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Lecture 3 Quiz 1

Lecture 3 Quiz 1 - Astronomy 100 Dr Wilson Lecture 3 An...

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Astronomy 100 - Dr. Wilson Lecture # 3 - 8/31/2010
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An Observational Astronomer: Tycho Brahe Tycho Brahe was a Danish nobleman who was born 3 years after the death of Copernicus. Brahe developed an observatory off the Danish coast on the island of Hveen. Tycho built the largest and most accurate naked-eye instruments yet constructed. He could measure angles to within 0.1º, or close to the limit the human eye can observe. He observed planetary positions for 20 years.
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Brahe’s Other Observations He observed what we now know to be a supernova in 1572 which he showed was located farther away than the Earth’s moon. He observed a comet in 1577 and showed this comet orbited the Sun and not the Earth. He showed that this comet traveled in an elongated orbit with varying speed.
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Tycho Brahe (cont.) He not only made careful measurements, but he recorded the accuracy of each measurement. Tycho was an observer, not a theorist.
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Tycho Brahe and Johannes Kepler Brahe was forced to leave Denmark and moved to Prague One year before his death, Brahe hired a young German mathematics teacher to serve as his assistant. His assistant was Johannes Kepler . Brahe wanted Kepler to prove that his own system (i.e. the Tychonic) was correct. Kepler promised to do so, but instead worked to prove the Copernican system.
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Johannes Kepler Kepler was the first astronomer to publicly assert his belief in the Copernican system in print. Kepler did so in the book The Cosmic Mystery which was published in 1594. Kepler was also a famous astrologer and a mystic. Kepler thought the planets made musical sounds as they orbited the Sun.
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Johannes Kepler Brahe gave his observational notes to Kepler just before he died in 1601. Tycho’s best data had been gathered for Mars. Based on circles and epicycles Kepler’s best model for Mars matched Tycho’s data to an accuracy of 0.13º (8 arcminutes).
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Johannes Kepler Yet, this error exceeded the error in Tycho’s measurements, which bothered Kepler. Kepler worked for 8 years on the orbit of Mars. Kepler’s persistence led him to abandon circles and try other shapes. The shape that worked for Mars and all of the other known planets was the ellipse .
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The Conic Sections
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Johannes Kepler and the Ellipse The Ellipse The ellipse is a geometrical shape every point of which is the same total distance from two fixed points (the foci ). Eccentricity is the distance between the foci divided by the longer of the two axes of the ellipse (i.e., the major axis, a). Eccentricity is also equal to the focal distance, c, divided by the semi-major axis.
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How to draw an ellipse with a pencil, two pins, and a string
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h = twice the focal distance g = the major axis
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Ellipses with same eccentricy But with different major axes Ellipses with same major axis But with different eccentricities
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Kepler’s First Two Laws of Planetary Motion 1st Law: Each planet’s path around the Sun is an ellipse, with the Sun at one focus of the ellipse and the other focus being empty.
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