Universal Gravitation


 Franklin Harrell
 8 months ago
 Views:
Transcription
1 Universal Gravitation
2 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 motion, During his career, Kepler was a mathematics teacher at a seminary school in Graz, Austria, an assistant to astronomer Tycho Brahe, He also did fundamental work in the field of optics, invented an improved version of the refracting telescope (the Keplerian Telescope), and helped to legitimize the telescopic discoveries of his contemporary Galileo Galilei.
3 Geocentric Model A model of the solar system which holds that the earth is at the centre of the universe and all other bodies are in orbit around it.
4 Heliocentric Model Theory of the universe that states the sun is the centre, and that the earth revolves around it.
5 There where also a wide variety of other different models that tried to explain the motion of the planets. Many of these where very complicated and hard to understand. Other Models
6 Kepler's Three LAWS Kepler's laws of planetary motion are three mathematical laws that describe the motion of planets in the Solar System
7 The path of the planets about the sun are elliptical in shape, with the centre of the sun being located at one focus. Kepler s First Law
8 Kepler s Second Law An Imaginary line drawn from the centre of the sun to the centre of the planet will sweep out equal areas in equal intervals of time.
9 Kepler s Second Law
10 Kepler s Third Law The ratio of the squares of the periods of any two planets revolving about the sun is equal to the ratio of the cubes of their average distances from the sun. Thus, if T a and T b are their periods and r a and r b are their average distances from the sun, then we get a following equation. 2 3 T r a a T r b b
11 Astronomical Units (AU) An AU is a unit of distance that is defined as the average distance between the Sun and Earth.
12 Example problem: (Using Keplers third law to find an orbital period) Galileo discovered four moons of Jupiter. Io, which he measured to be 4.2 units from the center of Jupiter, has a period of 1.8 days. He measured the radius of Ganymede s orbit to be 10.7 units. Use Kepler s third law to find the period of Ganymede. T T r r a b a b? 1.8days 10.7units 4.2units 2 3 T a r a T r b b T r T 2 2 a a b rb 3 T units 4.2units a 1.8days Ta 7.3days 3
13 Example problem (Using Keplers third law to find an orbital radius) The fourth moon of Jupiter, Callisto, has a period of 16.7 days. Find its distance from Jupiter using the same units as Galileo used. R a =18.5 units
14 Example problem Copernicus found the period of Saturn to be 29.5 earth years and it s orbital radius to be 9.2 AU. Use these measurements and units to predict the orbital radius of Mars, whose period is 687 days. r b =1.47 AU
15 Newton's Law of Universal Gravitation The force of gravity is proportional to the product of the two masses that are interacting and inversely proportional to the square of the distance between their centres mm F G 1 2 g r 2 Where: F is the Gravitational Force G is the Gravitational Constant ( N m 2 /kg 2 ) m 1 is the mass of first object m 2 is the mass of second object r is the distance between the objects
16 Example problem Determine the force of gravitational attraction between the earth (m = 5.98 x kg) and a 70kg physics student if the student is standing at sea level, a distance of 6.37 x 10 6 m from earth's centre. F= 688 N
17 Example problem A 65.0 kg astronaut is walking on the surface of the moon, which has a mean radius of 1.74x10 3 km and a mass of 7.35x10 22 kg. What is the weight of the astronaut? 105 N
18 Example problem Now let s use Newton s law of universal gravitation to calculate the force of gravity here on Earth. mm 1 2 Fg G r 2 F g Fg m m ( ) As you can see Newton s law of universal gravitation is really another version of his second law of motion F=ma
19 Gravitational Fields So far we have studied gravitational interaction in two related manners. First, we studied it in terms of energy AKA. gravitational potential Energy Then in terms of force. AKA Weight
20 Yet there is another way to look at gravitational interactions. We can study it in terms of what is called a gravitational field. In the simplest form, we define a gravitational field as a region in which gravitational force can be experienced. For example here on earth at sea level we can experience the force of gravity. More specifically we are said to be within a gravitational field with a field intensity of 9.8 m/s 2 What we have traditionally referred to as, the value of g (g = 9.8 m/s 2 ), is a specific case example of the strength of the gravitational field intensity here on earth at sea level.
21 Gravitational field intensity will change in strength as the separation between the two mass changes We have already seen this in the case where the value of g is larger at the bottom of a trench, and smaller on top of a mountain
22 The following is a diagram of the gravitational field intensity of both the earth and moon system. Can be seen that both the magnitude and direction of the value g changes with location.
