Kepler's Laws and Newton's Laws


 Berenice Griffin
 1 years ago
 Views:
Transcription
1 Kepler's Laws and Newton's Laws Kepler's Laws Johannes Kepler ( ) developed a quantitative description of the motions of the planets in the solar system. The description that he produced is expressed in three ``laws''. Kepler's First Law: The orbit of a planet about the Sun is an ellipse with the Sun at one focus. Figure 1 shows a picture of an ellipse. It is constructed by specifying two focus points, F1 and F2, of the ellipse. All points on the ellipse, such as P in Figure 1, have the property that the sum of the distance between P and F1 and the distance between P and F2 is a constant. The dimension of an ellipse is often described by giving its major axis and minor axis. In descriptions of orbits in the solar system, however, it is more common to use the semimajor axis to describe the size of the orbit, and the eccentricity of the ellipse to describe its shape. The eccentricity is given by the ratio of the distance between the two focus points to the length of the major axis of the ellipse. The periapsis, or the shortest distance between the orbiting body and the central mass, is determined by the product of the semimajor axis and the complement of the eccentriciy (1  e): if the body is orbiting the sun, this is the perihelion, symbolized by q): q = a (1  e). A circle is a special case of an ellipse, with an eccentricity of 0, or so that q = a. Kepler's Second Law: A line joining a planet and the Sun sweeps out equal areas in equal intervals of time. Figure 2 illustrates Kepler's Second Law. Consider the line between the Sun and point A on the elliptical orbit. After a certain amount of time, the planet will have moved along the orbit to point B, and the line between the Sun and the planet will have swept over the cross hatched area in the figure. Kepler's Second Law states that for any two positions of the planet along the orbit that are separated by the same amount of time, the area swept out in this manner will be the same. Thus, suppose that it takes the planet the same amount of time to go between positions C and D as it did for the planet to go between positions A and B. Kepler's Second Law then tells us that the second cross hatched area between C, D, and the Sun will be the same as the cross hatched area between A, B, and the Sun. Kepler's Second Law is valuable because it gives a quantitative statement about how fast the object will be moving at any point in its orbit. Note that when the planet is closest to the Sun, at perihelion, Kepler's Second Law says that it will
2 be moving the fastest. When the planet is most distant from the Sun, at aphelion, it will be moving the slowest. Kepler's Third Law: The squares of the sidereal periods of the planets are proportional to the cubes of their semimajor axes. We have defined the semimajor axis of the orbit above, in our discussion of Kepler's First Law. The sidereal period of a planet's orbit is the time that it takes a planet to complete one orbit around the Sun. Kepler discovered a quantitative relationship between these two properties of the orbit. If P is the period of the orbit, measured in years, and a is the semimajor axis of the orbit, measured in Astronomical Units, then P 2 = a 3 Newton's Laws Kepler's Laws are wonderful as a description of the motions of the planets. However, they provide no explanation of why the planets move in this way. Moreover, Kepler's Third Law only works for planets around the Sun and does not apply to the Moon's orbit around the Earth or the moons of Jupiter. Isaac Newton ( ) provided a more general explanation of the motions of the planets through the development of Newton's Laws of Motion and Newton's Universal Law of Gravitation. Newton's Laws of Motion One way to describe the motion of an object it to specify its position at different times. Consider the car in Figure 3. We can tell where it is at different times as it travels down a road. It starts at milepost 0. One minute later it is between mileposts 1 and 2 at a distance of about 1.3 miles from the start. Two minutes later, the car has gotten to a distance of about 3.3 miles from the start. In general, we could specify a unique position for the car at any time. For example, we might have written down where the car was at a time 1.5 minutes after the start, and even if we hadn't, we're pretty sure that the car was, in fact, somewhere. Mathematicians call this kind of a relationship a function. When we say that the position of the car is a function of time, it just means that there is a unique location for the car for any time. For a planetary orbit, we can describe the orbit in the same way, by providing the position of the planet along the orbit for all times. Another useful property for describing motion is the velocity of the object. Velocity is defined to be the change of position with change in time. Thus, for our car moving along the road, we can find the velocity by dividing the distance travelled by the time it takes to travel that distance. In our example, during the first minute, the car travels 1.3 miles along the road. Thus, the car's velocity would be 1.3 miles per minute (or about 78 miles per hour!) on the average during that first minute. It is important to note that physicists are very particular about the definition of velocity, and when we state a velocity we always make a statement about the direction of the motion. In our one dimensional case, this corresponds to my statement that the the car moved along the road. In general, if we were looking at a road map, we
