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Transcript
The Copernican
Cosmos
Ptolemaic Universe: “Epicycles Upon Epicycles”
-80 epicycles in the Ptolemaic system
-34 in the Copernican system
Copernicus:
 Application of Occam’s razor? Yes.
Epicycles overpopulate the heavens.
Overly complex system.
Three incorrect assumptions
 Earth was the center of the universe
 Uniform circular motion in the heavens
 Planets made from a perfect, unchanging
substance not found on the Earth
(quintessence).
Copernican Revolution
 Copernican Revolution is a term which
applies to the transition from a geocentric
cosmological model to a heliocentric
model.
Copernican model
Tycho and Stellar
Parallaxes
 Bio (1546-1601)
-scientist (astronomer)
-the nose
Sextant
Sextant
-measures the angles between two objects, generally a celestial
object and the horizon
Modern sextant
Why is the sextant
important to science?
Brahe used them for stellar measurements
Better navigation for ships
Observation of a stellar parallax for
Tycho? No, a parallax is not observed until
1838 with the help of a strong telescope.
Parallax
 Illustration
Tycho’s Cosmological
Model
Tycho’s Cosmological Model
 Tried to reconcile Ptolemaic and
Copernican systems
the five planets orbit the Sun, while the Moon and the Sun orbit the stationary Earth.
Sphere of fixed stars remained. Brahe supported his model by observing that the stars
did not shift (i.e., he could not observe parallaxes).
Other Contributions to
Science
 Studies on the new star of 1572
 Studies on comet of 1574
Both challenge the veracity of the Aristotelian
contention that the heavens are inalternable,
incorruptible.
 Tycho’s cosmology merges the Ptolemaic and
Copernican systems. Geocentric universe with
the planets revolving around the sun.
 Why? He could not observe a stellar parallax
(shifting of the stars) which would involve great
distances of empty space which was an
implausible notion (horror vacui-nature abhors a
vacuum).
 Made and used a sextant for stellar
measurements. Sextant has practical uses for
seafaring.
 Discovery of star (nova) of 1572 and comet of
1574 turns Aristotle’s thesis of the inalterability of
the heavens on its head.
 Assumption of uniform circular
motion (planetary circular orbits).
Johannes Kepler
1571-1630
Kepler’s Three Laws of
Planetary Motion
-First Law. Orbit of every planet is elliptical, with the sun as one of the foci.
Kepler’s Three Laws of
Planetary Motion
-Second Law. The radius vector (of a planet) traverses equal areas in equal times.
Kepler’s Three Laws of
Planetary Motion
-Third Law. T 2 = R 3
the square of the time of one orbital period (T2) is equal to the cube of its average orbital radius (R3).
Problem: What is Venus’s average distance from the sun? Well, we know Venus takes 224.7 earth days to orbit the
sun. Venus’s orbital period then would be 224.7/365 or.61 earth years. Since T 2 = R 3, then
.612=R3 or
.3721= R3
3√ .3721
= 3√ R 3
.71926=R
Which would be .71926 AU (astronomical units). If one AU for earth
is 93,000,000 miles, then Venus’s average distance would be
66,859,484.352618 miles.
Next time, class
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