23 We can also see gravitational field intensity by looking at Newton s law of universal gravitation mm 1 2 Fg G r 2 If we now substitute in the values for Earth at sea level we get F g m ( ) Now simplified to get Fg 9.8m 2
24 We can now see that the gravitational field intensity (g) can be found by the manner mm 1 2 Fg G r 2 F g m ( ) Fg 9.8m 2
25 From this it can be seen that the universal formula for gradational field intensity is g G m r 1 2 Or equivalently, if the gravitational force (weight) is known and radius is not. g F m g 2
26 Example problem A mass of 4.60 kg is placed 6.37x10 6 m from the center of a planet and experiences a gravitational force of attraction of 45.1 N. Calculate the gravitational field intensity at this location. 9.8 m/s 2
27 Example problem An astronaut is sitting on the seat of a kg lunar rover, on the surface of the Moon. The seat is 50.0 cm above the centre of mass of the rover. What gravitational field intensity does the rover exert on the astronaut? N/kg [down]
28 Tying universal gravitation to circular motion Since the planets are not flying off into space (ie in a straight line) there must be a force causing them to stay in orbit, which would have to be some sort of centripetal force. F c mv p r 2
29 Here the gravitational force of the sun can be thought of as that centripetal force which is causing the circular motion. mm F G s g r 2 p
30 So if the gravitational force is the centripetal force, we can equate them to get m m m v G s p p r 2 r 2 G m s r which gives us a formula for calculating orbital velocity v 2 v m s G r
31 We also know that for circular motion Therefor by substituting this in for the velocity we get v r 2 T m G r s 2 r T 2 Then rearrange to get r T 3 Gm s Where m s is the mass of the planet or star which the object is orbiting around
32 Example problem How fast is the moon moving as it orbits Earth at a distance of 3.84 x 10 5 km from earth s centre? v m s G r 1.02x10 3 m/s
33 Example problem A satellite in low Earth orbit is 225 km above the surface. What is it s orbital velocity? 7.78 km/s
34
35 Weightlessness Fact or Myth?
36 To help answer this lets examine the fallowing scenario. If a space station has an orbit of 226 km, and an astronaut has a mass of 65 kg use Newton's law of gravitation to find their weight mm s Fg G r 2 p
37 In actual fact there is no such thing as weightlessness, NASA coined the phase micro gravity to describe the condition of apparent weightlessness. This is the feeling an object would experience during free fall and is caused by simply not having a normal force to counteract the force of gravity. Simply put a person can be weightless right here on Earth simply by removing their normal force. AKA. If they are in free fall.
38
39 Question? What keeps a satellite up in orbit? What prevents it from falling out of the sky? Answer: Nothing! It is falling! It just keeps missing the earth.
40 What is a satellite? An object that revolves around a planet in a circular or elliptical path is termed a satellite. The moon is Earth's original satellite but there are many manmade satellites, mostly closer to Earth. The path that a satellite follows is termed an orbit.
41 An object, such as a javelin, that is projected horizontally will fall to earth describing a parabolic arc.
42 A bullet fired by a rifle is projected at a higher velocity than the javelin so will travel further but must still fall to earth describing a parabolic arc. The part that is different here is the fact that the Earth is in fact round. For this reason the curvature of the Earth itself becomes significant, and allows the bullet to gain extra range before landing.
43 If we could, however, fire a rocket with a large enough velocity, the rocket would cover enough distance in a short amount of time, so that the curvature of the Earths would fall out from under the rocket. And the rocket would continually miss the surface of the earth as it falls.
44 The Earth would still cause a gravitational pull which would have the effect of continuously changing the rockets direction. If the direction is continuously changing while the speed remains constant then we have circular motion where the centripetal force is caused be the gravitational force. This is what we refer to as an object in orbit.
45 In short, the rocket is always falling to the Earth, but it keeps missing
46
47 Newton s Cannon Fire a pig out of a cannon from the top of a high mountain. The pig falls towards the earth. If too low of a initial speed, the pig noseplants into the earth. However, there is a certain speed at which the pig falls toward the earth at the same rate as the earth's surface curves away. The pig then "misses" the earth and keeps "falling around it", (i.e. pigs in space)
48
49 Geostationary Orbit A geostationary orbit is one in which a satellite orbits the earth at exactly the same speed as the earth turns and at the same latitude, specifically zero, the latitude of the equator. A satellite orbiting in a geostationary orbit appears to be hovering in the same spot in the sky, and is directly over the same patch of ground at all times.