3 might say that the velocity was 1.3 miles per minute towards the East  if the street ran towards the East. Velocity always is specified by both a value and a direction. A final useful property for describing motion is the acceleration of the object. Just as the velocity describes the rate of change in the position of the object, the acceleration describes the rate of change of the velocity. In our example, the car moved farther during its second minute of travel than it did during its first minute. The average velocity during the second minute would be 2 miles per minute (120 miles per hour), since the car covered two miles from 1.3 to 3.3 during the oneminute time interval from 1 minute after the start to 2 minutes after the start. The velocity increased a lot (0.7 miles per minute) between the first minute of travel and the second minute of travel, and we describe this change by the acceleration. In this case, the car's velocity increased by 0.7 miles per minute in a time interval of one minute. Thus, we'd say that the average acceleration of the car during this time was 0.7 miles per minute PER MINUTE  acceleration is the rate of change of the velocity. Like velocity, acceleration has both a value and a direction implied. In our example, the direction was ``along the road'', but in a more general case, the acceleration is not necessarily in the same direction as the velocity. An especially good example for understanding the solar system is the case of uniform circular motion. Lets consider the case below of a car moving around a circle. The speed is constant in this motion, but the direction is changing continuously  note the arrows showing the direction of motion in the figure  so there must be an acceleration here. The acceleration in this special case of circular motion is called the centripetal acceleration. It is always in the direction of the center of the circle, as indicated in the figure, and it has a value, A, of A = v 2 / R where v is the speed of the object along its circular path, and R is the radius of the circle. Newton's First Law of Motion: A body remains at rest or moves in a straight line at a constant speed unless it is acted upon by an outside force.
4 If you look back at the definition of acceleration, you will see that: (1) a body at rest is not accelerating; and (2) a body moving in a straight line at a constant speed is not accelerating either. Thus, the first law of Newton says that objects do not accelerate unless they are acted upon by an outside force. Newton's Second Law of Motion: If a force, F, works on a body of mass M, then the acceleration, A, is given by F = M A The first law said that if there is acceleration, then there is a force. Newton's second law gives a quantitative relationship between the force and the acceleration that is observed. The relationship depends on a new property of the object, its mass. The mass is simply a measure of the amount of material in the object; mass is conventionally measured in grams or kilograms. Note that the second law implies that, for a given force, a less massive body will accelerate more than a more massive body. This is consistent with the world you are familiar with. Shove your kid brother, he might move a long way; shove Shaquille O'Neal with the same force and he won't move that far... Newton's Third Law of Motion: If one body exerts a force on a second body, the second body exerts an equal and opposite force on the first. This law is sometimes called the ``ActionReaction'' law. Consider what happens if you are in one row boat and you pull on a line attached to a second row boat. When you pull the line, you exert a force on the second boat. But, by the third law, the other boat exerts an equal and opposite force back on you. Thus, if the second row boat has a large shipment of bricks in it so it is very heavy, your lighter boat may do all the moving even though you are doing all the pulling. Implications for the Planets The elliptical orbits of the planets have such small eccentricities that, to a very good approximation, we can think of them as circles. (Only very precise measurements, like those available to Kepler, are able to detect the difference.) This means that we can use the idea of uniform circular motion to analyze planetary motion. In that section, we revealed that a body in uniform circular motion was constantly accelerating towards the center of its circular track. Thus, according to Newton's first law of motion, there must be a force acting on the planet that is always directed toward the center of the orbit  that is toward the Sun! Newton's second law of motion allows us to state what the magnitude of that force must be. The required force is just the mass of the Earth times its acceleration. We know that the acceleration of an object moving in uniform circular motion is A = V 2 /R. Thus, we can calculate the force that is required to keep the Earth on its circular path and compare it to physical theories about what that force might be. This is what Newton later did, although he did it first for the Moon rather than the Earth, to learn about the force of Gravity. Finally, let us consider an implication of the ``actionreaction'' law. If there is a force that attracts the Earth toward the Sun, then there must be an equal and opposite force attracting the Sun towards the Earth. Why, then, doesn't the Sun move? The answer is that it does move, but by a very small amount since the mass of the Sun is about half a million times that of the Earth. Thus, when subjected to the equal and opposite force required by the third law, it accelerates about half a million times less than the Earth as well. For this reason, to a very good approximation, we can treat the Sun as stationary in our studies of planetary motion. Newton's Universal Law of Gravitation By now you must be wondering: ``What is the Force that keeps the Earth going around the Sun?'' Newton's great discovery was the force of {\sl gravity}, which is an attractive force that occurs between two masses. The Universal Law of Gravitation is usually stated as an equation: F gravity = G M 1 M 2 / r 2
