Foundations-Copernican Revolution Lecture 2: Newton: Gravity and the Laws of Motion

Ancient Observatories Ancient Peoples around the world made places to mark dates from the celestial calendar and/or observe the sky  Chaco Canyon, New Mexicohttp://  Chichen Itza  Angor Wat, Cambodia  Medicine Wheel, Saskatchewan, Canada  Stonehenge, England  Abu Simbel, Egypt

Science vs. Pseudo-science  What makes science different?  What do we know?  How do we know it?  Why do we believe it?  Is what we know supported by the evidence?  Kuhn Paradigm  Thomas Kuhn: Structure of Scientific Revolution  Navigating the web of a 1000 lies

End of the world in 2012? December 21, 2012 See National Geographic and NASA websites on thisNational Geographic NASA  Mayan Calendar – long count calendar enters a new cycle Each cycle is 5, years–  The sun will cross in front of the center of the Milky Way But this has happened many times before No significant increase in gravitational interaction  Sun will be in solar maximum – more solar flares and storms This has happened may times before  A tenth planet known to the ancients that would hit us by end of the year would be visible to astronomers for past decade Why the hype?

Copernican model would have been a triumph of the Scientific Method Except It did not fit the data Scientific Method: a)Make high quality observations of some natural phenomenon b)Come up with a theory that explains the observations c)Use the theory to predict future behavior d)Make further observations to test the theory e)Refine the theory, or if it no longer works, make a new one - Occam’s Razor: Simpler Theories are better -You can prove a theory WRONG but not RIGHT Observation Theory Prediction

a) planets move on epicycles. b) planets orbit the Sun in the same direction. c) Earth moves faster in its orbit. d) they are closer than Uranus. e) they rotate quickly on their axes. Mars, Jupiter, and Saturn show retrograde motion because Question 1

a) planets move on epicycles. b) planets orbit the Sun in the same direction. c) Earth moves faster in its orbit. d) they are closer than Uranus. e) they rotate quickly on their axes. Mars, Jupiter, and Saturn show retrograde motion because Question 1 As Earth overtakes and “ passes ” the outer planets, they seem to slow down and then reverse direction.

a) why planets moved in the sky. b) why Earth was at the center. c) why retrograde motion occurred. d) why Earth wobbled on its axis. e) why inner planets were always seen near the Sun. Epicycles were used in Ptolemy ’ s model to explain Question 2

a) why planets moved in the sky. b) why Earth was at the center. c) why retrograde motion occurred. d) why Earth wobbled on its axis. e) why inner planets were always seen near the Sun.. Epicycles were used in Ptolemy ’ s model to explain Question 2 Planets were assumed to move uniformly on an epicycle, as it moved uniformly around Earth.

a) craters on the Moon b) sunspots c) lunar maria d) satellites of Jupiter e) stars of the Milky Way Which of Galileo ’ s initial observations was most challenging to established geocentric beliefs? Question 3

a) craters on the Moon b) sunspots c) lunar maria d) satellites of Jupiter e) stars of the Milky Way Which of Galileo ’ s initial observations was most challenging to established geocentric beliefs? Question 3 Seeing four moons clearly move around Jupiter disproved that everything orbited Earth and showed Earth could orbit the Sun and not lose its moon, too.

Question 4 Earth is closer to the Sun in January. From this fact, Kepler ’ s 2 nd law tells us a)Earth orbits slower in January. b)Earth orbits faster in January. c)Earth ’ s orbital speed doesn ’ t change.

Earth is closer to the Sun in January. From this fact, Kepler ’ s 2 nd law tells us a)Earth orbits slower in January. b)Earth orbits faster in January. c)Earth ’ s orbital speed doesn ’ t change. Kepler ’ s 2 nd law means that a planet moves faster when closer to its star. Faster Slower Question 4

At this time, actual distances of planets from Sun were unknown, but were later measured. One technique is "parallax" "Earth-baseline parallax" uses telescopes on either side of Earth to measure planet distances.

Timelines of the Big Names Copernicus Galileo Brahe Kepler Newton

Kepler's Third Law The square of a planet's orbital period is proportional to the cube of its semi-major axis. P 2 is proportional to a 3 or P 2  a 3 (for circular orbits, a=b=radius). Translation: the larger a planet's orbit, the longer the period. a b

3. Square of period of planet ’ s orbital motion is proportional to cube of semimajor axis. Kepler ’ s laws: 1.3 The Laws of Planetary Motion

Newton ( ) Kepler's laws were basically playing with mathematical shapes and equations and seeing what worked. Newton's work based on experiments of how objects interact. His three laws of motion and law of gravity described how all objects interact with each other.