Planetary 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 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 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 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 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 informationNm kg. The magnitude of a gravitational field is known as the gravitational field strength, g. This is defined as the GM
Copyright FIST EDUCATION 011 0430 860 810 Nick Zhang Lecture 7 Gravity and satellites Newton's Law of Universal Gravitation Gravitation is a force of attraction that acts between any two masses. The gravitation
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 informationLesson 9. Luis Anchordoqui. Physics 168. Tuesday, October 24, 17
Lesson 9 Physics 168 1 Static Equilibrium 2 Conditions for Equilibrium An object with forces acting on it but that is not moving is said to be in equilibrium 3 Conditions for Equilibrium (cont d) First
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 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 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 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 informationEpisode 403: Orbital motion
Episode 40: Orbital motion In this episode, students will learn how to combine concepts learned in the study of circular motion with Newton s Law of Universal Gravitation to understand the (circular) motion
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 informationGravitation. Luis Anchordoqui
Gravitation Kepler's law and Newton's Synthesis The nighttime sky with its myriad stars and shinning planets has always fascinated people on Earth. Towards the end of the XVI century the astronomer Tycho
More informationGRAVITATIONAL FORCE NEAR EARTH
GRAVITATIONAL FORCE NEAR EARTH Recap: Gravitational Force Field Recall that gravity is an actionatadistance force that pulls on objects (regardless of their size or mass) without making any contact with
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 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 informationStudent: Ms. Elbein & Ms. Townsend Physics, Due Date: Unit 5: Gravity 1. HW5.1 Gravity Reading p. 1
Unit 5: Gravity 1 p. 1 Section 5.1: Gravity is More Than a Name Nearly every child knows of the word gravity. Gravity is the name associated with the mishaps of the milk spilled from the breakfast table
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 informationOrigin of the Oceans I. Solar System? Copernicus. Our Solar System
Origin of the Oceans I Our Solar System Solar System? To begin our study of the oceans, we must understand why they exist. Fundamental to this question is whether every planet has oceans, and, if not,
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 informationLecture 4: Kepler and Galileo. Astronomy 111 Wednesday September 6, 2017
Lecture 4: Kepler and Galileo Astronomy 111 Wednesday September 6, 2017 Reminders Online homework #2 due Monday at 3pm Johannes Kepler (15711630): German Was Tycho s assistant Used Tycho s data to discover
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 informationPSI AP Physics C Universal Gravity Multiple Choice Questions
PSI AP Physics C Universal Gravity Multiple Choice Questions 1. Who determined the value of the gravitational constant (G)? (A) Newton (B) Galileo (C) Einstein (D) Schrödinger (E) Cavendish 2. Who came
More informationAP Physics C Textbook Problems
AP Physics C Textbook Problems Chapter 13 Pages 412 416 HW16: 03. A 200kg object and a 500kg object are separated by 0.400 m. Find the net gravitational force exerted by these objects on a 50.0kg object
More informationSatellites and Kepler's Laws: An Argument for Simplicity
OpenStaxCNX module: m444 Satellites and Kepler's Laws: An Argument for Simplicity OpenStax College This work is produced by OpenStaxCNX and licensed under the Creative Commons Attribution License.0 Abstract
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 informationChapter 2 The Science of Life in the Universe
In ancient times phenomena in the sky were not understood! Chapter 2 The Science of Life in the Universe The Ancient Greeks The Scientific Method Our ideas must always be consistent with our observations!
More informationMotion in the Heavens
Motion in the Heavens Most ancient cultures believed that the earth was the centre of the universe. Most felt that the planets, stars, moon and sun revolved around the earth. This is known as a geocentric
More informationFinding Extrasolar Planets. I
ExtraSolar Planets Finding Extrasolar Planets. I Direct Searches Direct searches are difficult because stars are so bright. How Bright are Planets? Planets shine by reflected light. The amount reflected
More informationQuestion 8.1: the following: (a) You can shield a charge from electrical forces by putting it inside a hollow conductor. Can you shield a body from the gravitational influence of nearby matter by putting
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 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 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 informationProficient. a. The gravitational field caused by a. The student is able to approximate a numerical value of the
Unit 6. Circular Motion and Gravitation Name: I have not failed. I've just found 10,000 ways that won't work. Thomas Edison Big Idea 1: Objects and systems have properties such as mass and charge. Systems
More informationCan you shield a body from the gravitational influence of nearby matter by putting it inside a hollow sphere or by some other means?
