Gravity. Newton s Law of Gravitation Kepler s Laws of Planetary Motion Gravitational Fields


 Albert Hubbard
 2 years ago
 Views:
Transcription
1 Gravity Newton s Law of Gravitation Kepler s Laws of Planetary Motion Gravitational Fields
2 Simulation Synchronous Rotation eg75q SunEarthMoon System
3 Newton s Law of Gravitation r m 2 m 1 There is a force of gravity between any pair of objects anywhere. The force is proportional to each mass and inversely proportional to the square of the distance between the two objects. Its equation is: F G = G m 1 m 2 r 2 The constant of proportionality is G, the universal gravitation constant. G = N m 2 / kg 2. Note how the units of G all cancel out except for the Newtons, which is the unit needed on the left side of the equation.
4 F G = G m 1 m 2 r 2 Gravity Example How hard do two planets pull on each other if their masses are kg and kg and they 230 million kilometers apart? = ( N m 2 / kg 2 ) ( kg) ( kg) ( m) 2 = N This is the force each planet exerts on the other. Note the denominator is has a factor of 10 3 to convert to meters and a factor of 10 6 to account for the million. It doesn t matter which way or how fast the planets are moving.
5 3rd Law: ActionReaction In the last example the force on each planet is the same. This is due to to Newton s third law of motion: the force on Planet 1 due to Planet 2 is just as strong but in the opposite direction as the force on Planet 2 due to Planet 1. The effects of these forces are not the same, however, since the planets have different masses. For the big planet: a = ( N) / ( kg) = m/s 2. For the little planet: a = ( N) / ( kg) = m/s kg N N kg
6 Inverse Square Law The law of gravitation is called an inverse square law because the magnitude of the force is inversely proportional to the square of the separation. If the masses are moved twice as far apart, the force of gravity between is cut by a factor of four. Triple the separation and the force is nine times weaker. F G = G m 1 m 2 r 2 What if each mass and the separation were all quadrupled? answer: no change in the force
7 Calculating the Gravitational Constant In 1798 Sir Henry Cavendish suspended a rod with two small masses (red) from a thin wire. Two larger mass (green) attract the small masses and cause the wire to twist slightly, since each force of attraction produces a torque in the same direction. By varying the masses and measuring the separations and the amount of twist, Cavendish was the first to calculate G. Since G is only N m 2 / kg 2, the measurements had to be very precise.
8 Calculating the mass of the Earth Knowing G, we can now actually calculate the mass of the Earth. All we do is write the weight of any object in two different ways and equate them. Its weight is the force of gravity between it and the Earth, which is F G in the equation below. M E is the mass of the Earth, R E is the radius of the Earth, and m is the mass of the object. The object s weight can also be written as mg. F G = G m 1 m 2 r 2 = G M E m R E 2 = mg The m s cancel in the last equation. g can be measured experimentally; Cavendish determined G s value; and R E can be calculated at m (see next slide). M E is the only unknown. Solving for M E we have: M E = g R E 2 G = kg
9 Calculating the radius of the Earth This is similar to the way the Greeks approximated Earth s radius over 2000 years ago: R E s Earth is also the central angle of the arc. s = R E R E = s / m
10 Net Force Gravity Problem 40 m kg 3 asteroids are positioned as shown, forming a right triangle. Find the net force on the 2.5 million kg asteroid kg kg 60 m Steps: 1. Find each force of gravity on it and draw in the vectors. 2. Find the angle at the lower right. 3. One force vector is to the left; break the other one down into components. 4. Find the resultant vector: magnitude via Pythagorean theorem; direction via inverse tangent. answer: N at 14.6 above horizontal (N of W)
11 Falling Around the Earth y = 0.5 g t 2 { x = vt v Newton imagined a cannon ball fired horizontally from a mountain top at a speed v. In a time t it falls a distance y = 0.5 g t 2 while moving horizontally a distance x = vt. If fired fast enough (about 8 km/s), the Earth would curve downward the same amount the cannon ball falls downward. Thus, the projectile would never hit the ground, and it would be in orbit. The moon falls around Earth in the exact same way but at a much greater altitude.. continued on next slide
12 Necessary Launch Speed for Orbit R = Earth s radius t = small amount of time after launch x = horiz. distance traveled in time t y = vertical distance fallen in time t (If t is very small, the red segment is nearly vertical.) y = gt 2 / 2 x = vt x 2 + R 2 = (R + y) 2 = R 2 + 2R y + y 2 Since y << R, x 2 + R 2 R 2 + 2R y x 2 2R y v 2 t 2 2R(g t 2 / 2) v 2 R g. So, R R v ( m 9.8 m/s 2 ) ½ v 7900 m/s
13 Early Astronomers In the 2 nd century AD the Alexandrian astronomer Ptolemy put forth a theory that Earth is stationary and at the center of the universe and that the sun, moon, and planets revolve around it. Though incorrect, it was accepted for centuries. In the early 1500 s the Polish astronomer Nicolaus Copernicus boldly rejected Ptolemy s geocentric model for a heliocentric one. His theory put the sun stated that the planets revolve around the sun in circular orbits and that Earth rotates daily on its axis. In the late 1500 s the Danish astronomer Tycho Brahe made better measurements of the planets and stars than anyone before him. The telescope had yet to be invented. He believed in a PtolemaicCoperican hybrid model in which the planets revolve around the sun, which in turn revolves around the Earth.
