#### Transcript Galileo, Newton, and Einstein

25 pts of Extra Credit can be done, 10 pts of these points must be done before midterm (see page 41 of Student Handbook) The Class Web Site: astronomy.sierracollege.edu Lecture 3c: Galileo Galileo Galilei’s Major Works The Dialogue Concerning the Two Chief World Systems (1632) Discourse between three characters (Salviati, Sagredo, Simplicio) about the geocentric and heliocentric theories of the universe Led to his condemnation This wasn’t his first controversy … © Sierra College Astronomy Department 2 Lecture 3c: Galileo Galileo Galilei’s Controversy Sunspots (1613) irked some Jesuits Copernicus’ book banned by Catholic Church Led to decree of 1616 about the heliocentric universe Jesuit Orazio Grassi wrote book about Comets in 1619 Had correct view of extraterrestrial nature of comets Urban VIII becomes Pope in 1623 Good friend and supporter of Galileo Assayer written in response to Jesuit book Dedicated to Urban VIII Dialogue met with ire of some Jesuits and Pope Urban VIII Thought to be personal attack (SimplicioPope’s view) Book banned and led to heresy trial and conviction in 1633 © Sierra College Astronomy Department 3 Lecture 3c: Understanding Motion, Energy, and Gravity Going Towards a Grand Synthesis Galileo Galilei Inclined plane • Credited with setting the standard for studying nature through reliance on observation and experimentation to test hypotheses • The heavens had similar features to the Earth (contrast Aristotle) • Galileo was the first to develop our modern ideas of motion – made use of the inclined plane – Demonstrated that all objects at the Earth’s surface fall at the same rate regardless of mass – Proposed the concept of inertia that was to overthrow Aristotle’s notion that the natural motion of all earthly objects is to come to rest. René Descartes • Extended Galileo’s notion of inertia along the Earth’s surface to that of straight line motion • Proposed three laws of motion which would inspire Newton to create the now classical Three Laws of Motion © Sierra College Astronomy Department 4 Lecture 4: Newton Isaac Newton’s Grand Synthesis Robert Hooke • Had ideas of planetary motion: a central force is required to get planet to move in a circular path Kepler’s Theory The year Galileo died - 1642 - is the year Isaac Newton was born. Newton took the work of Galileo and Kepler and created an expansive theory of motion. © Sierra College Astronomy Department 5 Lecture 4: Newton Isaac Newton’s Accomplishments Extended school holiday 1665-1666: invent reflecting telescope invent calculus develop particle theory of optics discover laws of motion discover universal gravitation Lucasian Prof. of Math at Cambridge University © Sierra College Astronomy Department 6 Lecture 4: Newton Newton’s First Two Laws of Motion Inertia is the property of an object whereby it tends to maintain whatever velocity it has. Newton’s First Law (Law of Inertia): Unless an object is acted upon by a net, outside force, the object will maintain a constant speed in a straight line. Note: Speed and direction = velocity © Sierra College Astronomy Department Here First: Rock around Demo 7 Lecture 4: Newton Newton’s First Two Laws of Motion Acceleration is a measure of how rapidly the speed or direction of motion of an object is changing. An object at rest has a speed of zero. Newton’s first law says that a force is needed to change the speed and/or direction of an object’s motion. Demo © Sierra College Astronomy Department 8 Lecture 4: Newton Newton’s First Two Laws of Motion Some more definitions: Mass (M or m): quantity of inertia • An intrinsic property of an object • Not volume or weight • SI unit of measurement is a kilogram (kg) Weight (W): gravitational force between some object and a planetary body on which the object rests • On the Earth: 1 kilogram has an equivalent weight of 2.2 lbs. Density: Mass divided by Volume © Sierra College Astronomy Department 9 Lecture 4: Newton Newton’s First Two Laws of Motion Some more definitions: mass times velocity p=mv Angular momentum (or circular momentum) : mass times velocity times distance from center or axis of motion mvr Torque: a “twisting” force which changes the angular momentum Momentum: © Sierra College Astronomy Department 10 Lecture 4: Newton Newton’s First Two Laws of Motion Newton’s Second Law Acceleration is inversely proportional to the mass being accelerated. Acceleration = net force / mass Force = mass × acceleration, or F = ma Demo When the net force is zero, there is no acceleration. Another way of stating the 2nd law: “When a net 2nd law force acts on and object, it produces a change of momentum of in the direction in which the force acts” © Sierra College Astronomy Department 11 Lecture 4: Newton Newton’s Third Law Newton’s Third Law: When object X exerts a force on object Y, object Y exerts and equal and opposite force back on X. The Third Law is sometimes stated as “For every action there is an opposite and equal reaction,” but the first statement is more precise in terms of physical forces. This law does not “feel” right – be careful not to confuse force with acceleration © Sierra College