Question 8.1: the following: You can shield a charge from electrical forces by putting it inside a hollow conductor. Can you shield a body from the gravitational influence of nearby matter by putting it
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 informationGravitation. Objectives. The apple and the Moon. Equations 6/2/14. Describe the historical development of the concepts of gravitational force.
Gravitation Objectives Describe the historical development of the concepts of gravitational force. Describe and calculate how the magnitude of the gravitational force between two objects depends on their
More informationPlease turn on your clickers
Please turn on your clickers HW #1, due 1 week from today Quiz in class Wednesday Sections meet in Planetarium Honors meeting tonight in my office Sterling 5520 at 5:306pm Newton s First Law An object
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 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 informationChapter 3  Gravity and Motion. Copyright (c) The McGrawHill Companies, Inc. Permission required for reproduction or display.
Chapter 3  Gravity and Motion Copyright (c) The McGrawHill Companies, Inc. Permission required for reproduction or display. In 1687 Isaac Newton published the Principia in which he set out his concept
More informationEvidence that the Earth does not move: Greek Astronomy. Aristotelian Cosmology: Motions of the Planets. Ptolemy s Geocentric Model 21
Greek Astronomy Aristotelian Cosmology: Evidence that the Earth does not move: 1. Stars do not exhibit parallax: 21 At the center of the universe is the Earth: Changeable and imperfect. Above the Earth
More informationPrelab 4: Revolution of the Moons of Jupiter
Name: Section: Date: Prelab 4: Revolution of the Moons of Jupiter Many of the parameters astronomers study cannot be directly measured; rather, they are inferred from properties or other observations of
More informationAP Physics 1 Chapter 7 Circular Motion and Gravitation
AP Physics 1 Chapter 7 Circular Motion and Gravitation Chapter 7: Circular Motion and Angular Measure Gravitation Angular Speed and Velocity Uniform Circular Motion and Centripetal Acceleration Angular
More informationThe escape speed for an object leaving the surface of any celestial body of mass M and radius d is
83 Escape Speed Vocabulary Escape Speed: The minimum speed an object must possess in order to escape from the gravitational pull of a body. In Chapter 6, you worked with gravitational potential energy
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 informationFORCE. The 4 Fundamental Forces of Nature
FORCE  Force a push or pull. Results only from interaction with another object. Without interaction, forces cannot be present.  Measured in Newtons (N) 1 Newton is the amount of force required to give
More informationEarth Science, 11e. Origin of Modern Astronomy Chapter 21. Early history of astronomy. Early history of astronomy. Early history of astronomy
2006 Pearson Prentice Hall Lecture Outlines PowerPoint Chapter 21 Earth Science 11e Tarbuck/Lutgens This work is protected by United States copyright laws and is provided solely for the use of instructors
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 informationNSTA Web Seminar: Discover the Universe from Galileo to Today
LIVE INTERACTIVE LEARNING @ YOUR DESKTOP NSTA Web Seminar: Discover the Universe from Galileo to Today Presented by: Dr. Natalie Batalha Tuesday, January 20, 2009 International Year of Astronomy: Advances
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 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 informationEndofChapter Exercises
EndofChapter Exercises Exercises 1 12 are primarily conceptual questions that are designed to see if you have understood the main concepts of the chapter. Treat all balls with mass as point masses. 1.
More informationEarth Science Lesson Plan Quarter 4, Week 5, Day 1
Earth Science Lesson Plan Quarter 4, Week 5, Day 1 Outcomes for Today Standard Focus: Earth Sciences 1.d students know the evidence indicating that the planets are much closer to Earth than are the stars
More informationGravitational Fields
Gravitational Fields Examples 00 Currently, the space probe, Cassini, is between Jupiter and Saturn. Cassini s mission is to deliver a probe to one of Saturn s moons, Titan, and then orbit Saturn collecting
More informationEarth in Space. Guide for Reading How does Earth move in space? What causes the cycle of seasons on Earth?