14 Early Astronomers Both Galileo and Kepler contributed greatly to work of the English scientist Sir Isaac Newton a generation later. In the late 1500 s and early 1600 s the Italian scientist Galileo was one of the very few people to advocate the Copernican view, for which the Church eventually had him placed under house arrest. After hearing about the invention of a spyglass in Holland, Galileo made a telescope and discovered four moons of Jupiter, craters on the moon, and the phases of Venus. The German astronomer Johannes Kepler was a contemporary of Galileo and an assistant to Tycho Brahe. Like Galileo, Kepler believed in the heliocentric system of Copernicus, but using Brahe s planetary data he deduced that the planets move in ellipses rather than circles. This is the first of three planetary laws that Kepler formulated based on Brahe s data.
15 Kepler s Laws of Planetary Motion Here is a summary of Kepler s 3 Laws: 1. Planets move around the sun in elliptical paths with the sun at one focus of the ellipse. 2. While orbiting, a planet sweep out equal areas in equal times. 3. The square of a planet s period (revolution time) is proportional to the cube of its mean distance from the sun: T 2 R 3 These laws apply to any satellite orbiting a much larger body.
16 Kepler s First Law Planets move around the sun in elliptical paths with the sun at one focus of the ellipse. F 1 F 2 Sun Planet An ellipse has two foci, F 1 and F 2. For any point P on the ellipse, F 1 P + F 2 P is a constant. The orbits of the planets are nearly circular (F 1 and F 2 are close together), but not perfect circles. A circle is a an ellipse with both foci at the same pointthe center. Comets have very eccentric (highly elliptical) orbits. P
17 Kepler s Second Law (proven in advanced physics) While orbiting, a planet sweep out equal areas in equal times. A D Sun C B The blue shaded sector has the same area as the red shaded sector. Thus, a planet moves from C to D in the same amount of time as it moves from A to B. This means a planet must move faster when it s closer to the sun. For planets this affect is small, but for comets it s quite noticeable, since a comet s orbit is has much greater eccentricity.
18 Kepler s Third Law The square of a planet s period is proportional to the cube of its mean distance from the sun: T 2 R 3 Assuming that a planet s orbit is circular (which is not exactly correct but is a good approximation in most cases), then the mean distance from the sun is a constantthe radius. F is the force of gravity on the planet. F is also the centripetal force. If the orbit is circular, the planet s speed is constant, and v = 2 R / T. Therefore, M Sun F R m Planet G M m m v 2 R 2 = R Cancel m s and simplify: Rearrange: = m [2 R / T] 2 R G M R 2 = 4 T 2 = 2 R 3 G M 4 2 R T 2 Since G, M, and are constants, T 2 R 3.
19 Third Law Analysis 4 2 We just derived T 2 = R 3 GM It also shows that the orbital period depends on the mass of the central body (which for a planet is its star) but not on the mass of the orbiting body. In other words, if Mars had a companion planet the same distance from the sun, it would have the same period as Mars, regardless of its size. This shows that the farther away a planet is from its star, the longer it takes to complete an orbit. Likewise, an artificial satellite circling Earth from a great distance has a greater period than a satellite orbiting closer. There are two reasons for this: 1. The farther away the satellite is, the farther it must travel to complete an orbit; 2. The farther out its orbit is, the slower it moves, as shown: G M m m v 2 R 2 = G M R v = R
20 Third Law Example One astronomical unit (AU) is the distance between Earth and the sun (about 93 million miles). Jupiter is 5.2 AU from the sun. How long is a Jovian year? answer: Kepler s 3 rd Law says T 2 R 3, so T 2 = k R 3, where k is the constant of proportionality. Thus, for Earth and Jupiter we have: T E 2 = k R E 3 and T J2 = k R J 3 k s value matters not; since both planets are orbiting the same central body (the sun), k is the same in both equations. T E = 1 year, and R J / R E = 5.2, so dividing equations: T J 2 T E 2 R 3 J = R 3 T 2 J = (5.2) 3 T J = 11.9 years E continued on next slide
21 Third Law Example (cont.) What is Jupiter s orbital speed? answer: Since it s orbital is approximately circular, and it s speed is approximately constant: Jupiter is 5.2 AU from the sun (5.2 times farther than Earth is). v = d t = 2 (5.2)( miles) 1 year 11.9 years 365 days 1 day 24 hours 29,000 mph. Jupiter s period from last slide This means Jupiter is cruising through the solar system at about 13,000 m/s! Even at this great speed, though, Jupiter is so far away that when we observe it from Earth, we don t notice it s motion. Planets closer to the sun orbit even faster. Mercury, the closest planet, is traveling at about 48,000 m/s!
