Astronomy in the Middle Ages

Copernicus, Brahe, Kepler

http://tau.fesg.tu-muenchen.de/~iapg/web/fame/seiten/copernicus.php www.astronomes.com/i0_histoire/brahe.jpg antwrp.gsfc.nasa.gov/apod/image/kepler_hist.gif

Goethe: "Of all discoveries and opinions, none may have exerted a greater effect on the human spirit than the doctrine of Copernicus. The world had scarcely become known as round and complete in itself when it was asked to waive the tremendous privilege of being the center of the universe. Never, perhaps, was a greater demand made on mankind — for by this admission so many things vanished in mist and smoke! What became of our Eden, our world of innocence, piety and poetry; the testimony of the senses; the conviction of a poetic — religious faith? No wonder his contemporaries did not wish to let all this go and offered every possible resistance to a doctrine which in its converts authorized and demanded a freedom of view and greatness of thought so far unknown, indeed not even dreamed of."

Nicholas Copernicus

• Nicholas Copernicus was born in Poland in 1473. His uncle was a bishop, and Copernicus enjoyed the privilege of an excellent liberal arts education.

Copernicus (2)

• As an adult, Copernicus was employed by the Catholic Church. He pursued astronomy as a passionate hobby.

• During his studies, Copernicus examined

the writings of the ancient Greeks, especially Ptolemy. Copernicus was disgusted by the inconsistencies within Ptolemy’s model, especially the equant.

Copernicus (3)

• Because Copernicus considered the geocentric model unworkable, he revived the heliocentric model of Aristarchus.

• Copernicus published his ideas in an

influential book De Revolutionibus Orbium Coelestium (On the Revolutions of the Celestial Spheres.)

www.bo.astro.it/copernic/derevol.gif

The Copernican Model • Sun is at the center of the cosmos. • Earth rotates on its axis, and revolves

around the sun (explaining the daily or diurnal motion of the sun & stars.)

• All the heavenly bodies revolve around the sun (including the earth) on crystalline spheres which turn at constant velocities. (We again have the problems of how the sun & planets appear to speed up and slow down and the variations in retrograde motions!)

The Copernican Model (2)

• Copernicus realized that his model had to predict the existence of stellar parallax, but he explained why parallax wasn’t observed by arguing that the stars were much farther away than the ancients thought.

• This explanation has turned out to be very true!

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The Copernican Model (3)

• Copernicus’ model was much simpler and more elegant than the geocentric model, and it could be used, through geometry, to accurately measure the distances between the planets and the sun.

• It also explained retrograde motion in a much more natural way.

• But there were still problems.

Church resistance

• Through the centuries, the Church had interpreted several verses of Scripture to indicate that the Earth was the center of the universe.

• Ideas that questioned this Church teaching might lead people to question other teachings, threatening the Church’s religious and temporal power.

Tycho Brahe • About 75 years after

Copernicus’ birth, Tycho Brahe was born in Denmark (1546).

• Like Copernicus, Brahe was very well connected (related to the Danish royal family), and spent his nights pursuing his passionate hobby, observing the sky.

http://www.haverford.edu/physics-astro/songs/Tycho_Brahe.jpg

http://www.humanities.uci.edu/users/vfolkenflik/VRF%20Sources/tycho%20brahe%20large.jpg

Tycho Brahe (2)

• Tycho made 2 great contributions to astronomy. He built an observatory called the Uraniborg (Castle of the Heavens), where he also built and used excellent equipment to observe and record the positions of the planets and over 700 stars to an accuracy of 1 arcminute (1 / 21,600th of a circle).

Tycho’s quadrant (protractor). Used for measuring the declination of stars.

http://www.vialattea.net/pagine/astro1/Urani2.jpg

Uraniborg

http://boojum.as.arizona.edu/~jill/NS102_2006/Lectures/Lecture4/uraniborg.painting.jpg

Tycho Brahe (3)

• Tycho also observed a supernova in Cassiopeia in 1572. Tycho wrote to other astronomers all over Europe and as far away as China, asking for the position of the supernova in their skies.

• All the other astronomers reported the supernova in the same position in the sky. – Conclusion?

Tycho Brahe observing the supernova in 1572.

www.tayabeixo.org/articulos/tycho.htm

The 1st Nail in the Coffin

• Tycho’s observation of the supernova was the first nail in the coffin of the geocentric model.

• One of the premises of the ancients was that the universe was perfect and therefore unchanging. Here was evidence that the universe could and did change.

Johannes Kepler • Johannes Kepler was born in Germany in

1571, just one year before Brahe’s observation of the supernova.

• Kepler trained as a mathematician and taught math in Graz, Austria, where became obsessed with using math to describe and model the cosmos.

• Kepler couldn’t find an equation that would exactly fit the positions of Mars; he needed better data.

A Crucial Move

• In 1600, Kepler moved to Denmark to work as a mathematician for Tycho Brahe.

• Brahe needed Kepler’s superb mathematical mind, and Kepler needed Brahe’s excellent observations of the positions of the planets (especially Mars).

• In 1601 Tycho died. His widow reluctantly gave Kepler access to Brahe’s data.

Kepler’s Laws

• Using Brahe’s data, Kepler finally discovered the laws that describe the movement of the planets.

• Law 1: The orbits of the planets are

ellipses (not circles). The sun is at one focus of the ellipse, and the other focus is empty.

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Kepler’s Laws (2)

• The 2nd Law: A line joining the orbiting planet to the sun sweeps out equal areas in equal times. A consequence of this is that the planet travels fastest in its orbit at perihelion (closest point to the sun) and slowest in its orbit at aphelion (farthest point from the sun.)

Regions A, B, and C all have equal areas. A planet would move over those areas in equal times.

http://www.hyperhistory.com/online_n2/people_n2/science_n2/keplerlaw.html

Kepler’s 2nd Law

http://www.physics.northwestern.edu/Phyx103/web/kepler.html

Follow the hyperlink below, then scroll down the page to “Quicktime Movie of Kepler’s 2nd Law”.

Kepler’s 3rd Law

• Also called the Harmonic Law, the 3rd law states that the square of a planet’s orbital period (p, in years) is proportional to the cube of the planet’s average orbital distance (a, in Astronomical Units or AU)

p2 = a3

Example

• A planet is observed to have an orbital period of 8 years. What is its orbital distance from the sun?

• (8)2 = a3 (64)1/3 = 4 A.U.

• An Astronomical Unit or AU is the average distance between the earth and the sun (150,000,000 km or 93,000,000 miles.)