Earth in Space How does Earth move in space? What causes the cycle of seasons on Earth? The study of the moon, stars, and other objects in space is called astronomy. Ancient astronomers studied the movements
More information1. The Moon appears larger when it rises than when it is high in the sky because
21 Copyright 2016 All rights reserved. No reproduction or distribution without the prior written consent of 1. The Moon appears larger when it rises than when it is high in the sky because A. you are
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 informationKepler's Laws and Newton's Laws
Kepler's Laws and Newton's Laws Kepler's Laws Johannes Kepler (15711630) developed a quantitative description of the motions of the planets in the solar system. The description that he produced is expressed
More informationMotion, Energy, and Gravity. Reminder to take out your clicker and turn it on!
Motion, Energy, and Gravity Reminder to take out your clicker and turn it on! Attendance Quiz Are you here today? Here! (a) yes (b) no (c) Opening Day is here! x Clickers I have not been able to download
More informationPedagogical information
SHOOTING STAR Shooting Star, an interactive computer simulation using calculation power of super computers. Students should investigate and become familiar with Kepler's laws, Newton's theory of gravitation,
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 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 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 informationSpeed/Velocity in a Circle
Speed/Velocity in a Circle Speed is the MAGNITUDE of the velocity. And while the speed may be constant, the VELOCITY is NOT. Since velocity is a vector with BOTH magnitude AND direction, we see that the
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 informationPhysics 1100: Uniform Circular Motion & Gravity
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Physics 1100: Uniform Circular Motion & Gravity 1. In the diagram below, an object travels over a hill, down a valley, and around a loop the loop at constant
More informationChapter 4 Circular Motion and Gravitation Planetary Data Homework # 26
Planetary Data Homework # 26 PLANETARY DATA Mean Distance Mass from Sun Radius Period Planet (kg) (m) (m) (days) Sun 1.99 x 10 30 6.970 x 10 8 Mercury 3.30 x 10 23 5.791 x 10 10 2.439 x 10 6 87.97 Venus
More informationSlide 1 / The discovery of Universal Gravitation is associated with: Robert Hook Isaac Newton James Joule Max Plank Christian Huygens
Slide 1 / 22 1 The discovery of Universal Gravitation is associated with: Robert Hook Isaac Newton James Joule Max Plank hristian Huygens Slide 2 / 22 2 Two objects with equal masses of 1 kg each are separated
More informationExperiencing Acceleration: The backward force you feel when your car accelerates is caused by your body's inertia. Chapter 3.3
Experiencing Acceleration: The backward force you feel when your car accelerates is caused by your body's inertia. Chapter 3.3 Feeling of apparent weight: Caused your body's reaction to the push that the
More informationSpacecraft Dynamics and Control
Spacecraft Dynamics and Control Matthew M. Peet Arizona State University Lecture 1: In the Beginning Introduction to Spacecraft Dynamics Overview of Course Objectives Determining Orbital Elements Know
More information= v = 2πr. = mv2 r. = v2 r. F g. a c. F c. Text: Chapter 12 Chapter 13. Chapter 13. Think and Explain: Think and Solve:
NAME: Chapters 12, 13 & 14: Universal Gravitation Text: Chapter 12 Chapter 13 Think and Explain: Think and Explain: Think and Solve: Think and Solve: Chapter 13 Think and Explain: Think and Solve: Vocabulary:
More informationAstronomy Section 2 Solar System Test
is really cool! 1. The diagram below shows one model of a portion of the universe. Astronomy Section 2 Solar System Test 4. Which arrangement of the Sun, the Moon, and Earth results in the highest high
More informationNewton s Three Law of Motion
Born in England on Christmas day 1643. Overview Chapter 2b Copernican Revolution Bubonic Plague 1665 While home for 2 years with nothing to do he made his most profound discoveries and proposed his most
More information2010 Pearson Education, Inc. Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity
Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity 4.1 Describing Motion: Examples from Daily Life Some of the topics we will explore: How do we describe motion? (Speed,
More informationAP Physics QUIZ Gravitation
AP Physics QUIZ Gravitation Name: 1. If F1 is the magnitude of the force exerted by the Earth on a satellite in orbit about the Earth and F2 is the magnitude of the force exerted by the satellite on the
More informationChapter 18: Studying Space Astronomy: The Original Science