22 Third Law Practice Problem Venus is about AU from the sun, Mars AU. Venus takes days to circle the sun. Figure out how long a Martian year is. answer: 686 days
23 Uniform Gravitational Fields We live in what is essentially a uniform gravitational field. This means that the force of gravity near the surface of the Earth is pretty much constant in magnitude and direction. The green lines are gravitational field lines. They show the direction of the gravitational force on any object in the region (straight down). In a uniform field, the lines are parallel and evenly spaced. Near Earth s surface the magnitude of the gravitational field is 9.8 N/kg. That is, every kilogram of mass an object has experiences 9.8 N of force. Since a Newton is a kilogram meter per second squared, 1 N/kg = 1 m/s 2. So, the gravitational field strength is just the acceleration due to gravity, g. continued on next slide Earth s surface
24 Uniform Gravitational Fields (cont.) A 10 kg mass is near the surface of the Earth. Since the field strength is 9.8 N/ kg, each of the ten kilograms feels a 9.8 N force, for a total of 98 N. So, we can calculate the force of gravity by multiply mass and field strength. This is the same as calculating its weight (W = mg). 98 N 10 kg Earth s surface
25 Nonuniform Gravitational Fields Near Earth s surface the gravitational field is approximately uniform. Far from the surface it looks more like a sea urchin. The field lines are radial, rather than parallel, and point toward center of Earth. Earth get farther apart farther from the surface, meaning the field is weaker there. get closer together closer to the surface, meaning the field is stronger there.
Gravitation and the Motion of the Planets
Gravitation and the Motion of the Planets 1 Guiding Questions 1. How did ancient astronomers explain the motions of the planets? 2. Why did Copernicus think that the Earth and the other planets go around
More informationPlanetary Mechanics:
Planetary Mechanics: Satellites A satellite is an object or a body that revolves around another body due to the gravitational attraction to the greater mass. Ex: The planets are natural satellites of the
More informationGravitation and the Waltz of the Planets
Gravitation and the Waltz of the Planets Chapter Four Guiding Questions 1. How did ancient astronomers explain the motions of the planets? 2. Why did Copernicus think that the Earth and the other planets
More informationGravitation and the Waltz of the Planets. Chapter Four
Gravitation and the Waltz of the Planets Chapter Four Guiding Questions 1. How did ancient astronomers explain the motions of the planets? 2. Why did Copernicus think that the Earth and the other planets
More information7.4 Universal Gravitation
Circular Motion Velocity is a vector quantity, which means that it involves both speed (magnitude) and direction. Therefore an object traveling at a constant speed can still accelerate if the direction
More informationJanuary 19, notes.notebook. Claudius Ptolemaeus Second Century AD. Jan 5 7:37 AM
8.1 notes.notebook Claudius Ptolemaeus Second Century AD Jan 5 7:7 AM Copernicus: The Foundation Nicholas Copernicus (Polish, 147 154): Proposed the first modern heliocentric model, motivated by inaccuracies
More informationUniversal Gravitation
Universal Gravitation Johannes Kepler Johannes Kepler was a German mathematician, astronomer and astrologer, and key figure in the 17th century Scientific revolution. He is best known for his laws of planetary
More informationAnnouncements. Topics To Be Covered in this Lecture
Announcements! Tonight s observing session is cancelled (due to clouds)! the next one will be one week from now, weather permitting! The 2 nd LearningCurve activity was due earlier today! Assignment 2
More information9/12/2010. The Four Fundamental Forces of Nature. 1. Gravity 2. Electromagnetism 3. The Strong Nuclear Force 4. The Weak Nuclear Force
The Four Fundamental Forces of Nature 1. Gravity 2. Electromagnetism 3. The Strong Nuclear Force 4. The Weak Nuclear Force The Universe is made of matter Gravity the force of attraction between matter
More informationLecture 13. Gravity in the Solar System
Lecture 13 Gravity in the Solar System Guiding Questions 1. How was the heliocentric model established? What are monumental steps in the history of the heliocentric model? 2. How do Kepler s three laws
More informationCircular Motion. Gravitation
Circular Motion Gravitation Circular Motion Uniform circular motion is motion in a circle at constant speed. Centripetal force is the force that keeps an object moving in a circle. Centripetal acceleration,
More informationIntroduction To Modern Astronomy I
ASTR 111 003 Fall 2006 Lecture 03 Sep. 18, 2006 Introduction To Modern Astronomy I Introducing Astronomy (chap. 16) Planets and Moons (chap. 717) Ch1: Astronomy and the Universe Ch2: Knowing the Heavens
More informationAstronomy The Original Science
Astronomy The Original Science Imagine that it is 5,000 years ago. Clocks and modern calendars have not been invented. How would you tell time or know what day it is? One way to tell the time is to study
More informationAP PhysicsB Universal Gravitation Introduction: Kepler s Laws of Planetary Motion: Newton s Law of Universal Gravitation: Performance Objectives:
AP PhysicsB Universal Gravitation Introduction: Astronomy is the oldest science. Practical needs and imagination acted together to give astronomy an early importance. For thousands of years, the motions
More informationASTR 1010 Spring 2016 Study Notes Dr. Magnani
The Copernican Revolution ASTR 1010 Spring 2016 Study Notes Dr. Magnani The Copernican Revolution is basically how the West intellectually transitioned from the Ptolemaic geocentric model of the Universe
More informationPHYSICS. Chapter 13 Lecture FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E RANDALL D. KNIGHT Pearson Education, Inc.
