Tycho Brahe ( ) Tycho s Supernova. Tycho s Observations. Key Concepts: Lecture 8

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Key Concepts: Lecture 8 Contribution of Tycho Brahe: detailed observations of the planets.

as his own son. Trained as a lawyer but secretly studied astronomy after being impressed that mortals could predict astronomical events.

Supported by the King Frederick II of Denmark he built an observatory on the island of Hven financed by one ton of gold His adopted father had

Tycho s Observations He made a long series of very precise observations of the motions of the planets Very accurate since they were made with a

average to reduce the errors Made observations over many years 1576-1591 Realized the motions of planets did not match the predictions of

1 Key Concepts: Lecture 8 Contribution of Tycho Brahe: detailed observations of the planets. Kepler and his 3 Laws of Planetary Motion Galileo Tycho Brahe ( ) Danish born member of nobility Stolen by his uncle, who adopted him as his own son. Trained as a lawyer but secretly studied astronomy after being impressed that mortals could predict astronomical events. Very arrogant and hard to get along with and played the role of a courtly prince with a gold nose. Supported by the King Frederick II of Denmark he built an observatory on the island of Hven financed by one ton of gold His adopted father had saved Frederick from drowning, but then died of pneumonia. Tycho s Observations He made a long series of very precise observations of the motions of the planets Very accurate since they were made with a very large quadrant circle (<0.5 arc minute) [1 degree = 60 arc minutes i.e. we write this as 1 = 60 ] Made repeated observations and took the average to reduce the errors Made observations over many years Realized the motions of planets did not match the predictions of Ptolemy Tycho s Supernova The supernova of 1572 Noticed a brilliant star had appeared in constellation of Cassiopeia Observed that it faded slowly over the following 2 years Demonstrated that the universe was changing and imperfect Showed that it had the same position no matter where on Earth it was observed - thus it was at a great distance.

Tycho s Supernova today d=7500 light years How big is the supernova remnant? This picture taken in year ~2000A.D.

Tycho s Cosmology Didn t agree with the Copernican system Tycho placed the Earth at the center because: He could

He came up with a compromise Stationary Earth at center Sun moves around the Earth All other celestial bodies

born a commoner in Germany His father was a mercenary His mother, an inn-keeper's daughter, was a healer and

Went to college at Tubingen were he was recognized as a mathematical genius and went to teach math at a

wrong) to explain the motion of the 6 known planets.

Kepler and Brahe Meet Brahe had to leave Hven after Fredrick II drank himself to death.

Tycho knew he needed a mathematician to help him model his observations They meet Feb 4, 1600.

2 Tycho s Supernova today d=7500 light years How big is the supernova remnant? This picture taken in year ~2000A.D. How fast is the blast wave moving? Tycho s Cosmology Didn t agree with the Copernican system Tycho placed the Earth at the center because: He could not measure parallax of stars He believed in Aristotelian physics Realized that the Ptolemaic system didn t work He came up with a compromise Stationary Earth at center Sun moves around the Earth All other celestial bodies move around the Sun His model worked no better than Ptolemy s Needed better mathematics Kepler ( ) Was born a commoner in Germany His father was a mercenary His mother, an inn-keeper's daughter, was a healer and herbalist who was later tried for witchcraft. Went to college at Tubingen were he was recognized as a mathematical genius and went to teach math at a Protestant School in Graz While in Graz he worked on a complicated mathematical theory (that turned out to be wrong) to explain the motion of the 6 known planets. Attempted to get observational data of the motions of the planets to test his theory. Kepler and Brahe Meet Brahe had to leave Hven after Fredrick II drank himself to death. He went to Prague As a Protestant, Kepler was driven out of Graz when the Catholics took over the city. Tycho knew he needed a mathematician to help him model his observations They meet Feb 4, Formed an uneasy working relationship. Tycho feared that Kepler would become more famous than him, so he would only show him data on Mars (his most challenging object) Tycho died October 21, 1601, maybe from a burst bladder after following dinner party etiquette: not leaving table before host. Kepler received Tycho s data from the family following a death bed request by Tycho: Let me not seem to have died in vain.

Kepler Solves Mystery of Planetary Motions It took Kepler 8 years to solve the motion of Mars He tried various combinations of circular motions He finally abandoned circular motion and tried ovals

The other focus is empty & located in space Distance between the planet and the Sun changes as the planet moves along its elliptical orbit Planets move along orbits which have a special and regular