5 where F gravity is the attractive gravitational force between two objects of mass M 1 and M 2 separated by a distance r. The constant G in the equation is called the Universal Constant of Gravitation. The value of G is: G = 6.67 X meters 3 kilograms 1 seconds 2 Newton's great step was developing this law and using it, with his laws of motion, to explain the motion of lots of different things  from falling objects to planets. Amazingly, out of these simple and general rules, Newton was able to show that all of Kepler's descriptive laws for orbits followed as a direct consequence. When you combine Newton's gravitation and circular acceleration, which must balance in order for the object to remain in orbit, you get a nice relation between the period, distance, and mass of the central body. It beings by equating the centripetal force (F cent ) due to the circular motion to the gravitational force (F grav ): F grav = F cent F grav = m 2 / r 2 F cent = m 2 V 2 /r Let the Earth be m 1 and the Moon be m 2. For circular motion the distance r is the semimajor axis a. The orbital velocity of the Moon can be described as distance/time, or circumference of the circular orbit divided by the orbital period: V = 2 pi r /P so setting the forces equal yields m 2 / a 2 = m 2 V 2 /a note that the m 2 will cancel, so that circular orbital motion is independent of the mass of the orbiting body! / a 2 = ((2 pi a) 2 /P 2 )/a which we rearrange to place all the aterms on the right and all the Pterms on the left: /(4 pi 2 ) P 2 = a 3 which should look startlingly like Kepler's third law, but this time for the Earth's mass (or any other) instead of the sun's mass. To use a and P to solve for mass, manipulate once more so that m 1 = a 3 (4 pi 2 /G) / P 2 Course Home Page
Name: 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 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 informationGravitation 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 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 informationASTRO 1050 LAB #3: Planetary Orbits and Kepler s Laws
ASTRO 1050 LAB #3: Planetary Orbits and Kepler s Laws ABSTRACT Johannes Kepler (15711630), a German mathematician and astronomer, was a man on a quest to discover order and harmony in the solar system.
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 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 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 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 informationPHYS 106 Fall 2151 Homework 3 Due: Thursday, 8 Oct 2015
PHYS 106 Fall 2151 Homework 3 Due: Thursday, 8 Oct 2015 When you do a calculation, show all your steps. Do not just give an answer. You may work with others, but the work you submit should be your own.
More information5.1. Accelerated Coordinate Systems:
5.1. Accelerated Coordinate Systems: Recall: Uniformly moving reference frames (e.g. those considered at 'rest' or moving with constant velocity in a straight line) are called inertial reference frames.
More informationASTR 150. Planetarium Shows begin Sept 9th. Register your iclicker! Last time: The Night Sky Today: Motion and Gravity. Info on course website
Planetarium Shows begin Sept 9th Info on course website Register your iclicker! Last time: The Night Sky Today: Motion and Gravity ASTR 150 Hang on tight! Most math all semester get it over with right
More informationKEPLER S LAWS OF PLANETARY MOTION
KEPLER S LAWS OF PLANETARY MOTION In the early 1600s, Johannes Kepler culminated his analysis of the extensive data taken by Tycho Brahe and published his three laws of planetary motion, which we know
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 informationChapter 5 Part 2. Newton s Law of Universal Gravitation, Satellites, and Weightlessness
Chapter 5 Part 2 Newton s Law of Universal Gravitation, Satellites, and Weightlessness Newton s ideas about gravity Newton knew that a force exerted on an object causes an acceleration. Most forces occurred
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 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 informationUnit: Planetary Science
Orbital Motion Kepler s Laws GETTING AN ACCOUNT: 1) go to www.explorelearning.com 2) click on Enroll in a class (top right hand area of screen). 3) Where it says Enter class Code enter the number: MLTWD2YAZH
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 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 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 informationGravity. Newton s Law of Gravitation Kepler s Laws of Planetary Motion Gravitational Fields