PHYSICS FOR SCIENTISTS AND ENGINEERS A STRATEGIC APPROACH 4/E Chapter 13 Lecture RANDALL D. KNIGHT Chapter 13 Newton s Theory of Gravity IN THIS CHAPTER, you will learn to understand the motion of satellites
More informationGravity and the Orbits of Planets
Gravity and the Orbits of Planets 1. Gravity Galileo Newton Earth s Gravity Mass v. Weight Einstein and General Relativity Round and irregular shaped objects 2. Orbits and Kepler s Laws ESO Galileo, Gravity,
More informationPlanetary Orbits: Kepler s Laws 1/18/07
Planetary Orbits: Kepler s Laws Announcements The correct link for the course webpage http://www.lpl.arizona.edu/undergrad/classes/spring2007/giacalone_2062 The first homework due Jan 25 (available for
More informationChapter 4 Thrills and Chills +Math +Depth Acceleration of the Moon +Concepts The Moon is 60 times further away from the center of Earth than objects on the surface of Earth, and moves about Earth in an
More informationAP Physics Multiple Choice Practice Gravitation
AP Physics Multiple Choice Practice Gravitation 1. Each of five satellites makes a circular orbit about an object that is much more massive than any of the satellites. The mass and orbital radius of each
More information14.1 Earth Satellites. The path of an Earth satellite follows the curvature of the Earth.
The path of an Earth satellite follows the curvature of the Earth. A stone thrown fast enough to go a horizontal distance of 8 kilometers during the time (1 second) it takes to fall 5 meters, will orbit
More informationPhysics Unit 7: Circular Motion, Universal Gravitation, and Satellite Orbits. Planetary Motion
Physics Unit 7: Circular Motion, Universal Gravitation, and Satellite Orbits Planetary Motion Geocentric Models Many people prior to the 1500 s viewed the! Earth and the solar system using a! geocentric
More informationPHYS 155 Introductory Astronomy
PHYS 155 Introductory Astronomy  observing sessions: Sunday Thursday, 9pm, weather permitting http://www.phys.uconn.edu/observatory  Exam  Tuesday March 20,  Review Monday 6:309pm, PB 38 Marek Krasnansky
More informationLecture #5: Plan. The Beginnings of Modern Astronomy Kepler s Laws Galileo
Lecture #5: Plan The Beginnings of Modern Astronomy Kepler s Laws Galileo Geocentric ( Ptolemaic ) Model Retrograde Motion: Apparent backward (= EasttoWest) motion of a planet with respect to stars Ptolemy
More informationCircular Motion and Gravitation Notes 1 Centripetal Acceleration and Force
Circular Motion and Gravitation Notes 1 Centripetal Acceleration and Force This unit we will investigate the special case of kinematics and dynamics of objects in uniform circular motion. First let s consider
More informationClaudius Ptolemaeus Second Century AD. Jan 5 7:37 AM
Claudius Ptolemaeus Second Century AD Jan 5 7:37 AM Copernicus: The Foundation Nicholas Copernicus (Polish, 1473 1543): Proposed the first modern heliocentric model, motivated by inaccuracies of the Ptolemaic
More informationPhysics 12. Unit 5 Circular Motion and Gravitation Part 2
Physics 12 Unit 5 Circular Motion and Gravitation Part 2 1. Newton s law of gravitation We have seen in Physics 11 that the force acting on an object due to gravity is given by a well known formula: F
More informationIntro to Astronomy. Looking at Our Space Neighborhood
Intro to Astronomy Looking at Our Space Neighborhood Astronomy: The Original Science Ancient cultures used the movement of stars, planets and the moon to mark time Astronomy: the study of the universe
More informationGravitation Part I. Ptolemy, Copernicus, Galileo, and Kepler
Gravitation Part I. Ptolemy, Copernicus, Galileo, and Kepler Celestial motions The stars: Uniform daily motion about the celestial poles (rising and setting). The Sun: Daily motion around the celestial
More informationDays of the week:  named after 7 Power (moving) objects in the sky (Sun, Moon, 5 planets) Models of the Universe:
Motions of the Planets ( Wanderers ) Planets move on celestial sphere  change RA, Dec each night  five are visible to naked eye Mercury, Venus, Mars, Jupiter, Saturn Days of the week:  named after 7
More information6. Summarize Newton s Law of gravity and the inverse square concept. Write out the equation
HW due Today. 1. Read p. 175 180. 2. Summarize the historical account of Brahe and Kepler 3. Write out Kepler s 3 laws. 1) Planets in orbit follow an elliptical path, the Sun is located at a focus of the
More informationRotational Motion and the Law of Gravity 1
Rotational Motion and the Law of Gravity 1 Linear motion is described by position, velocity, and acceleration. Circular motion repeats itself in circles around the axis of rotation Ex. Planets in orbit,
More informationKepler, Newton, and laws of motion
Kepler, Newton, and laws of motion First: A Little History Geocentric vs. heliocentric model for solar system (sec. 2.22.4)! The only history in this course is this progression: Aristotle (~350 BC) Ptolemy
More informationJohannes Kepler ( ) German Mathematician and Astronomer Passionately convinced of the rightness of the Copernican view. Set out to prove it!