3 Kepler Solves Mystery of Planetary Motions It took Kepler 8 years to solve the motion of Mars He tried various combinations of circular motions He finally abandoned circular motion and tried ovals and other geometric shapes He found that an ellipse could produce the motions of the planets Kepler s 1 st Law of Elliptical Orbits (1609) Planets move in elliptical orbits with the Sun at one focus The other focus is empty & located in space Distance between the planet and the Sun changes as the planet moves along its elliptical orbit Planets move along orbits which have a special and regular geometrical shape Gets rid of idea of uniform circular motions Properties of Ellipses Ellipses: The shape is defined by the separation between the two foci of the ellipse When the foci coincide the shape is a circle As the foci separate from each other the ellipse gets flatter The amount by which an ellipse differs from a circle is defined as an ellipse s eccentricity Each point on an ellipse has the property that the sum of its distances to the two foci is the same The line through the foci to both sides of the ellipse is called the major axis Kepler s 2 nd Law of Equal Areas (1609) Kepler noted that Mars speeds up when it approaches the Sun He found that a line drawn between the Sun and a planet sweeps out an equal area in an equal period of time anytime during its orbit Planetary motions are non-uniform but vary in a regular way Planets move more slowly when they are far from the Sun and fastest when they are near the Sun The increase in speed as a planet moves toward the Sun makes it appear that the Sun is pulling on the planet

Kepler s 3 rd (Harmonic) Law (1618) The Harmonic Law P 2 = k a 3 P is the period of the planet s orbit a is the planet s average distance to the Sun k is a constant which is the same for all planets

their orbits Astronomy Enters a New Era! Astronomical objects are viewed as actual bodies not distant ethereal or mythical entities.

4 Kepler s 3 rd (Harmonic) Law (1618) The Harmonic Law P 2 = k a 3 P is the period of the planet s orbit a is the planet s average distance to the Sun k is a constant which is the same for all planets The more distant a planet from the Sun The slower it moves in its orbit The longer it takes to complete an orbit Since a single constant works for all planets suggests a single physical cause for their orbits Astronomy Enters a New Era! Astronomical objects are viewed as actual bodies not distant ethereal or mythical entities. Realization that the laws of nature are the same for both the Earthly and Heavenly domains. Kepler s Laws Kepler s scheme correctly described planetary motions when compared to the accurate observations of Tycho Together laws 2 and 3 imply that there exists a force, between the Sun and planets, that weakens with increasing distance Invested Sun with physical properties necessary for the uniform description of planetary motions Kepler recognized there must be a force at work but could not figure out what it was. He speculated it may be magnetism, which, of course, is wrong. Galileo Born in the Italian renaissance; contemporary of Kepler. Father was a professional lute player & amateur mathematician. Galileo studied medicine at the University of Pisa but then quit. Spent 4 years at home, tinkering and reading Virgil and Ovid and studying mathematics with a tutor. At 25 appointed professor of mathematics at Pisa & lectured on mathematics, astronomy & poetry. fired because he taught against Aristotelian beliefs. Moved to University of Padua - invented scientific instruments & conducted experiments. Financial troubles led him to construct & market the telescope.

Galileo: The Father of Modern Science Galileo s Telescopic Observations Before Galileo Science was memorizing the knowledge of the

mountains, valleys, craters Measured height of mountains from their shadow & got correct answer Galileo & His Telescope Galileo s

5 Galileo: The Father of Modern Science Galileo s Telescopic Observations Before Galileo Science was memorizing the knowledge of the ancients (Babylonian's & Greeks) Insight was based on philosophical ideas Galileo Experimentation was the basis for testing knowledge TRUST NO ONE!! See for yourself New insight came from explaining experimental results The Moon: Moon not a perfect orb Saw features on surface, e.g. mountains, valleys, craters Measured height of mountains from their shadow & got correct answer Galileo & His Telescope Galileo s Telescopic Observations Jupiter: Constructed his telescope in 1609 telescopes & spyglasses already in existence for ~30 years His telescope was very primitive Objects appeared only 10 times bigger Optical quality was very poor First to use telescope for astronomical observations All his telescopic observations refute the Aristotelian view of the universe Saw Jupiter as a disk with features - Red Spot Jupiter is a physical body like the Moon or Earth Discovered the four brightest satellites orbiting Jupiter Not every object revolves around the Earth

Galileo s Telescopic Observations Venus: Observed many phases of Venus Venus is a body like the Moon Observed more phases than compatible with

rather than Latin for masses - best seller resulted in many telescope sales Critics attack him claiming telescopic observations were faulty

of the constant) Telescope & Galileo Milky Way: Resolved the Milky Way into many Stars A seemingly infinite number of stars Sun: Observed Sun and

model, Galileo realized the need to develop a new physics to replace that of Aristotle.

