How did Copernicus, Tycho, & Kepler challenge the Earth-centered idea?
· Copernicus proposed the sun-centered model (published in 1543)
· He used the model to determine the layout of solar system (planetary distances in AU)
· the model was no more accurate than the Ptolemaic model in predicting planetary positions, because it still used perfect circles
Tycho Brahe (1546-1601)
· Brahe compiled the most accurate (1 arc minute) naked eye measurements ever made of planetary positions
· He still could not detect stellar parallax, and thus still thought Earth must be at the center of the solar system (but recognized that other planets go around the Sun)
· He hired Kepler, who used Tycho's observations to discover the truth about planetary motion
Johannes Kepler (1571-1630)
· Kepler 1st tried to match Tycho's observations with circular orbits
· But an 8-arcminute discrepancy led him eventually to ellipses
What is an ellipse?
· an ellipse looks like an elongated circle
What are Kepler's 3 Laws of planetary motion?
1. Kepler's 1st Law: The orbit of each planet around the Sun is an ellipse with the Sun at one focus
2. Kepler's 2nd Law: As a planet moves around its orbit, it sweeps out equal areas in equal times (this means that a planet travels faster when it is nearer to the Sun and slower when it is farther from the Sun)
3. Kepler's 3rd Law: More distant planets orbit the Sun at slower average speeds, obeying the relationship
1. p² = a³
2. p = orbital period in years
3. a = average distance from Sun in AU
An asteroid orbits the Sun at an average distance a=4AU. How long does it take to orbit the Sun?
(Hint: Remember that p² = a³)
· B. 8 YEARS (a³ = 4 x 4 x 4 = 64² [square root] = pà8
How did Galileo solidify the Copernican revolution?
· Galileo Galilei (1564-1642) overcame major objections to Copernican view. Three key objects rooted in the Aristotelian view were the following:
1. Earth could not be moving because objects in air would be left behind
2. Noncircular orbits are not "perfect" as Heavens should be
3. If Earth were really orbiting sun, we'd detect stellar parallax
· Overcoming the 1st Objection (Nature of Motion):
oGalileo's experiments showed that objects in air would stay with a moving Earth
§ Aristotle thought that all objects naturally come to rest
§ Galileo showed that objects will stay in motion unless a force acts to slow them down (Newton's 1st law of Motion)
· Overcoming the 2nd Objection (Heavenly Perfection):
oTycho's observations of comet and supernova already challenged this idea
oUsing his telescope, Galileo saw:
§ Sunspots on the Sun ("imperfections")
§ Mountains and valleys on the Moon (proving it is not a perfect sphere)
· Overcoming 3rd Objection (Parallax):
oTycho thought he had measured stellar distances, so lack of parallax seemed to rule out an orbiting Earth
oGalileo showed stars must be much farther than Tycho thought - in part by using his telescope to see that the Milky Way is countless individual stars
oIf stars were much farther away, then lack of detectable parallax was no longer so troubling
oGalileo also saw 4 moons orbiting Jupiter, proving that not all objects orbit Earth
oGalileo's observations of phases of Venus proved that it orbits the sun and not Earth
oIn 1633 the Catholic church ordered Galileo to recant his claim that Earth orbits the Sun
§ His book on the subject was removed from Church's index of banned books in 1824
§ Galileo was formally vindicated by the Church in 1992
How did Copernicus, Tycho, & Kepler challenge the Earth-centered idea?
· Copernicus created a Sun-centered model; Tycho provided the data needed to improve this model; Kepler found a model that fit Tycho's data
How did Galileo solidify the Copernican revolution?
· His experiments and observations overcame the remaining objections to the Sun-centered solar system
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