Astronomy Department 3rd Law Demo 12 Lecture 4: Newton Motion in a Circle Motion of an object in a circle at constant speed (uniform circular motion) is an example of acceleration by changing direction. Centripetal (“center-seeking”) force is the force directed toward the center of the curve along which the object is moving. What happens if the centripetal force is removed? board Demo © Sierra College Astronomy Department 13 Lecture 4: Newton The Law of Universal Gravitation This law states that between every two objects there is an attractive force, the magnitude of which is directly proportional to the mass of each object Grav and inversely proportional to the square of Law the distance between the centers of the objects (inverse square law). In equation form: F = GM1M2 / d 2 Another where G is a constant, M and m are the form masses, and r is the distance between their centers. F = GMm / r 2 © Sierra College Astronomy Department 14 Weight of an object away from Earth 1/16 1/4 1/9 Grav Law Lecture 4: Newton The Law of Universal Gravitation According to Newton, gravity not only makes objects fall to Earth but keeps the Moon in orbit around the Earth and keeps the planets in orbit around the Sun. He could therefore explain the planets’ motions and why Kepler’s laws worked. © Sierra College Astronomy Department Cannon Grav Law 16 Lecture 4: Newton The Law of Universal Gravitation Grav Law Testing the Law of Universal Gravitation Because the distance from the center of the Earth to the Moon is about 60 times the distance from the center of the Earth to its surface, the centripetal acceleration of the Moon should be (1/60²) or 1/3600 of the acceleration of gravity on Earth. Newton’s calculations showed this to be the case and confirmed the validity of his theory of gravitation. © Sierra College Astronomy Department 17 Lecture 4: Newton Conservation Laws Demo • Under certain conditions, certain physical quantities will not change in time • These unchanging quantities are said to be conserved • Three important conservation laws for astronomy • (linear) momentum • angular momentum • energy © Sierra College Astronomy Department 18 Lecture 4: Newton Conservation Laws Demo Momentum (Along a Line) and Conservation • The momentum of an object with mass m and velocity v is given as p = mv • The momentum of a system of objects is P = p1 + p2 + … = m1v1 + m2v2 + … • If the absence of external forces acting on the system, P remains constant for all time - this is the Conservation of Momentum • Examples: Rockets and billiard balls • For more than one direction, conservation of momentum is applied in each direction separately © Sierra College Astronomy Department Pool 19 Lecture 4: Newton Demo Conservation of Angular Momentum • Angular Momentum and Conservation – Spinning objects and objects in orbit are said to possess angular momentum – In the absence of a “twisting force” or torque, a spinning object will maintain its angular momentum - this is the Conservation of Angular Momentum – Orbital angular momentum • The orbital angular momentum, J, of an object is the product of that object’s mass m, speed of rotation v, and distance from the center of rotation r: Skater J = mvr • The conservation of J means that (in the absence of an outside torque) as the distance to the spin axis decreases (contraction), the speed increases • This is what Kepler really observed as his 2nd Law of Planetary Motions (the Law of Equal Areas) Orbit © Sierra College Astronomy Department 20 Lecture 4: Understanding Motion, Energy, and Gravity Conservation of Angular Momentum • Angular Momentum and Conservation (continued) – Rotational angular momentum • An object (like the Earth) will continue to spin at the same rate as long as there is no net torque on it – Precession is the result of an external torque (observed for the Earth) • In a system of objects, the total angular momentum can be conserved (no outside torque), but the objects may transfer rotational angular energy between themselves – The slowing of the Earth’s day is due to the transfer of rotational angular momentum of the Earth to orbital angular momentum of the Moon © Sierra College Astronomy Department 21 Lecture 4: Newton Energy is conserved too! • Types of energy: Demo – Kinetic: the energy of moving objects (½ mv2) • Ex: cars in motion, planets going around the sun, molecules jostling in the air • Thermal energy is a important subcategory (next slide) Energy cycle – Radiative: energy carried by light (photons) – Potential: stored energy which may be converted later into kinetic or radiative energy • Ex: A rock perched on a ledge, chemical (or nuclear) bonds in an atom (or nucleus) (more later). • MKS unit for energy: Joule – 4,184 joules are in one food calorie – Typical adult eats 2500 calories = 10 million joules © Sierra College Astronomy Department 22 Lecture 4: Newton Temperatures Temperature is the measure of the average kinetic energy of a system of particles • Thermal energy depends on temperature and density Higher Fahrenheit scale: freezing 32°F/boiling 212°F. Lower Kinetic Celsius scale: freezing 0°C/boiling 100°C. Kelvin scale: 0 K = absolute zero (-273°C) 273 K = freezing point of water (0 °C) Thermal dependence 373 K = boiling point of water (100 °C) Note that Kelvin and Celsius degrees are the “same size.” © Sierra College Astronomy Department Temperature scales 23 Lecture 4: Newton Potential Energy in Astronomy Of the many types of potential energy, two are of particular importance in astronomy Gravitational potential energy: How much energy would one get from motions due to gravity? This energy get converted in kinetic energy. Mass-energy: How much energy is stored in the atom or nucleus? E mc © Sierra College Astronomy Department 2 24 Lecture 4: Newton Conservation of Energy Conservation of Energy states that in an isolated system, although energy may change from one form to another, the total amount of energy must remain constant Energy cannot be created nor destroyed, but can be transferred between different types • Ex: As a ball is dropped, its potential energy gets converted to kinetic energy such that the sum of the kinetic and potential energies remains constant The ultimate source of all the energy in the Universe is the Big Bang © Sierra College Astronomy Department 25 Lecture 4: Newton Newton’s Laws and Kepler’s Laws Newton showed mathematically (using calculus) that Kepler’s laws derive from the inverse square law for gravitation and the equation of motion (F = ma). Newton modified Kepler’s third law, showing that the masses are an important factor. 2 p = 3 Ka /(M 1 + M2) where K=4p2/G Objects orbit their center of mass © Sierra College Astronomy Department COM 26 Lecture 4: Newton Examples of Newton’s Laws Orbits: Circular and Escape Speed • Just how much speed does take to orbit the Earth? To leave the Earth? See Mathematical Insight 4.4 GM Vc R 2GM Ve R • Notice that it requires only √2 times the circular velocity to escape from the planet • For the Earth Vc = 8 km/s and Ve = 11 km/s Escape • For comparisons, be careful with M and R © Sierra College Astronomy Department 27 Lecture 4: Newton Examples of Newton’s Laws Feather Hammer Surface Gravity is the gravitational attraction at the surface of a planet or star. It is the acceleration on a mass created by the local gravitational force. GM Acceleration due to gravity at surface (See Mathematical g 2 Insight 4.5): R • Note independence of g with respect to m • For comparisons, be careful with M and R 2 • Notice Weight (W) = mg = GMm/R © Sierra College Astronomy Department 28 Lecture 4: Newton Examples of Newton’s Laws Weightlessness • Weight is the force that counters gravity creating a zero net force • Weightlessness is the absence of the countering force • People in orbit around the Earth feel weightless because gravity is not countered by a surface connected to the Earth Changing Orbits • Objects in orbit around each other do not spontaneously change into other orbital configurations. • The orbital energy of the system must change through: – Gravitational encounters (encounters with a third object) – Atmospheric drag (friction that diverts kinetic energy into other forms) © Sierra College Astronomy Department 29 Lecture 4: Newton The Importance of Newton’s Laws Kepler’s laws can be derived from them. They explain tides and precession. Their use predicted the existence of the planet Neptune. They provide a way to measure things quantitatively and predict the motion of things. Newton laid the foundation for our notion of the Universe. © Sierra College Astronomy Department 30 Lecture 4: Newton Tides tides Moon and Sun pull on Earth causing the water to rise producing tides • The Moon provides 2/3 of the tidal force, the Sun 1/3 Earth’s rotation provides daily rise and fall of tides Moon’s revolution about Earth cause half-monthly rise and fall of tides • Spring tide: Moon and Sun on same or opposite side of the Spring Earth Neap • Neap tide: Moon and Sun at perpendicular angles to the Earth © Sierra College Astronomy Department 31 Leading bulge Lecture 4: Newton Tides Effects of Tides on EarthMoon System Causes Moon’s synchronous rotation Tidal forces make Moon recede • Moon steals energy from Earth Tidal forces slow Earth’s rotation • Moon steals energy from Earth Tidal forces create Roche Limit • How close can something large be to planet/star until it breaks apart? © Sierra College Astronomy Department 32 Other slides © Sierra College Astronomy Department 33 Lecture 4: Newton Beyond Newton to Einstein Newton assumed time was absolute. Einstein’s Special Theory of Relativity showed this was not true. Newton proposed that inertial mass was equivalent to gravitational mass. Subsequent measurements confirmed this coincidence. Einstein in his General Theory of Relativity showed mathematically that the two types of masses are indeed equivalent. © Sierra College Astronomy Department 34 Lecture 4: Newton Beyond Newton to Einstein Principle of equivalence states that the effects of the force of gravity are indistinguishable from those of acceleration. The general theory predicts that light will curve in the presence of a massive object. This prediction, made in 1907, was first confirmed during a solar eclipse in 1919. © Sierra College Astronomy Department D-13 D-14 35