6 Galileo s Telescopic Observations Venus: Observed many phases of Venus Venus is a body like the Moon Observed more phases than compatible with Ptolemaic model Starry Messenger Telescopic Observations described in Siderius Nuncius (Starry Messenger) March 12, 1610 written in Italian rather than Latin for masses - best seller resulted in many telescope sales Critics attack him claiming telescopic observations were faulty Kepler supported Galileo s observations with his own telescopic observations Moons of Jupiter obeyed Kepler s 3rd law (but with a different value of the constant) Telescope & Galileo Milky Way: Resolved the Milky Way into many Stars A seemingly infinite number of stars Sun: Observed Sun and discovered Sunspots: measured the rotation rate Showed that Sun was not perfect Galileo & A New Physics To prove the validity of Copernican model, Galileo realized the need to develop a new physics to replace that of Aristotle. He revised the notion of natural & forced motions on Earth downward motion - needs a force - GRAVITY horizontal motion is natural, with no forces, objects would move in a uniform way because of their INERTIA (or momentum)

Describing Motion Position Velocity Rate of change of position (speed & direction) 80 km/hr Acceleration 40 km/hr Rate of change of velocity 2 examples of acceleration: (a) Change in speed but

on it Solves problem in Aristotelian physics of why motion doesn t stop immediately when force is removed.

Galileo experimented with balls and inclined planes to study inertia (b) Change in direction but not speed Describing Motion Position Velocity Rate of change of position (involves a speed &

7 Describing Motion Position Velocity Rate of change of position (speed & direction) 80 km/hr Acceleration 40 km/hr Rate of change of velocity 2 examples of acceleration: (a) Change in speed but not direction Inertia (an object keeps moving because of its momentum) New description of natural motion Inertia is defined as the tendency of a body to keep moving after all forces stop acting on it Solves problem in Aristotelian physics of why motion doesn t stop immediately when force is removed. Horizontal motion of objects through the air viewed as natural, unforced motion due to object s inertia. Galileo experimented with balls and inclined planes to study inertia (b) Change in direction but not speed Describing Motion Position Velocity Rate of change of position (involves a speed & direction) Acceleration Rate of change of velocity 2 examples of acceleration: Gravity New description of forced motion on Earth Falling is not a natural motion but forced and due to gravity Gravity acts on all bodies in the same way in the absence of air resistance or other forces rate of acceleration is the same for all masses Experiments with falling objects - Leaning Tower of Pisa

Galileo s Cosmology Copernican liked Copernican order supported by telescopic observations supported by new laws of motions on Earth

Giordano Bruno s Cosmology 1548-1600 There are countless suns and countless earths all rotating around their suns in exactly the same

We see only the suns because they are the largest bodies and are luminous, but their planets remain invisible to us because they are

On the Infinite Universe and Worlds, 1584 Tried for heresy by the Roman Inquisition and burned at the stake, in part, for these views.

8 Galileo s Cosmology Copernican liked Copernican order supported by telescopic observations supported by new laws of motions on Earth Memorial to Giordano Bruno, Campo de Fiori, Rome But ignored work of Kepler Heavens separate from Earth Universe may be infinite Giordano Bruno s Cosmology There are countless suns and countless earths all rotating around their suns in exactly the same way as the seven planets of our system. We see only the suns because they are the largest bodies and are luminous, but their planets remain invisible to us because they are smaller and non-luminous. On the Infinite Universe and Worlds, 1584 Tried for heresy by the Roman Inquisition and burned at the stake, in part, for these views. Galileo & the Inquisition Galileo declared himself a believer in the Copernican System in 1613 Warned to stop teaching the Copernican model as truth by Catholic Church in 1616 Friend, Cardinal Barberini became Pope Urban VIII in 1623 Publishes Dialogue on the Two Chief World Systems with approval of Church in Comparison of Geocentric & Heliocentric models

Galileo s Inquisition Dialogue: takes form of a conversation between 3 philosophers Salviati : brilliant philosopher who eloquently argues for the Copernican system Simplicio (Simpleton):

recant & Excommunicated Eppur Si Muove Placed under perpetual house arrest Dialogue placed on forbidden list along with works of Copernicus & Kepler Removed from forbidden list in 1835 Galileo

9 Galileo s Inquisition Dialogue: takes form of a conversation between 3 philosophers Salviati : brilliant philosopher who eloquently argues for the Copernican system Simplicio (Simpleton): defends Geocentric model using the Pope s favorite arguments Sagredo: 3rd philosopher who is quick to see the truth in Salviati s arguments Pope angry - orders Inquisition Galileo forced to recant & Excommunicated Eppur Si Muove Placed under perpetual house arrest Dialogue placed on forbidden list along with works of Copernicus & Kepler Removed from forbidden list in 1835 Galileo finally cleared in 1992 by Pope John Paul II, acknowledging the errors committed by the Church tribunal that judged the scientific positions of Galileo. Statue of Galileo erected in the Vatican in 2008

Ptolemy (125 A.D.) Ptolemy s Model. Ptolemy s Equant. Ptolemy s Model. Copernicus Model. Copernicus ( )

Ptolemy (125 A.D.) Ptolemy s Model. Ptolemy s Equant. Ptolemy s Model. Copernicus Model. Copernicus ( ) Ptolemy (125 A.D.) Designed a complete geometrical model of the universe that accurately predicted planetary motions with errors within 5 0 Most of the geometric devices and basic foundations of his model