Chapter 18: Studying Space 18.1 Astronomy: The Original Science What is Astronomy? Astronomy is the study of the universe People in ancient cultures used the seasonal cycles of the stars, planets, and
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 information12/1/2014. Chapter 5 Circular Motion; Gravitation. Contents of Chapter 5. Contents of Chapter Kinematics of Uniform Circular Motion
Lecture PowerPoints Chapter 5 Physics: Principles with Applications, 7 th edition Giancoli Chapter 5 Circular Motion; Gravitation This work is protected by United States copyright laws and is provided
More information4. Gravitation & Planetary Motion. Mars Motion: 2005 to 2006
4. Gravitation & Planetary Motion Geocentric models of ancient times Heliocentric model of Copernicus Telescopic observations of Galileo Galilei Systematic observations of Tycho Brahe Three planetary laws
More informationLecture Presentation. Chapter 6 Preview Looking Ahead. Chapter 6 Circular Motion, Orbits, and Gravity
Chapter 6 Preview Looking Ahead Lecture Presentation Chapter 6 Circular Motion, Orbits, and Gravity Text: p. 160 Slide 62 Chapter 6 Preview Looking Back: Centripetal Acceleration In Section 3.8, you learned
More informationOrigin of Modern Astronomy Chapter 21
Origin of Modern Astronomy Chapter 21 Early history of astronomy Ancient Greeks Used philosophical arguments to explain natural phenomena Also used some observa:onal data (looking at the night sky) Ancient
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 informationBenefit of astronomy to ancient cultures
Benefit of astronomy to ancient cultures Usefulness as a tool to predict the weather (seasons) Usefulness as a tool to tell time (sundials) Central Africa (6500 B.C.) Alignments Many ancient cultures built
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 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 informationASTRONOMY QUIZ NUMBER 1
ASTRONOMY QUIZ NUMBER. You read in an astronomy atlas that an object has a negative right ascension. You immediately conclude that A) the object is located in the Southern Sky. B) the object is located
More information/////// ///////////// Module ONE /////////////// ///////// Space
// // / / / / //// / ////// / /// / / // ///// ////// ////// Module ONE Space 1 Gravity Knowledge and understanding When you have finished this chapter, you should be able to: define weight as the force
More informationGeneral Physics I. Lecture 7: The Law of Gravity. Prof. WAN, Xin 万歆.
General Physics I Lecture 7: The Law of Gravity Prof. WAN, Xin 万歆 xinwan@zju.edu.cn http://zimp.zju.edu.cn/~xinwan/ Outline Newton's law of universal gravitation Motion of the planets; Kepler's laws Measuring
More informationConceptual Physics Projectiles Motion of Planets
Conceptual Physics Projectiles Motion of Planets Lana Sheridan De Anza College July 19, 2017 Last time angular momentum gravity gravitational field black holes Overview projectile motion orbital motion
More informationPhysics 111. Tuesday, November 9, Universal Law Potential Energy Kepler s Laws. density hydrostatic equilibrium Pascal s Principle
ics Tuesday, ember 9, 2004 Ch 12: Ch 15: Gravity Universal Law Potential Energy Kepler s Laws Fluids density hydrostatic equilibrium Pascal s Principle Announcements Wednesday, 89 pm in NSC 118/119 Sunday,
More informationKepler s Laws Simulations
Kepler s Laws Simulations Goto: http://csep10.phys.utk.edu/guidry/java/kepler/kepler.html 1. Observe the speed of the planet as it orbits around the Sun. Change the speed to.50 and answer the questions.
More informationBasic Physics. What We Covered Last Class. Remaining Topics. Center of Gravity and Mass. Sun Earth System. PHYS 1411 Introduction to Astronomy
PHYS 1411 Introduction to Astronomy Basic Physics Chapter 5 What We Covered Last Class Recap of Newton s Laws Mass and Weight Work, Energy and Conservation of Energy Rotation, Angular velocity and acceleration
More informationExam 1 Astronomy 114. Part 1
Exam 1 Astronomy 114 Part 1 [140] Select the most appropriate answer among the choices given. 1. If the Moon is setting at 6AM, the phase of the Moon must be (A) first quarter. (B) third quarter. (C)
More informationIntroduction to Astronomy
Introduction to Astronomy AST01113 (Astronomía) Semester 2014B Prof. Thomas H. Puzia Newton s Laws Big Ball Fail Universal Law of Gravitation Every mass attracts every other mass through a force called
More information4π 2 G(M1+M2 ) p2 = Newton s 3 Laws of Motion AST 105. Introduction to Astronomy: The Solar System. Newton's Version of Kepler's Third Law
REVIEW Newton s 3 Laws of Motion AST 105 Introduction to Astronomy: The Solar System Announcement: First Midterm this Thursday 02/25 Newton's Version of Kepler's Third Law Newton's Version of Kepler's
More information