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Renaissance Astronomy Astronomy 1-1 Lecture 04-1 Cast of Characters Nicolaus Copernicus (1473-1543) Galileo Galilei (1564-1642) Telescopic observations Circular motion of planets supporting Copernicus around sun Isaac Newton (1642-1727) Tycho Brahe (1546-1601) Laws of gravity Recorded planets' positions Explained elliptical orbits Johannes Kepler (1571-1630) Deduced elliptical motions Laws of planetary motion Astronomy 1-1 Lecture 04-2 Nicolaus Copernicus Discrepancies between observed and predicted positions Sun at the center and the planets moved about the Sun Suggested that Earth rotated about its own axis (day, night cycle) Earth's axis of rotation titled with respect to orbit (seasons), and Earth's axis of rotation wobbled (precession) Astronomy 1-1 Lecture 04-3 Nicolaus Copernicus Problems still Used circular orbits Only privately circulated ideas at first Tried to publish a larger volume Publisher afraid of Church - Inserted a disclaimer stating that what was being presented was only a mathematical tool and not reality Copernicus missed all the controversy because he died just after receiving the first printed copy on his death bed Astronomy 1-1 Lecture 04-4 Giordano Bruno Expanded on Copernicus' work Stellar region was not finite Earth and Sun were just like other heavenly bodies Universe was homogeneous Space and time - infinite Burned at the stake Astronomy 1-1 Lecture 04-5 Tycho Brahe 1546 - 1601 Danish nobleman noted for his detailed and accurate observations Developed a geo-heliocentric system Johannes Kepler was his assistant Astronomy 1-1 Lecture 04-6 Tycho Brahe In 1572 Brahe made two observations 1) Observed a supernova - an exploding star Showed no evidence for parallax – therefore very far away 2) Detailed observations concerning a comet Its orbit was not circular Brought notoriety and money Astronomy 1-1 Lecture 04-7 Johannes Kepler (1571-1630) Believed in heliocentric system Distances of planets from Sun were based on regular geometric solids imbedded within each other Appropriated data from Brahe Orbit of Mars Mars did not move at constant rate along orbit Therefore could not be on circular path Concluded it must be an ellipse with the Sun at one of the focii If orbit had been that of Jupiter or Saturn, doubtful he would have seen this So long as the mother, Ignorance, lives, it is not safe for Science, the offspring, to divulge the hidden causes of things. Astronomy 1-1 Lecture 04-8 Kepler's Laws of Planetary Motion 1) Each planet moves around the sun in an orbit whose shape is that of an ellipse, with the sun at one focal point 2) A straight line joining the planet and the sun sweeps out equal areas in space in equal intervals in time 3) The squares of the periods of any two planets have the same ratio as the cubes of their semi-major axes If P is the period and R is the semi-major axis, this can be expressed in equation form as P12 P22 Astronomy 1-1 = R13 R23 Lecture 04-9 Kepler’s 2nd Law Kepler's Laws Demonstrations Astronomy 1-1 Lecture 04-10 Heliocentric view not accepted No observable stellar parallax Stellar parallax too small for equipment of the day Why do we not feel movement? How does the Earth drag the Moon with it? Astronomy 1-1 Lecture 04-11 Galileo Galilei (1564-1642) Built telescope based on work by a Dutchman, Hans Lippershey Saw: Thousands of stars in what was thought to be diffuse band in the Milky Way Craters on the Moon Not the perfect object it was thought to be Sun spots and solar rotation Again an imperfect object. Moons orbiting Jupiter That Venus went through phases just as the Moon does Can only happen if Venus orbits the Sun! Otherwise impossible to see Venus in its full phase Astronomy 1-1 Lecture 04-12 Galileo Galilei Concluded that the Earth is not the center of everything! Reminiscent of Copernican theory of solar system Galileo ran into problems with the Church, which still held to the geocentric point of view, despite the accumulating evidence that it was not correct Galileo was forced to refute his belief in the Copernican theory and was sentenced in effect to house arrest Astronomy 1-1 Lecture 04-13 Physical Underpinnings What was still missing was the why of the Copernican system Models of anything should have underpinnings in theory Unless new ground is being broken Astronomy 1-1 Lecture 04-14 Isaac Newton (1642-1727) Responsible for many ideas concerning how things work The Calculus Nature of light and its properties Cohesive picture of how objects move Astronomy 1-1 Lecture 04-15 Mass Each object has something