Johannes Kepler (15711630) German Mathematician and Astronomer Passionately convinced of the rightness of the Copernican view. Set out to prove it! Kepler s Life Work Kepler sought a unifying principle
More information18. Kepler as a young man became the assistant to A) Nicolaus Copernicus. B) Ptolemy. C) Tycho Brahe. D) Sir Isaac Newton.
Name: Date: 1. The word planet is derived from a Greek term meaning A) bright nighttime object. B) astrological sign. C) wanderer. D) nontwinkling star. 2. The planets that were known before the telescope
More informationMost of the time during full and new phases, the Moon lies above or below the Sun in the sky.
6/16 Eclipses: We don t have eclipses every month because the plane of the Moon s orbit about the Earth is different from the plane the ecliptic, the Earth s orbital plane about the Sun. The planes of
More informationEarly Theories. Early astronomers believed that the sun, planets and stars orbited Earth (geocentric model) Developed by Aristotle
Planetary Motion Early Theories Early astronomers believed that the sun, planets and stars orbited Earth (geocentric model) Developed by Aristotle Stars appear to move around Earth Observations showed
More informationCH 8. Universal Gravitation Planetary and Satellite Motion
CH 8 Universal Gravitation Planetary and Satellite Motion Sir Isaac Newton UNIVERSAL GRAVITATION Newton: Universal Gravitation Newton concluded that earthly objects and heavenly objects obey the same physical
More informationUnit 3 Lesson 2 Gravity and the Solar System. Copyright Houghton Mifflin Harcourt Publishing Company
Florida Benchmarks SC.8.N.1.4 Explain how hypotheses are valuable if they lead to further investigations, even if they turn out not to be supported by the data. SC.8.N.1.5 Analyze the methods used to develop
More informationThe History of Astronomy. Theories, People, and Discoveries of the Past
The History of Astronomy Theories, People, and Discoveries of the Past Early man recorded very little history. Left some clues in the form of petrographs. Stone drawings that show eclipses, comets, supernovae.
More informationAstronomy Notes Chapter 02.notebook April 11, 2014 Pythagoras Aristotle geocentric retrograde motion epicycles deferents Aristarchus, heliocentric
Around 2500 years ago, Pythagoras began to use math to describe the world around him. Around 200 years later, Aristotle stated that the Universe is understandable and is governed by regular laws. Most
More informationHistory of Astronomy. PHYS 1411 Introduction to Astronomy. Tycho Brahe and Exploding Stars. Tycho Brahe ( ) Chapter 4. Renaissance Period
PHYS 1411 Introduction to Astronomy History of Astronomy Chapter 4 Renaissance Period Copernicus new (and correct) explanation for retrograde motion of the planets Copernicus new (and correct) explanation
More informationUnit 5 Gravitation. Newton s Law of Universal Gravitation Kepler s Laws of Planetary Motion
Unit 5 Gravitation Newton s Law of Universal Gravitation Kepler s Laws of Planetary Motion Into to Gravity Phet Simulation Today: Make sure to collect all data. Finished lab due tomorrow!! Universal Law
More information7 Study Guide. Gravitation Vocabulary Review
Date Period Name CHAPTER 7 Study Guide Gravitation Vocabulary Review Write the term that correctly completes the statement. Use each term once. Kepler s second law Newton s law of universal gravitation
More informationGravitation & Kepler s Laws
Gravitation & Kepler s Laws What causes YOU to be pulled down to the surface of the earth? THE EARTH.or more specifically the EARTH S MASS. Anything that has MASS has a gravitational pull towards it. F
More informationIn so many and such important. ways, then, do the planets bear witness to the earth's mobility. Nicholas Copernicus
In so many and such important ways, then, do the planets bear witness to the earth's mobility Nicholas Copernicus What We Will Learn Today What did it take to revise an age old belief? What is the Copernican
More informationA Very Brief History of Statics and Dynamics
UNIVERSAL GRAVITION A Very Brief History of Statics and Dynamics The idea that a force causes motion goes back to the 4 th century B.C., when the Greeks were developing ideas about science. Aristotle (38433
More informationHow big is the Universe and where are we in it?
