Download Galileo`s Motion, Newton`s Gravity

Mars or Bust! A 325 Year
Journey
Andrew Rivers, Northwestern University
Curiosity Landing Video
Mars Entry Descent & Landing (EDL): 7
Minutes of Terror
Mars JPL Curiosity Landing Trailer
Gravity
Drag force
Newton’s 2nd Law
Momentum Conservation
Constant acceleration motion
Mars Odyssey image of Curiosity Descent
Xkcd on the Mars Landing
First image from Mars Curiosity Hazard camera
Mars Opportunity rover winter panorama of Greeley Haven
Image Credit: NASA/JPLCaltech/Malin Space Science
Systems
Mars Curiosity Self-Portrait
Image Credit: NASA/JPL/UA
Curiosity tracks seen by Mars Reconnaissance Orbiter
Gravity and the Dance of the Planets
Gravity cannot be held
responsible for people falling
in love.
-Albert Einstein
The planets from the Messenger space probe from near the center of the solar
system. Image credit: NASA
The Scientific Lexicon
Theory
Predictions &
Testing
Hypothesis
Observations
Theory: A conceptual framework to explain a
range of observations. Substantiated by repeated
testing. The WHY and the end goal of science.
Tools of
the Trade
Testing: Hypotheses make
specific predictions which may
be tested
Tools of the Trade: Scientific
methods or techniques used in
testing
Hypothesis: A proposed, testable
explanation for an observation or
observations
Laws: Generalization of a set of
Laws scientific observations, often in
mathematical form. Doesn’t say
WHY.
Motions in Sky
Ptolemy vs.
Copernicus
Kepler’s Laws
Motions in the Sky
Day-Night Cycle: Stars rotate
overhead with a 1-day period
Path of Planets: Planets, Sun and Moon
travel same path through the sky: The ecliptic.
Retrograde Motion: Planets
generally move from West-toEast night to night, but
occasionally move backward.
The ecliptic: The apparent path of the sun
in the sky. Planets follow in this plane.
Ecliptic
Image Credit: Miloslav Druckmüller (UM FSI, Brno Univ. of Technology), Shadia Habbal (IfA, Univ. of Hawaii)
Zodiacal light from dust in the solar system plane traces the path of the ecliptic from horizon
to horizon. The solar system is oriented at about 60 degrees With respect to the Milky Way
Ptolemy vs. Copernicus
• Ptolemy
– Earth centered universe with
epicycles
• Copernican model
– Earth rotates, revolves around sun
– Sun at center of solar system
Ptolemy vs. Copernicus: Retrograde motion.
A model of the Ptolemaic model
of geocentrism. (Image
credit:Brian Brondel, wikibooks
Backwards motion explained
with loop-the-loop epicycles
Backwards motion by perspective
change. A “passing” effect.
Ptolemy vs. Copernicus: Parallax Motion.
The Earth Moves? How can we tell?
Tycho Brahe uses
Stellar Parallax
Tycho Brahe
"Eppur si muove“,
Galileo Galilei
Prediction: Copernicus predicts changing perspective,
therefore a back and forth parallax motion over a year
Result: Brahe sees no parallax. Failure for Copernican Theory?
Cosmological models
• In Ptolemy's system
– The heavens were wholly other
– Model only descriptive not predictive
• No attempt to describe why objects moved
around Earth at various speeds
• Copernican theory also didn’t say
anything about why planets orbited
stars
Ptolemy vs. Copernicus: Galileo’s Observations.
Galileo’s Telescope
Advocating for the Copernican
Theory, Galileo published his
results in Sidereus Nuncius
(Sidereal/Starry Messenger).
The Sun and Moon.
Galileo noted sunspots on the sun
and mountains and craters on the
Moon. Not perfect spheres, but
physical worlds like our own.
Not a direct test of Copernican theory, but suggestive.
Earth not unique in kind, but in a family of worlds
Testing Copernicus: Galileo’s Observations
Jupiter’s moons: a model
solar system
Moon & Sun: breakdown of perfection of
the heavens
Jupiter and moons Io, Europa,
Ganymede, and Callisto
The Moons of Jupiter.
“Stars that moved”
A model Copernican solar system
with Jupiter in the role of the Sun
Some objects didn’t revolve around Earth!
Like the planets around the Sun,
period increased with angular
distance from Jupiter
Not a direct test of Copernican theory
Testing Copernicus: Galileo’s Observations
Jupiter’s moons: a model
Copernican solar system
Moon & Sun: breakdown of perfection of the heavens
Phases of Venus: Phases
matched Copernican theory
Montage of Venus images
Image Credit: Efrain Morales
The Phases of Venus.
Changing Phases: Venus is either a “morning star or evening star” rising
ahead or setting behind the sun. It’s phases change through this motion
Size of Venus: Venus is closer to Earth when it is pointed toward sun and
therefore it’s thin crescent phase is larger.
• Venus is brightest when farthest from the
sun in the sky.