Gravity Newton s Law of Gravitation Kepler s Laws of Planetary Motion Gravitational Fields Simulation Synchronous Rotation https://www.youtube.com/watch?v=ozib_l eg75q SunEarthMoon System https://vimeo.com/16015937
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 informationVISUAL PHYSICS ONLINE
VISUAL PHYSICS ONLINE EXCEL SIMULATION MOTION OF SATELLITES DOWNLOAD the MS EXCEL program PA50satellite.xlsx and view the worksheet Display as shown in the figure below. One of the most important questions
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 informationAstronomy A BEGINNER S GUIDE TO THE UNIVERSE EIGHTH EDITION
Astronomy A BEGINNER S GUIDE TO THE UNIVERSE EIGHTH EDITION CHAPTER 1 The Copernican Revolution Lecture Presentation 1.0 Have you ever wondered about? Where are the stars during the day? What is the near
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 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 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 Revolution of the Moons of Jupiter
The Revolution of the Moons of Jupiter Overview: During this lab session you will make use of a CLEA (Contemporary Laboratory Experiences in Astronomy) computer program generously developed and supplied
More informationMOTION IN THE SOLAR SYSTEM ENGAGE, EXPLORE, EXPLAIN
MOTION IN THE SOLAR SYSTEM ENGAGE, EXPLORE, EXPLAIN ENGAGE THE ATTRACTION TANGO THE ATTRACTION TANGO In your science journal, on the next clean page, title the page with The Attraction Tango. In your group,
More informationKey Points: Learn the relationship between gravitational attractive force, mass and distance. Understand that gravity can act as a centripetal force.
Lesson 9: Universal Gravitation and Circular Motion Key Points: Learn the relationship between gravitational attractive force, mass and distance. Understand that gravity can act as a centripetal force.
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 informationF = ma. G mm r 2. S center
In the early 17 th century, Kepler discovered the following three laws of planetary motion: 1. The planets orbit around the sun in an ellipse with the sun at one focus. 2. As the planets orbit around the
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 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 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 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 informationChapter 14 Satellite Motion
1 Academic Physics Mechanics Chapter 14 Satellite Motion The Mechanical Universe Kepler's Three Laws (Episode 21) The Kepler Problem (Episode 22) Energy and Eccentricity (Episode 23) Navigating in Space
More informationSatellite Communications
Satellite Communications Lecture (3) Chapter 2.1 1 Gravitational Force Newton s 2nd Law: r r F = m a Newton s Law Of Universal Gravitation (assuming point masses or spheres): Putting these together: r
More informationKepler s Laws of Orbital Motion. Lecture 5 January 30, 2014
Kepler s Laws of Orbital Motion Lecture 5 January 30, 2014 Parallax If distance is measured in parsecs then d = 1 PA Where PA is the parallax angle, in arcsec NOTE: The distance from the Sun to the Earth
More information(b) The period T and the angular frequency ω of uniform rotation are related to the cyclic frequency f as. , ω = 2πf =
PHY 302 K. Solutions for problem set #9. Nontextbook problem #1: (a) Rotation frequency of 1 Hz means one revolution per second, or 60 revolutions per minute (RPM). The prelp vinyl disks rotated at 78
More informationRadial Acceleration. recall, the direction of the instantaneous velocity vector is tangential to the trajectory
Radial Acceleration recall, the direction of the instantaneous velocity vector is tangential to the trajectory 1 Radial Acceleration recall, the direction of the instantaneous velocity vector is tangential
More informationName Period Date Earth and Space Science. Solar System Review
Name Period Date Earth and Space Science Solar System Review 1. is the spinning a planetary object on its axis. 2. is the backward motion of planets. 3. The is a unit less number between 0 and 1 that describes
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 informationEXAM #2. ANSWERS ASTR , Spring 2008
EXAM #2. ANSWERS ASTR 1101001, Spring 2008 1. In Copernicus s heliocentric model of the universe, which of the following astronomical objects was placed in an orbit around the Earth? The Moon 2. In his
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 informationVISUAL PHYSICS ONLINE
VISUAL PHYSICS ONLINE PRACTICAL ACTIVITY HOW DO THE PANETS MOVE? One of the most important questions historically in Physics was how the planets move. Many historians consider the field of Physics to date
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 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 informationMaking Sense of the Universe (Chapter 4) Why does the Earth go around the Sun? Part, but not all, of Chapter 4
Making Sense of the Universe (Chapter 4) Why does the Earth go around the Sun? Part, but not all, of Chapter 4 Based on part of Chapter 4 This material will be useful for understanding Chapters 8 and 11
More informationKepler s Laws of Orbital Motion. Lecture 5 January 24, 2013
Kepler s Laws of Orbital Motion Lecture 5 January 24, 2013 Team Extra Credit Two teams: Io & Genius Every class (that is not an exam/exam review) will have a question asked to a random member of each team
More information1. The bar graph below shows one planetary characteristic, identified as X, plotted for the planets of our solar system.