Announcements Results of clicker questions from Monday are on ICON. First homework is graded on ICON. Next homework due one minute before midnight on Tuesday, September 6. Labs start this week. All lab
More informationThe Scientific Revolution
The Scientific Revolution What is a Revolution? A Revolution is a complete change, or an overthrow of a government, a social system, etc. The Scientific Revolution In the 1500s and 1600s the Scientific
More informationToday. Planetary Motion. Tycho Brahe s Observations. Kepler s Laws Laws of Motion. Laws of Motion
Today Planetary Motion Tycho Brahe s Observations Kepler s Laws Laws of Motion Laws of Motion In 1633 the Catholic Church ordered Galileo to recant his claim that Earth orbits the Sun. His book on the
More informationChapter 5 Review : Circular Motion; Gravitation
Chapter 5 Review : Circular Motion; Gravitation Conceptual Questions 1) Is it possible for an object moving with a constant speed to accelerate? Explain. A) No, if the speed is constant then the acceleration
More informationLearning Objectives. one night? Over the course of several nights? How do true motion and retrograde motion differ?
Kepler s Laws Learning Objectives! Do the planets move east or west over the course of one night? Over the course of several nights? How do true motion and retrograde motion differ?! What are geocentric
More informationChapter 13: universal gravitation
Chapter 13: universal gravitation Newton s Law of Gravitation Weight Gravitational Potential Energy The Motion of Satellites Kepler s Laws and the Motion of Planets Spherical Mass Distributions Apparent
More informationEclipses and Forces. Jan 21, ) Review 2) Eclipses 3) Kepler s Laws 4) Newton s Laws
Eclipses and Forces Jan 21, 2004 1) Review 2) Eclipses 3) Kepler s Laws 4) Newton s Laws Review Lots of motion The Moon revolves around the Earth Eclipses Solar Lunar the Sun, Earth and Moon must all be
More informationPractice Test DeAnza College Astronomy 04 Test 1 Spring Quarter 2009
Practice Test DeAnza College Astronomy 04 Test 1 Spring Quarter 2009 Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. Mark answer on Scantron.
More information1 Astronomy: The Original Science
CHAPTER 18 1 Astronomy: The Original Science SECTION Studying Space BEFORE YOU READ After you read this section, you should be able to answer these questions: How do astronomers define a day, a month,
More informationExam #1 Study Guide (Note this is not all the information you need to know for the test, these are just SOME of the main points)
Exam #1 Study Guide (Note this is not all the information you need to know for the test, these are just SOME of the main points) Moon Phases Moon is always ½ illuminated by the Sun, and the sunlit side
More informationPhysics Test 7: Circular Motion page 1
Name Physics Test 7: Circular Motion page 1 hmultiple Choice Read each question and choose the best answer by putting the corresponding letter in the blank to the left. 1. The SI unit of angular speed
More informationEarly Models of the Universe. How we explained those big shiny lights in the sky
Early Models of the Universe How we explained those big shiny lights in the sky The Greek philosopher Aristotle (384 322 BCE) believed that the Earth was the center of our universe, and everything rotated
More informationBy; Jarrick Serdar, Michael Broberg, Trevor Grey, Cameron Kearl, Claire DeCoste, and Kristian Fors
By; Jarrick Serdar, Michael Broberg, Trevor Grey, Cameron Kearl, Claire DeCoste, and Kristian Fors What is gravity? Gravity is defined as the force of attraction by which terrestrial bodies tend to fall
More informationPull out a ½ sheet or use the back of your old quiz
Pull out a ½ sheet or use the back of your old quiz Weekly Schedule Today Hw # 2 due Quiz # 2 Geocentric vs. Heliocentric models Kepler s Laws Astronomy InteracGves Newton and Gravity Lecture tutorials
More informationCIRCULAR MOTION AND UNIVERSAL GRAVITATION
CIRCULAR MOTION AND UNIVERSAL GRAVITATION Uniform Circular Motion What holds an object in a circular path? A force. String Friction Gravity What happens when the force is diminished? Object flies off in
More informationTHE SUN AND THE SOLAR SYSTEM
Chapter 26 THE SUN AND THE SOLAR SYSTEM CHAPTER 26 SECTION 26.1: THE SUN S SIZE, HEAT, AND STRUCTURE Objectives: What is the Sun s structure and source of energy? Key Vocabulary: Fusion Photosphere Corona
More informationSpace Notes Covers Objectives 1 & 2
Space Notes Covers Objectives 1 & 2 Space Introduction Space Introduction Video Celestial Bodies Refers to a natural object out in space 1) Stars 2) Comets 3) Moons 4) Planets 5) Asteroids Constellations
More informationChapter 13. Universal Gravitation
Chapter 13 Universal Gravitation Planetary Motion A large amount of data had been collected by 1687. There was no clear understanding of the forces related to these motions. Isaac Newton provided the answer.