• Predicted illumination of Venus matched the
heliocentric prediction
Phases of Venus
Animation
Direct test of Copernican
theory! Phases matched.
Far away from sun=h
up in sky at sunset
Close to sun,
setting right after
Venus goes through phases, like the moon, depending on it’s
position in the sky relative to the sun
Modifying the Hypothesis: Kepler
complicates Copernican Theory
• Unlike Brahe, Johannes Kepler
believed in the Copernican system
• Motion of planets did not match
theory’s prediction.
– Epicycles still required!
– Mar’s orbit most deviant
• Kepler’s (painful) solution:
– Planets orbit in ellipses
Kepler postage stamp,
Germany, Guinea
Republic, 1994
Kepler’s first law of planetary motion
• Planets orbit in ellipses with the
sun at one focus.
– Ellipses are close to circular
Complication: Orbits not
perfect circles.
Kepler’s First Law Sketch
Image Credit: Carolyn Brinkworth & Claire Thomas
Kepler’s Second Law
• The line joining the planet to the Sun
sweeps out equal areas in equal times
as the planet travels around the ellipse
Fastest
Slowest
Complication: Speed of planet
varies throughout its orbit.
Kepler’s Third Law
• Relates period (T) or time it takes a planet to
orbit the sun and radius of orbit (r).
r=1 AU
T=1 yr
r=9.6 AU
T=29.7 yr
r=30.1 AU
T=164.8 yr
Period longer
with greater orbit
radius: outer
planets take longer
Not just because
greater distance to
travel. They also
go slower.
Keplers third law plot shows the relationship between orbital period and orbit radius
Test: All planets match, fit
mathematical relationship.
Summary: Kepler and Motion of Planets
Kepler’s First Law.
Kepler’s Second Law.
Kepler’s Third Law.
The Universality of Kepler’s Laws
Black Hole at Center of
Milky Way
Image Credit: A. Ghez
Kepler’s Laws were universal: they worked for all orbiting
objects. For the planets around the Sun, the moons of Jupiter and
the stars in the center of the Milky Way around a black hole
Summary
• Kepler’s Laws purely empirical
– Say nothing about why planets
• move in ellipses
• move faster closer to the sun
• have the relationship between period and
radius of orbit observed
• For the first time the theory of
Copernicus became more accurate
than Earth centered system
Question: Why are the complications of Kepler
any better than the epicycles of Ptolemy?
What about the “Why”?
• Ptolemy's system
– The heavens were wholly other
– Model only descriptive not predictive
• No attempt to describe why objects moved around Earth
at various speeds
• Copernican theory also didn’t say anything
about why planets orbited stars
• Philosophical arguments only
• Newton’s Realization
– To understand the motion of the planets, it is first
necessary to understand motion!
Explaining diverse
phenomena under one
elegant framework
Unification!
Separating science
from philosophy
The Scientific Method
Motions in Sky
Ptolemy vs.
Copernicus
Kepler’s Laws
Foundations:
Theory of Motion
Galileo vs.
Aristotle
Newton’s Laws
r
m F
F
M
Aristotle’s Theory of Motion
• Aristotle’s Law of Inertia
– A body, not acted on by any force remains at
absolute rest
– Force is proportional to velocity
– Have to push on something to keep in moving at a
constant speed.
Galileo’s Principle of Inertia
• The Motion studies of Galileo
• inclined planes
– Release balls at continually
decreased angles
– If all friction was removed,
moving objects would
never stop (even as angles
approached zero)
– objects in motion would
remain in motion
http://ircamera.as.arizona.edu/NatSci102/NatSci102/lectures/galileo.htm
Theory
of Motion
Newton’s First Law of Motion
• A body at rest remains at rest
• A body moving in a straight line
maintains a constant speed in the
same direction
Cautionary image from
the Montana-Wyoming
safety council.
Definition: acceleration=change in velocity
Vector=magnitude and
direction
Speeding up: changing magnitude
of vector=acceleration
Circular motion at constant
speed=changing direction of
vector=acceleration
Centripetal
Acceleration
Theory of
Motion
Newton’s 2nd Law of Motion
• Clarification of the First law
• What causes the acceleration?
– A force
• Relationship between force and acceleration
• m is called the inertial mass
– “Laziness” of an object, resistance to acceleration.
Newton’s Third Law of Motion
• Forces come in pairs
• For every “action” there is an equal
and equal and opposite “reaction”
• Example: I exert a rightward force on
the wall, the wall exerts an equal and
opposite leftward force on me
Equal and opposite force of
friction propels us forward
Summary: Newton’s Theory of Motion
Newton’s First Law.
Newton’s Third Law.
Forces come in pairs
Objects in motion…
Newton’s Second Law.
Acceleration always in same direction as net force
Motions in Sky
Ptolemy vs.
Copernicus
Kepler’s Laws
Foundations:
Theory of Motion
Galileo vs.
Aristotle
Law of gravity
Newton’s Laws
r
m F
F
Foundations:
Theory of Gravity
M
The Unification of Sir Isaac Newton
As Below
So Above
Newton’s Apple Tree
Voyager 1 leaving Solar System
The grandest unification in the history of science?
