraterrestrial nature of comets Urban VIII becomes Pope in 1623Urban VIII becomes Pope in 1623

Good friend and supporter of GalileoGood friend and supporter of GalileoAssayerAssayer written in response to Jesuit bookwritten in response to Jesuit book

Dedicated to Urban VIIIDedicated to Urban VIII Dialogue Dialogue met with ire of some Jesuits and Pope Urban VIIImet with ire of some Jesuits and Pope Urban VIII

Thought to be personal attack (SimplicioThought to be personal attack (SimplicioPope’s view)Pope’s view)Book banned and led to heresy trial and conviction in 1633Book banned and led to heresy trial and conviction in 1633


Other SlidesOther Slides

Fall 2005



The Rebirth of AstronomyThe Rebirth of Astronomy

The Islamic world had many astronomical works that The Islamic world had many astronomical works that originated from Spain to Asia.originated from Spain to Asia. Some works were translated Greek works which were Some works were translated Greek works which were

otherwise lostotherwise lost In Europe the birth of universities started critical thinking In Europe the birth of universities started critical thinking

of the ancient Greek ideasof the ancient Greek ideas Oresme (1330 -1382): relative motionOresme (1330 -1382): relative motion Buridan (c1300 -1358): impetusBuridan (c1300 -1358): impetus

New ObservationsNew Observations Bacon (c1220 -1292) – experimentation the best way to acquire Bacon (c1220 -1292) – experimentation the best way to acquire

knowledgeknowledge Purbach, Regiomontanus – found errors in the Ptolemy tables Purbach, Regiomontanus – found errors in the Ptolemy tables

(mid 1400s)(mid 1400s)


Astronomy ClubAstronomy Club

Meets every Wednesday Meets every Wednesday at 9:30 AM in St-2at 9:30 AM in St-2

(Third Hour room)(Third Hour room)Fall 2005

Documents

© Sierra College Astronomy Department1 Lecture 3b: A Sun-Centered System Nicolaus Copernicus (1473 – 1543) Copernicus, a contemporary of Columbus, worked