Newton's First Law of Motion DEMO - Smash the HAND

Newton's First Law of Motion Last time – Demo of objects at rest Demo – nature of how objects move  Hover disk

Newton ’ s laws of motion explain how objects interact with the world and with each other. Newton ’ s first law: An object at rest will remain at rest, and an object will move in a straight line at constant speed if and only if the sum of forces that act on it are balanced. 1.4 Newton ’ s Laws

Newton's Second Law of Motion When a force, F, acts on an object with a mass, m, it produces an acceleration, a, equal to the force divided by the mass. a = F net m or F net = ma acceleration is a change in velocity or a change in direction of velocity.

Newton's Second Law of Motion Demo - Force and Acceleration Fan Carts

Clicker Question: Why didn’t my hand get crushed by the hammer? A: My bones are actually stronger than steel. B: The plate has a lot of inertia C: The plate is very strong D: The force of gravity kept the plate from moving

Newton's Third Law of Motion To every action there is an equal and opposite reaction. Or, when one object exerts a force on a second object, the second exerts a force on first, that is:  Equal in magnitude  Opposite in direction  Of the same type

Newton's Third Law of Motion DEMO: CART DEMO: Force Probes A. Cart 1 will exert a larger force on Cart 2 than Cart 2 exerts on Cart 1 B. Cart 2 will exert a larger force on Cart 1 than Cart 1 exerts on Cart 2 C. The carts will exert forces of equal magnitude on each other D. Not possible to determine

Newton's Law of Gravity For two objects of mass m 1 and m 2, separated by a distance R, the force of their gravitational attraction is given by: F = G m 1 m 2 R 2 F is the gravitational force. G is the "gravitational constant". An example of an "inverse-square law". Your "weight" is just the gravitational force between the Earth and you.

Gravity For two massive objects, the gravitational force is proportional to the product of their masses divided by the square of the distance between them. 1.4 Newton ’ s Laws

Gravity On Earth ’ s surface, the acceleration due to the force of gravity (Newton’s 2 nd Law) is approximately constant, and directed toward the center of Earth. 1.4 Newton ’ s Laws

Falling Objects DEMO: paper and ball Movie: Hammer and FeatherHammer and Feather

Gravity The gravitational pull of the Sun keeps the planets moving in their orbits. 1.4 Newton ’ s Laws

Newton’s Laws and Gravity Massive objects actually orbit around their common center of mass; if one object is much more massive than the other, the center of mass is not far from the center of the more massive object. For objects more equal in mass, the center of mass is between the two.

Throwing a ball into orbit

Kepler ’ s laws are a consequence of Newton ’ s laws. 1.4 Newton ’ s Laws The orbit of a planet around the Sun has the common center of mass (instead of the Sun) at one focus.

Escape Velocity Velocity needed to completely escape the gravity of a planet. The stronger the gravity, the higher the escape velocity. Examples: Earth 11.2 km/s Jupiter 60 km/s Deimos (moon of Mars) 7 m/s = 15 miles/hour Consider Helium Gas at room temperature (300 K) E = kT = 4.1 x erg E = 0.5 m v 2 = 4.1 x erg so v = 1 km/sec on average, but sometimes more

Newton's Laws of Motion Newton ’ s Zeroeth Law of Motion Objects are dumb. They do not know the past and they are not good predictors of the future. They only know what forces act on them right now. Newton ’ s First Law of Motion Every object continues in a state of rest or a state of motion with a constant speed in a straight line unless acted on by an unbalanced force. Newton ’ s 2nd Law of Motion When a force, F, acts on an object with a mass, m, it produces an acceleration, a, equal to the force divided by the mass. Newton ’ s Third Law of Motion For every action there is an equal and opposite reaction. Or, when one object exerts a force on a second object, the second object exerts an equal and opposite force on the first. a = F net m

Newton's Law of Gravity For two objects of mass m 1 and m 2, separated by a distance R, the force of their gravitational attraction is given by: F = G m 1 m 2 R 2 F is the gravitational force. G is the universal "gravitational constant". An example of an "inverse-square law". Your "weight" is just the gravitational force between the Earth and you. M = r v 2 G

What happens if ball is thrown harder than what is needed to go into circular orbit?

Escape Velocity Velocity needed to completely escape the gravity of a planet. The stronger the gravity, the higher the escape velocity. Examples: Earth 11.2 km/s Jupiter 60 km/s Deimos (moon of Mars) 7 m/s = 15 miles/hour Consider Helium Gas at room temperature (300 K) E = kT = 4.1 x erg E = 0.5 m v 2 = 4.1 x erg so v = 1 km/sec on average, but sometimes more