More informationWhat is a Revolution? A Revolution is a complete change, or an overthrow of a government, a social system, etc.
CW10 p374 Vocab What is a Revolution? A Revolution is a complete change, or an overthrow of a government, a social system, etc. The Scientific Revolution In the 1500s and 1600s the Scientific Revolution
More informationChapter 2. The Rise of Astronomy. Copyright (c) The McGrawHill Companies, Inc. Permission required for reproduction or display.
Chapter 2 The Rise of Astronomy Copyright (c) The McGrawHill Companies, Inc. Permission required for reproduction or display. Periods of Western Astronomy Western astronomy divides into 4 periods Prehistoric
More informationcosmogony geocentric heliocentric How the Greeks modeled the heavens
Cosmogony A cosmogony is theory about ones place in the universe. A geocentric cosmogony is a theory that proposes Earth to be at the center of the universe. A heliocentric cosmogony is a theory that proposes
More information,.~ Readlng ~ What,~,~~ is a geocentric system? Chapter3 J 73
Earth at the Center When the ancient Greeks watched the stars move across the sky, they noticed that the patterns of the stars didn t change. Although the stars seemed to move, they stayed in the same
More informationChapter 4. The Origin Of Modern Astronomy. Is okay to change your phone? From ios to Android From Android to ios
Chapter 4 The Origin Of Modern Astronomy Slide 14 Slide 15 14 15 Is Change Good or Bad? Do you like Homer to look like Homer or with hair? Does it bother you when your schedule is changed? Is it okay to
More information2.4 The Birth of Modern Astronomy
2.4 The Birth of Modern Astronomy Telescope invented around 1600 Galileo built his own, made observations: Moon has mountains and valleys Sun has sunspots, and rotates Jupiter has moons (shown): Venus
More informationProjectile Motion. Conceptual Physics 11 th Edition. Projectile Motion. Projectile Motion. Projectile Motion. This lecture will help you understand:
Conceptual Physics 11 th Edition Projectile motion is a combination of a horizontal component, and Chapter 10: PROJECTILE AND SATELLITE MOTION a vertical component. This lecture will help you understand:
More informationINTRODUCTION: Ptolemy geocentric theory Nicolas Copernicus Heliocentric theory TychoBrahe Johannes Kepler
INTRODUCTION: Ptolemy in second century gave geocentric theory of planetary motion in which the Earth is considered stationary at the centre of the universe and all the stars and the planets including
More informationLecture 16. Gravitation
Lecture 16 Gravitation Today s Topics: The Gravitational Force Satellites in Circular Orbits Apparent Weightlessness lliptical Orbits and angular momentum Kepler s Laws of Orbital Motion Gravitational
More informationSection 37 Kepler's Rules
Section 37 Kepler's Rules What is the universe made out of and how do the parts interact? That was our goal in this course While we ve learned that objects do what they do because of forces, energy, linear
More informationChapter 1 The Copernican Revolution
Chapter 1 The Copernican Revolution The Horse Head nebula in the Orion constellation (Reading assignment: Chapter 1) Learning Outcomes How the geocentric model accounts for the retrograde motion of planets?
More informationChapter 02 The Rise of Astronomy
Chapter 02 The Rise of Astronomy Multiple Choice Questions 1. The moon appears larger when it rises than when it is high in the sky because A. You are closer to it when it rises (angularsize relation).
More informationConceptual Physics 11 th Edition
Conceptual Physics 11 th Edition Chapter 10: PROJECTILE AND SATELLITE MOTION This lecture will help you understand: Projectile Motion FastMoving Projectiles Satellites Circular Satellite Orbits Elliptical
More informationhttp://radicalart.info/physics/vacuum/index.html The Scientific Revolution In the 1500s and 1600s the Scientific Revolution changed the way Europeans looked at the world. People began to make conclusions
More informationGravitation. Makes the World Go Round
Gravitation Makes the World Go Round Gravitational Force The Force of gravity is an attractive force felt between all objects that have mass. G=6.67x1011 N m 2 /kg 2 Example 1: What is the Force of Gravity
More informationEarth Science, 13e Tarbuck & Lutgens
Earth Science, 13e Tarbuck & Lutgens Origins of Modern Astronomy Earth Science, 13e Chapter 21 Stanley C. Hatfield Southwestern Illinois College Early history of astronomy Ancient Greeks Used philosophical
More informationChapter. Origin of Modern Astronomy
Chapter Origin of Modern Astronomy 22.1 Early Astronomy Ancient Greeks Astronomy is the science that studies the universe. It includes the observation and interpretation of celestial bodies and phenomena.
More informationName: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due on Tuesday, Jan. 19, 2016
Name: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due on Tuesday, Jan. 19, 2016 Why are celestial motions and forces important? They explain the world around us.
More informationThe History of Astronomy. Please pick up your assigned transmitter.