1. The bar graph below shows one planetary characteristic, identified as X, plotted for the planets of our solar system. Which characteristic of the planets in our solar system is represented by X? A)
More informationThe Heliocentric Model of Copernicus
Celestial Mechanics The Heliocentric Model of Copernicus Sun at the center and planets (including Earth) orbiting along circles. inferior planets  planets closer to Sun than Earth  Mercury, Venus superior
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 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 informationAstronomy 101 Exam 2 Form Dkey
Astronomy 101 Exam 2 Form Dkey 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 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 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 informationKNOWLEDGE TO GET FROM TODAY S CLASS MEETING
KNOWLEDGE TO GET FROM TODAY S CLASS MEETING Class Meeting #5, Friday, January 29 th, 2016 1) GRAVITY: (text pages 111112, 123) 2) Isaac Newton s LAWS of MOTION (briefly) (text pages 115117) 3) Distances
More informationLecture 15  Orbit Problems
Lecture 15  Orbit Problems A Puzzle... The ellipse shown below has one focus at the origin and its major axis lies along the xaxis. The ellipse has a semimajor axis of length a and a semiminor axis
More informationGRAVITATION. F = GmM R 2
GRAVITATION Name: Partner: Section: Date: PURPOSE: To explore the gravitational force and Kepler s Laws of Planetary motion. INTRODUCTION: Newton s law of Universal Gravitation tells us that the gravitational
More informationA = 6561 times greater. B. 81 times greater. C. equally strong. D. 1/81 as great. E. (1/81) 2 = 1/6561 as great Pearson Education, Inc.
Q13.1 The mass of the Moon is 1/81 of the mass of the Earth. Compared to the gravitational force that the Earth exerts on the Moon, the gravitational force that the Moon exerts on the Earth is A. 81 2
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 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 informationUniversal Gravitation
Universal Gravitation Newton s Law of Universal Gravitation Every particle in the Universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely
More informationOctober 19, NOTES Solar System Data Table.notebook. Which page in the ESRT???? million km million. average.
Celestial Object: Naturally occurring object that exists in space. NOT spacecraft or manmade satellites Which page in the ESRT???? Mean = average Units = million km How can we find this using the Solar
More informationCopyright 2008 Pearson Education, Inc., publishing as Pearson AddisonWesley.
Chapter 13. Newton s Theory of Gravity The beautiful rings of Saturn consist of countless centimetersized ice crystals, all orbiting the planet under the influence of gravity. Chapter Goal: To use Newton
More informationPatterns in the Solar System (Chapter 18)
GEOLOGY 306 Laboratory Instructor: TERRY J. BOROUGHS NAME: Patterns in the Solar System (Chapter 18) For this assignment you will require: a calculator, colored pencils, a metric ruler, and meter stick.
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 informationChapter 4. Motion and gravity
Chapter 4. Motion and gravity Announcements Labs open this week to finish. You may go to any lab section this week (most people done). Lab exercise 2 starts Oct 2. It's the long one!! Midterm exam likely
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 informationCircular Motion and Gravitation. Centripetal Acceleration
Circular Motion and Gravitation Centripetal Acceleration Recall linear acceleration 3. Going around a curve, at constant speed 1. Speeding up vi vi Δv a ac ac vi ac 2. Slowing down v velocity and acceleration
More informationSatellite meteorology
GPHS 422 Satellite meteorology GPHS 422 Satellite meteorology Lecture 1 6 July 2012 Course outline 2012 2 Course outline 2012  continued 10:00 to 12:00 3 Course outline 2012  continued 4 Some reading
More informationOccam s Razor: William of Occam, 1340(!)
