Mars or Bust A 325 Year Journey Andrew

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 2 nd 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 Ec lipt Day-Night Cycle: Stars rotate overhead with a 1 -day period ic Path of Planets: Planets, Sun and Moon travel same path through the sky: The ecliptic. Retrograde Motion: Planets generally move from West-to. East 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 (If. A, 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 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/Nat. Sci 102/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 2 nd 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 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 3 rd Law) 2 r m M Force decreases with distance (Inverse Square Law)

From gravity to Kepler’s 3 rd 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 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 same as the gravitational mass? • The laziness “m” term in F=ma • 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?