The History of Astronomy Please pick up your assigned transmitter. When did mankind first become interested in the science of astronomy? 1. With the advent of modern computer technology (mid20 th century)
More informationToday. Planetary Motion. Tycho Brahe s Observations. Kepler s Laws of Planetary Motion. Laws of Motion. in physics
Planetary Motion Today Tycho Brahe s Observations Kepler s Laws of Planetary Motion Laws of Motion in physics Page from 1640 text in the KSL rare book collection That the Earth may be a Planet the seeming
More informationBasics of Kepler and Newton. Orbits of the planets, moons,
Basics of Kepler and Newton Orbits of the planets, moons, Kepler s Laws, as derived by Newton. Kepler s Laws Universal Law of Gravity Three Laws of Motion Deriving Kepler s Laws Recall: The Copernican
More informationHow Astronomers Learnt that The Heavens Are Not Perfect
1 How Astronomers Learnt that The Heavens Are Not Perfect Introduction In this packet, you will read about the discoveries and theories which changed the way astronomers understood the Universe. I have
More information6.1 Newtonian Gravitation
6.1 Newtonian Gravitation Early in the formation of our galaxy, tiny gravitational effects between particles began to draw matter together into slightly denser configurations. Those, in turn, exerted even
More information5. Universal Laws of Motion
5. Universal Laws of Motion If I have seen farther than others, it is because I have stood on the shoulders of giants. Sir Isaac Newton (164 177) Physicist Image courtesy of NASA/JPL Sir Isaac Newton (164177)
More informationCh. 22 Origin of Modern Astronomy Pretest
Ch. 22 Origin of Modern Astronomy Pretest Ch. 22 Origin of Modern Astronomy Pretest 1. True or False: Early Greek astronomers (600 B.C. A.D. 150) used telescopes to observe the stars. Ch. 22 Origin of
More informationAstr 2320 Tues. Jan. 24, 2017 Today s Topics Review of Celestial Mechanics (Ch. 3)
Astr 2320 Tues. Jan. 24, 2017 Today s Topics Review of Celestial Mechanics (Ch. 3) Copernicus (empirical observations) Kepler (mathematical concepts) Galileo (application to Jupiter s moons) Newton (Gravity
More informationChapter 12 Gravity. Copyright 2010 Pearson Education, Inc.
Chapter 12 Gravity Units of Chapter 12 Newton s Law of Universal Gravitation Gravitational Attraction of Spherical Bodies Kepler s Laws of Orbital Motion Gravitational Potential Energy Energy Conservation
More informationObservational Astronomy  Lecture 4 Orbits, Motions, Kepler s and Newton s Laws
Observational Astronomy  Lecture 4 Orbits, Motions, Kepler s and Newton s Laws Craig Lage New York University  Department of Physics craig.lage@nyu.edu February 24, 2014 1 / 21 Tycho Brahe s Equatorial
More informationModels of the Solar System. The Development of Understanding from Ancient Greece to Isaac Newton
Models of the Solar System The Development of Understanding from Ancient Greece to Isaac Newton Aristotle (384 BC 322 BC) Third in line of Greek thinkers: Socrates was the teacher of Plato, Plato was the
More informationKNOWLEDGE TO GET FROM TODAY S CLASS MEETING
KNOWLEDGE TO GET FROM TODAY S CLASS MEETING Class Meeting #6, Monday, February 1 st, 2016 1) GRAVITY: finish up from Fri, Jan 29 th (pages 111112, 123) 2) Isaac Newton s LAWS of MOTION (briefly) (pages
More informationGravity and the Laws of Motion
Gravity and the Laws of Motion Mass Mass is the amount of stuff (matter) in an object. Measured in grams (kg, mg, cg, etc.) Mass will not change unless matter is added or taken away. Weight Weight is the
More informationPhysics General Physics. Lecture 8 Planetary Motion. Fall 2016 Semester Prof. Matthew Jones
Physics 22000 General Physics Lecture 8 Planetary Motion Fall 2016 Semester Prof. Matthew Jones 1 First Midterm Exam Tuesday, October 4 th, 8:009:30 pm Location: PHYS 112 and WTHR 200. Covering material
More informationChapter 5 Lecture Notes
Formulas: a C = v 2 /r a = a C + a T F = Gm 1 m 2 /r 2 Chapter 5 Lecture Notes Physics 2414  Strauss Constants: G = 6.67 1011 Nm 2 /kg 2. Main Ideas: 1. Uniform circular motion 2. Nonuniform circular
More informationAstronomy 101 Exam 2 Form Akey
Astronomy 101 Exam 2 Form Akey Name: Lab section number: (In the format M0**. See back page; if you get this wrong you may not get your exam back!) Exam time: one hour and twenty minutes Please put bags
More informationAstronomy 101 Exam 2 Form Bkey
Astronomy 101 Exam 2 Form Bkey Name: Lab section number: (In the format M0**. See back page; if you get this wrong you may not get your exam back!) Exam time: one hour and twenty minutes Please put bags
More information