inherent to it - MASS This is a measure of the amount of matter within it Mass is not the same as weight! Weight is related to mass The mass of an object is the same no matter where it is in the universe Weight is dependent upon where the object is It is the mass of an object that determines how it responds to the various influences acting upon it The more massive an object, the more difficult it is to change the state of its motion Astronomy 1-1 Lecture 04-16 First Law of Motion Newton summarized this in his First law which states A body at rest remains at rest and a body in motion moves at constant speed in a straight line unless acted upon by an outside force An implication of this statement is that circular motion is not a natural motion Astronomy 1-1 Lecture 04-17 Second Law of Motion How does an object, of a certain mass, respond to an external force? The object will undergo an acceleration that is directly proportional to the force exerted on the object and inversely proportional to the mass of the object This can be expressed mathematically as F = ma Acceleration is defined to be either a change in the speed of an object and/or a change in its direction Astronomy 1-1 Lecture 04-18 Third Law of Motion Newton also realized that when two objects interact with each other that each exerts the same force on the other This is often stated as follows: For every force (action) on one body, there is an equal and opposite force (reaction) acting on another body It must be remembered that these forces are acting on different bodies Astronomy 1-1 Lecture 04-19 Newton's work showed that linear motion is the natural motion Circular motion therefore is not a natural motion, thus a force is required to produce it Newton deduced that the object at the center of the motion must be responsible for the force that keeps the second object in motion about the center Newton concluded that the Sun must exert such a force on each planet, otherwise they would fly off in a straight line By using Kepler's third law and other observations Newton formulated his Universal Law of Gravitation Astronomy 1-1 Lecture 04-20 Law of Universal Gravitation Every particle in the universe attracts every other particle with a force proportional to the product of their masses and inversely proportional to the square of the distance between them F =G Astronomy 1-1 m1m 2 r 2 Lecture 04-21 Gravity Gravity is the interaction of two objects with each other. For objects that are separated from each other, the objects act as if all of the mass were concentrated at the center of the objects All objects on Earth experience the same gravitational acceleration g which is given by g= GM R2 Where G is the gravitational constant, M is the mass of the Earth, and R is the radius of the Earth Astronomy 1-1 Lecture 04-22 Energy The energy that we will deal with comes in two basic varieties: Kinetic Energy This is the energy due to either linear or rotational motion Potential Energy This is stored energy that can be converted into kinetic energy Nature's processes often convert one form of energy into the other Astronomy 1-1 Lecture 04-23 Total Energy In the relative motion of one body with respect to another, an important quantity is the total energy If the potential energy of one body with respect to the other is larger than its kinetic energy, the body is bound to the other This is the case for all the planets orbiting the Sun and for the moons orbiting their respective planets If the kinetic energy of the body is larger than its potential energy with respect to the other body, the body is free Astronomy 1-1 Lecture 04-24 Escape Velocity For one body to be able to escape from another body, its kinetic energy must be greater than or equal to its potential energy Kinetic Energy ≥ Potential Energy The necessary velocity for this to occur is called the escape velocity The escape velocity from a planet is given by v= GM R This will be of concern for planets with "weak" gravity as far as their atmospheres are concerned Astronomy 1-1 Lecture 04-25 Center of Mass With respect to the motion of one body moving about another, both objects are in fact in motion about a common point A point known as the center of mass If one body is much larger than the other one, this point is often contained within the large one, giving the appearance of the smaller one just moving about the larger one with the large one being at rest Astronomy 1-1 Lecture 04-26 Center of Mass Two identical masses Slightly differing masses Major difference in mass Very large difference in mass Astronomy 1-1 Lecture 04-27