Reading: OpenStax, Chapter 2, Section 2.2 &2.4, Chapter 3, Sections 3.13.3 Chapter 5, Section 5.1 Last time: Scales of the Universe Astro 150 Spring 2018: Lecture 2 page 1 The size of our solar system,
More informationA SIMULATION OF THE MOTION OF AN EARTH BOUND SATELLITE
DOING PHYSICS WITH MATLAB A SIMULATION OF THE MOTION OF AN EARTH BOUND SATELLITE Download Directory: Matlab mscripts mec_satellite_gui.m The [2D] motion of a satellite around the Earth is computed from
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 informationAstron 104 Laboratory #4 Gravity and Orbital Motion
Name: Date: Section: Astron 104 Laboratory #4 Gravity and Orbital Motion Section 5.5, 5.6 Introduction No astronomical object can stand still gravity makes certain of this. Newton s Law of Universal Gravitation
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 informationThe Cosmic Perspective Seventh Edition. Making Sense of the Universe: Understanding Motion, Energy, and Gravity. Chapter 4 Lecture
Chapter 4 Lecture The Cosmic Perspective Seventh Edition Making Sense of the Universe: Understanding Motion, Energy, and Gravity 2014 Pearson Education, Inc. Making Sense of the Universe: Understanding
More informationOutline for Today: Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Gravitational Potential Energy. Hello!
PHY131H1F  Class 13 Outline for Today: Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Gravitational Potential Energy Under the Flower of Kent apple tree in the Woolsthorpe
More informationChapter 9 Lecture. Pearson Physics. Gravity and Circular Motion. Prepared by Chris Chiaverina Pearson Education, Inc.
Chapter 9 Lecture Pearson Physics Gravity and Circular Motion Prepared by Chris Chiaverina Chapter Contents Newton's Law of Universal Gravity Applications of Gravity Circular Motion Planetary Motion and
More informationCopyright 2010 Pearson Education, Inc. GRAVITY. Chapter 12
GRAVITY Chapter 12 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 informationWhat is a Satellite? A satellite is an object that orbits another object. Ex. Radio satellite, moons, planets
Planetary Orbit Planetary Orbits What shape do planets APPEAR to orbit the sun? Planets APPEAR to orbit in a circle. What shape do the planets orbit the sun??? Each planet Orbits the Sun in an ellipse
More informationPhysics Mechanics. Lecture 29 Gravitation
1 Physics 170  Mechanics Lecture 29 Gravitation Newton, following an idea suggested by Robert Hooke, hypothesized that the force of gravity acting on the planets is inversely proportional to their distances
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 informationv lim a t = d v dt a n = v2 R curvature
PHY 02 K. Solutions for Problem set # 6. Textbook problem 5.27: The acceleration vector a of the particle has two components, the tangential acceleration a t d v dt v lim t 0 t (1) parallel to the velocity
More informationLecture 1a: Satellite Orbits
Lecture 1a: Satellite Orbits Meteorological Satellite Orbits LEO view GEO view Two main orbits of Met Satellites: 1) Geostationary Orbit (GEO) 1) Low Earth Orbit (LEO) or polar orbits Orbits of meteorological
More informationAPS 1030 Astronomy Lab 79 Kepler's Laws KEPLER'S LAWS
APS 1030 Astronomy Lab 79 Kepler's Laws KEPLER'S LAWS SYNOPSIS: Johannes Kepler formulated three laws that described how the planets orbit around the Sun. His work paved the way for Isaac Newton, who derived
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 informationGravitation. Kepler s Law. BSc I SEM II (UNIT I)
Gravitation Kepler s Law BSc I SEM II (UNIT I) P a g e 2 Contents 1) Newton s Law of Gravitation 3 Vector representation of Newton s Law of Gravitation 3 Characteristics of Newton s Law of Gravitation
More informationOrbits. Objectives. Orbits and unbalanced forces. Equations 4/7/14
Orbits Objectives Describe and calculate how the magnitude of the gravitational force between two objects depends on their masses and the distance between their centers. Analyze and describe orbital circular
More informationIf Earth had no tilt, what else would happen?
A more in depth explanation from last week: If Earth had no tilt, what else would happen? The equator would be much hotter due to the direct sunlight which would lead to a lower survival rate and little
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 informationAcceleration in Uniform Circular Motion
Acceleration in Uniform Circular Motion The object in uniform circular motion has a constant speed, but its velocity is constantly changing directions, generating a centripetal acceleration: a c v r 2
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 informationOutline for Today: Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Gravitational Potential Energy
PHY131H1F  Class 13 Outline for Today: Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Gravitational Potential Energy Under the Flower of Kent apple tree in the Woolsthorpe
More information