Newton’s Universal Gravity
Image Credit: Lowe, Singapore, OMO: Dirt is Good ad campaign
Any two masses attract each
other (Earth and Apple)
Larger masses (more inertia)
are harder to accelerate)
The Invention of Gravity
• Gravity Known
• Newton’s Leap: Postulate a Universal law
• Force between any two objects is
– Proportional to the mass of the objects
– Inversely proportional to the square of the
distance
• The constant of proportionality that makes
this an equality is called G
– The Universal gravitational constant
• The full relation is
• The mass in the equation is called the
gravitational mass
– Gravitational mass=inertial mass
• Why should they be the same?
• Apollo 15 Feather-Hammer Drop
Mystery: Why do different masses fall at same rate?
– Why is the inertial mass
• The laziness “m” term in F=ma
– The same as the gravitational mass?
• The attractiveness term in the universal
law of gravitation
– These terms are talking about different
things, why should they be exactly the
same?
Galileo’s Leaning tower of Pisa
ball drop experiment.
Apollo astronaut tests Galileo’s
experiment on the Moon
Theories often make
new, innovative
predictions
Cavendish Experiment
Any two masses attract!
Gravitational force between mass
pairs (m & M) causes wire to twist
Measuring force leads to
determination of G, the
gravitational constant
Unification: How is falling like orbiting?
Consider a cannon
The greater the initial speed v, the farther it travels
before hitting ground.
Even greater speed v=escape
If speed v is great enough, the Earth
curves out from under cannonball at
the same rate as it falls.
Not zero gravity for objects in
orbit, actually it’s free-fall!
Traveling on the “vomit comet”
Acceleration is
centripetal
Acceleration is in same
direction as gravitational pull
(toward center of circle)
r
M
m
F
F
Equal & Opposite Forces
(Newton’s 3rd Law)
2r
m
M
Force decreases with distance
(Inverse Square Law)
From gravity to Kepler’s 3rd law
• Apply Newton’s new physics to motion
of planets.
• Use force from gravity and new laws of
motion to predict the periods of the
orbits
Force responsible for acceleration
of Earth is Universal Gravitation
Force Framework
Grav force from sun
Accelerates Earth
Acceleration is
centripetal
Combine
Solve
Earth travels a
distance along the
circumference of
a circle
Kepler’s
Third
Law
Hubble Space Telescope
G from Cavendish
Experiment
Mass of the Earth m can be measured by knowing the orbital
period T of a satellite and its distance r from the earth’s center
Halley’s Comet
Edmund Halley Served as
“Newton’s Muse”, urging
Newton to back up his claim
of solving Kepler’s Laws. He
also funded the Principia.
Halley computed the orbit of a comet to show
that it was repeating, and he predicted its return
in 1758, one of the first tests of Newton’s theory.
Shape of the Earth
Newton predicted that because of the
“centrifugal” force, the Earth should be
flattened at the equator. Missions to
Lapland and Peru confirmed the oblate
spheroid shape.
“You choosing mid those frozen wastes
to roam, confirmed what Newton found
who stayed at home.
Voltaire (to de Maupertuis)
Summary
• Newton’s law of gravity universal
– Ties heavens/earth together under same
physical law
• Newton’s laws of motion + law of gravity
= Kepler’s third law
• Kepler’s third law allows measurement of
the mass of orbiting objects
– Need period of orbit T + separation r
Motions in Sky
Ptolemy vs.
Copernicus
Kepler’s Laws
Foundations:
Theory of Motion
Galileo vs.
Aristotle
Law of gravity
Newton’s Laws
r
m F
F
Foundations:
Theory of Gravity
M
Predictions &
Tests of gravity
Problems with Newton’s Gravity
• Action at a distance
– How is the gravitational force communicated
across a distance?
• How does the Earth “know” about the sun?
• Where’s the string?
•
•
Why is the inertial mass
•
The laziness “m” term in F=ma
The same as the gravitational mass?
•
The attractiveness term in the universal
law of gravitation
Leads to different masses
falling at same rate
“It is inconceivable that inanimate brute matter should,
without mediation of something else which is not matter,
operate on and affect other matter without mutual contact. ...
That gravity should be innate, inherent and essential to matter,
so that one body may act upon another at-a-distance, through
a vacuum, without the mediation of anything else by and
through which their action may be conveyed from one to
another, is to me so great an absurdity that I believe no man,
who has in philosophical matters a competent faculty of
thinking, can ever fall into it. So far I have explained the
phenomena by the force of gravity, but I have not yet
ascertained the cause of gravity itself. ... and I do not arbitrarily
invent hypotheses.”
(Newton. Letter to Richard Bentley 25 Feb. 1693)
How do we know the Earth revolves
around the sun?
Why do different masses
fall at the same rate?
How do you measure the
mass of the Earth?
How does Newton’s
theory of gravity and
motion explain Kepler’s
Second Law?