Astro 120 Spring 2016: Lecture 8 page 1
Reading: Chap. 4, Sect.1, 2, and 4, and Web-based article on orbits for next Thursday
Homework 3: Due today
Homework 4: Due next Thursday (or Tuesday if you want it graded before Exam 1)
Exam 1: Tuesday, February 15; practice questions etc. posted next week
towards the modern view
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Brief review of last time: Og through Tycho Brahe
Early Science
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• Greek Astronomy: perfect, immutable heavens, with Earth at the center
• uniform circular motions - epicycles
• computational scheme consistent with observations
1200s: Ptolemy’s method off by several degrees
• response: add more epicycles . . .
1543: Copernicus
• moved sun to center -----> Revolutionary!
• 1580: Tycho Brahe
• The Renaissance
• precise positions of planets
• stars are fixed, therefore very distant
• sky is not immutable
• Copernicus - Sun to the center
• Tycho Brahe - detailed observations to test Copernican model
• 1 stick in Aristotle’s eye - heavens are changeable & imperfect
• Galileo - telescope views of planets + physics experiments
• 2nd stick in Aristotle’s eye - Venus phases, Jupiter’s moons
• 3rd stick in Aristotle’s eye - experiments refute Aristotle’s physics
• 1609: Galileo
• astronomer: telescope studies show Copernicus right
• physicist: experiments with Gravity
Astro 120 Spring 2016: Lecture 8 page 3
Astro 120 Spring 2016: Lecture 8 page
1610 - Johannes Kepler
Kepler’s Law #1
mathematician and klutz
used Tycho’s data on the motion of Mars:
with no circular motion bias
to discover
Kepler’s Laws
of Planetary Motion
These are simple empirical laws explaining
planetary motion, derived from data only,
with no preconceptions.
Astro 120 Spring 2016: Lecture 8 page 2
• Planets orbit the sun in ELLIPTICAL orbits
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around the sun, with the sun at one ‘focus’
of the ellipse.
abandonment of “perfect circular motion”
4
Astro 120 Spring 2016: Lecture 8 page 5
The Earth’s orbit is an ellipse
Anatomy of an ellipse
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Astro 120 Spring 2016: Lecture 8 page 6
DEFINITION
where your distance from two fixed points adds up to a constant
FOCI - the two reference points
MAJOR AXIS
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longest dimension of ellipse
contains foci
usually refer to “semimajor axis” a
ECCENTRICITY
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measure of the flatness of the ellipse
e= (distance between foci) / 2a
e = 0 for a circle (semimajor axis = radius)
0 ≤ e ≤ 1 for an ellipse
e = 1 for a parabola
Astro 120 Spring 2016: Lecture 8 page
Kepler’s Law #2
• A line joining the planet to the Sun
sweeps out equal areas in equal times.
• abandon concept of constant speed
Astro 120 Spring 2016: Lecture 8 page
7
Kepler’s Law #3
• The Law of Periods:
Period2 = (semimajor axis)3
P2 = a3
(P in years, a in A.U.)
Bigger orbit (larger a) —> longer Period
planet moves faster when closer to the Sun
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Astro 120 Spring 2016: Lecture 8 page 9
Astro 120 Spring 2016: Lecture 8 page 10
Kepler’s 3rd Law
a[a.u.] P2
a3
P /a
0.0581
0.0580
1.0021
0.723
0.3782
0.3779
1.0008
1
1
1
1
1
1.881
1.524
3.5382
3.5396
0.9996
11.86
5.203
140.66
140.85
0.9986
29.42
9.539
865.54
867.98
0.9972
84.01
19.19
7057.7
7066.8
0.9987
164.8
30.06
27159
27162
0.9999
Planet
P[y]
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
0.241
0.387
0.615
2
3
Astro 120 Spring 2016: Lecture 8 page11
Astro 120 Spring 2016: Lecture 8 page 12
1666: Isaac Newton
mathematician: Invented calculus as a youth . . .
SYNTHESIZED:
Galileo’s Experiments
+
Kepler’s Laws
+
Calculus
into Physical Laws;
the basis of Modern Science
Apple falls -> Earth and apple attract each other
Moon and Earth attract each other, too
If moon moves sideways as it falls, it could forever
circle the Earth...
If moon moves sideways as it falls, it could forever
circle the Earth...
Newton’s Legacy
Astro 120 Spring 2016: Lecture 8 page 13
• Force of Gravity pulls planets towards Sun
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Newton’s Laws:
Newton #1: The Law of Inertia
• without gravity, planets would fly away in straight lines
A body moves at a constant velocity unless an
unbalanced force acts on it
Newton’s theory of gravity explains -simply- the
orbits of the planets
Understanding motions of the planets was the principal
discovery of astronomy from prehistory through 1700.
• Velocity: speed and direction
• example: 65 mph southbound
• Improved observations (”technology”) demanded
•
• Force: something that changes a body’s velocity
more precise models of the Solar System
This precision was
• something that changes body’s speed and/or direction
• an external “push” or “pull”
• approached by complex models (epicycles, etc.) but
• achieved by discovery of the underlying simplicity: Gravity
Astro 120 Fall 2015: Lecture 9 page 15
Astro 120 Spring 2016: Lecture 8 page 14
• Inertia: resistance to change in velocity
Newton’s Laws:
Astro 120 Spring 2016: Lecture 8 page 16
Newton #2: The Law of Force
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Force = mass x acceleration
Acceleration:
• (rate of) change in velocity
= (rate of) change in speed and/or direction
• examples:
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0mph to 60 mph in 12 seconds (accel.)
60 to 0 in 10 seconds (decel.)
turning left at the light (change in direction)
mass vs. weight
Inertia: a=F/m
• bigger mass: smaller accel. for same force
• inertia: resistance to acceleration by a force
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example: linebackers are big, wide receivers are small
example: shot put vs. golf ball
mass <–> inertia
weight <–> force