Download Kepler`s Laws and Galileo 8/31/2016

Brahe and Kepler 1580-1630
• Brahe discovered a supernova, determined it was “far away”,
became famous, and was given an island for an observatory
 20 year od data on planet angular positions, and planet
geocentric parallax
• Kepler (mathematician, astrologer) hired by/succeeded Brahe to
analyze data. He also discovered a supernova and analyzed it, and
became famous. Last two supernovas observed in Milky Way
Galazy. Determined 3 Laws of planetary motion (1600-1630)
• Few “modern” tools (no calculus, no graph paper, no log tables)
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Observations of Brahe 1580-1600
• No telescopes, just “long sticks”
where one could easily measure
both angular coordinates at once
by “flipping” the device
• Measure relative location of
planets to stars (and moon). If do
at dusk and dawn for saw Mars
have a distance measurement
using parallax
• As far as I can tell Brahe was
mostly in Vienna and Prague and
not on his island
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Kepler’s Data Analysis
• Kepler figured out correct orbital shape (circle vs
ellipse vs circle with circle, etc)
• Mercury and Venus relatively easy. Will be PHYS
162H activity 2. Looks like an ellipse
• Mars, Jupiter and Saturn tougher, especially as
Jupiter has 12 year orbit and Saturn 30 years 
Kepler mostly did Mars as about 2 years and so
Brahe’s data had 10 orbits of Mars around the Sun
• Orbital period for all planets easy
• Distance better measured for closer. Ratio easier
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Kepler’s Laws of Motion
• A big step was realizing that
Earth’s orbit about the Sun also
wasn’t a circle – mostly he used
relative location of Mars after
repeated orbits around the Sun
(Mars is close and so most
accurate measurements)
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Apparent Shift = Parallax
• A moving observer sees fixed objects move.
• Near objects appear to move more than far objects
• The effect is due to the change in observation point,
and is used by our eyes for depth perception.
Geocentric parallaxEarth as base
Heliocentric parallax-use orbit about Sun
as base. Use for stars as need telescope
angle A
Earth
angle B
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Kepler’s Laws of Planetary
Motion (1630)
FIRST LAW: The orbit of a planet is an
ellipse with the sun at one focus.
A line connecting the two foci in the
ellipse always has the same length.
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Kepler’s Second Law
• The line joining a planet and the sun sweeps
equal areas in equal time.
The planet moves
slowly here.
The planet moves
quickly here.
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Kepler’s Third Law
• The square of a planet’s period is proportional to the cube of
the length of the orbit’s semimajor axis.
• Mathematically, T2/a3 = constant (=1 if use 1 Earth year and
1 AU as units)
• The constant is the same for all objects orbiting the Sun
 same process determines all planets’ motions
direction of orbit
semimajor axis: a
The time for one
orbit is one period: T
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Mean Distance Sidereal
from Sun
Orbital Period
AU
Mercury 0.387
Venus
0.723
Pe
0.241
0.615
Earth
Mars
Jupiter
1.000
1.881
11.857
1.000
1.524
5.203
Saturn 9.537
Uranus 19.191
Neptune 30.069
29.424
83.749
163.727
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Third Law Example
• Jupiter compared to Earth
• If we measure that it takes Jupiter 11.9 years to
orbit the Sun then:
distance 3(Jupiter-Sun) = period(Jupiter)2
distance = period2/3
distance = (11.9*11.9)1/3
distance = (142)1/3 = 5.2 AU
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Mean Distance Sidereal
from Sun
Orbital Period
AU
Mercury 0.387
Venus
0.723
Pe
0.241
0.615
Earth
Mars
Jupiter
Saturn
1.000
1.881
11.857
29.424
1.000
1.524
5.203
9.537
Uranus 19.191
Neptune 30.069
D3
.05
0.4
1
3.5
140
866
P2
.05
0.4
1
3.5
140
866
83.749
163.727
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• All other orbits obey Kepler’s law (with different
constant related to mass of system)
• Moons of Jupiter, satellites about Earth, two stars
about each, material in Milky Way Galaxy
• Due to same underlying physics
• They needed to develop Physics as a science:
understand motion, forces, and gravity
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• Kepler correctly determined the motion of the
planets.
• Did not address WHY. Simply what curve best
matched orbits and some arithmetical relationships
• The WHY was determined by physicists like Galileo
and Newton.
• They needed to develop Physics as a science:
understand motion, forces, and gravity
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Galileo 1564-1642
• Professor of art, mathematics, natural philosophy,
astronomy in Florence, Pisa, Padua with occasional
“contract” work for various Dukes, etc
• Very strong proponent of the scientific method – use of
observations to test theories
• Early work:motion, and practical elements like hydrostatics
• 1609: first person to use a telescope for astronomy 
became the most famous scientist/celebrity in Europe
• Last 25 years of life was often in trouble with the Catholic
Church. His celebrity helped to save him
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Galileo – Telescope - 1610
• Jupiter had at least 4 moons which circled it (something besides Earth
could be the center of motion); there were many more stars,
mountains on moon  Book Starry Messenger
• Venus had definite phases and clearly orbiting Sun
• Observed sunspots (patches on Sun). Sun revolved on own axis.
Wasn’t “perfect” and changes in unpredictable manner
• Observed Saturn’s rings but was confused as to what they were
• Wrote book on Copernican vs Ptolemaic models in 1632, nominally
with Church’s permission. But it offended Church. Dialogue
Concerning the Two Chief World Systems. In Italian. Character in
book Simplicio defended Church’s position
 spent last 10 years of his life in house arrest. Catholic church said
contrary to scriptures……Church admits in error in 1992
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Jupiter’s Moons (1610)
4 moons can be seen with a
small telescope. Change
position with time  how long
it takes to go around vs
distance from Jupiter
More discovered: Pluto now has 4 moons
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Phases of Venus (1610)
Venus has phases like
the Moon which are
easily explained by
having it orbit the Sun
and impossible to
explain if the Earth was
at the center of the Solar
System
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Sunspots
Sunspots are now known
to be magnetic storms.
Allows the rotation of
the Sun to be readily
observed. Seen without
telescopes before Galileo
but his observations
were of higher quality
and showed Sun’s 25
day rotation
 Sun isn’t “perfect” and rotates like Earth
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