1 Kepler s Laws of Planetary Motion

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "1 Kepler s Laws of Planetary Motion"

Transcription

1 1 Kepler s Laws of Planetary Motion 1.1 Introduction Johannes Kepler published three laws of planetary motion, the first two in 1609 and the third in The laws were made possible by planetary data of unprecedented accuracy collected by Tycho Brahe. The laws were both a radical departure from the astronomical prejudices of the time and profound tools for predicting planetary motion with great accuracy. Kepler, however, was not able to describe in a significant way why the laws worked. 1.2 First Law: Law of Ellipses The orbit of a planet is an ellipse where one focus of the ellipse is the sun. An ellipse is defined by two focii and all points for which the sum of the distances are the same. The semimajor axis (a) is the long distance from the center to edge of the ellipse. If r 1 and r 2 are the distances from the focii to any point on the ellipse, then r1 + r2 = 2a. The short axis is called the semiminor axis. How elliptical an orbit is can be described by the eccentricity (e). The eccentricity is equal to the distance between a focus and the center (c) of the ellipses divided by the semimajor axis (a). That is, e = c/a. The NAAP Eccentricity Demonstrator ( shows ellipses for different values of a and c. Note c is always less than a by definition. (a) The NAAP Eccentricity Demonstration can be accessed at http: //astro.unl.edu/naap/pos/animations/ellipsedemo.swf. (b) Equal areas over equal time. Figure 1: Kepler s First and Second Laws 1.3 Second Law: Law of Equal Areas A line from the planet to the sun sweeps out equal areas in equal amounts of time. With elliptical orbits a planet is sometimes closer to the sun than it is at other times. The point at which it is closest is called perihelion. The point at which a planet is farthest is called aphelion. Kepler s second law basically says that the planets speed is not constant moving slowest at aphelion and fastest at perihelion. The law allows an astronomer to calculate the orbital speed of a planet at any point. Figure 1(b) shows a diagram of this law. 1.4 Third Law: Law of Harmonies The period of a planet s orbit squared is proportional to its average distance from the sun cubed. The average distance of a planet from the sun is equal to its semimajor axis (a). If the period (P ) is measured in years and the semimajor axis (a) is given in astronomical units (the earth sun distance is 1 AU) then Kepler s Third Law can be written: P 2 = a 3 1 / 7

2 However, this equation is only good for our solar system. Isaac Newton was able to derive a more general form of the equation using his Law of Gravitation. 2 Newton and Planetary Motion 2.1 Introduction In 1687 Isaac Newton published Philosophiae Naturalis Principia Mathematica, a work of immense and profound impact. Newton s pronounced three laws of motion and a law of universal gravitation. They were a united set of principles which applied not only to the heavens but also to the earth in a uniform way. Their simplicity and extremely broad applicability forever changed astronomy. 2.2 First Law of Motion: Law of Inertia A body remains at rest, or moves in a straight line (at a constant velocity), unless acted upon by a net outside force. The law of inertia did not originate with Newton, nevertheless it is integral to his system of mechanics. An object in motion will remain in motion unless something acts upon it. Because a planet is moving in an ellipse (i.e. not a straight line) this law states that there must be some force acting upon the planet. If there were no force, the planet would fly off in a straight line. Figure 2: When the string is released, the ball will fly straight away, not along the curve. 2.3 Second Law of Motion: F = ma The acceleration of an object is proportional to the force acting upon it. The first law says that if no force is acting on an object, it will remain in motion. The second law tells how the motion will change when a force acts upon the object. Velocity is how fast an object is moving (speed or magnitude) and the direction it is moving. Acceleration is a change in velocity. An accelerating object can either change how fast it is moving, the direction it is moving, or both. 2.4 Third Law: Law of Reciprocal Actions For every action, there is an equal and opposite reaction. The law can be more fully stated as, Whenever one body exerts force upon a second body, the second body exerts an equal and opposite force upon the first body. That is, when the sun pulls on a planet with the force of gravity, the planet pulls on the sun with a force of equal magnitude. But, because the sun is so much more massive than the planet, Newton s second law says that the sun will experience much less acceleration. 2 / 7

3 2.5 Law of Universal Gravitation F = Gm 1m 2 r 2 Every object in the Universe attracts every other object with a force directed along the line of centers for the two objects that is proportional to the product of their masses and inversely proportional to the square of the separation between the two objects. While the law does not explain what gravity is, it does say how the force of gravity works. From this law and his laws of motion, Newton was able to derive all of Kepler s Laws of Planetary Motion. 3 Pre-Lab Questions 1. Match the following definitions with the proper law. C Kepler s First Law A. only a force acting on an object can change its motion B Kepler s Second Law B. planets move faster when close to the sun D Kepler s Third Law C. planets orbit the sun in elliptical paths A Newton s First Law D. planets with large orbits take a long time to complete an orbit 2. When written as P 2 = a 3, Kepler s Third Law (with P in years and a in AU) is applicable to... A. any object orbiting our sun. B. any object orbiting any star. C. any object orbiting any other object. 3. For a planet in an elliptical orbit to sweep out equal areas in equal amounts of time it must... A. move slowest when near the sun. B. move fastest when near the sun. C. move at the same speed at all times. D. have a perfectly circular orbit. 4. If a planet is twice as far from the sun at aphelion than at perihelion, then the strength of the gravitational force at aphelion will be as it is at perihelion. A. four times as much B. twice as much C. the same D. one half as much E. one quarter as much 4 Procedure Everything in this lab will require you to open the NAAP Planetary Orbit Simulator from this link: 3 / 7

4 4.1 Kepler s First Law Click on the Kepler s First Law tab if it is not already (it s open by default), and enable all 5 check boxes in the bottom center of the display. The white dot is the simulated planet. One can click on it and drag it around. Change the size of the orbit with the semimajor axis slider. Note how the background grid indicates change in scale while the displayed orbit size remains the same. (You can change the value of a slider by clicking on the slider bar or by entering a number in the value box.) Change the eccentricity and note how it affects the shape of the orbit. Be aware that the ranges of several parameters are limited by practical issues that occur when creating a simulator rather than any true physical limitations. The semi-major axis is limited to 50 AU since that covers most of the objects we are interested in our solar system and the eccentricity is limited to 0.7 since the ellipses would be hard to fit on the screen for larger values. Note that the semi-major axis is aligned horizontally for all elliptical orbits created in this simulator, where they are randomly aligned in our solar system. Animate the simulated planet. You may need to increase the animation rate for very large orbits or decrease it for small ones. The planetary presets set the simulated planets parameters to those like our solar system s planets. Explore these options. 1. For what eccentricity is the secondary focus (which is usually empty) located at the sun? What is the shape of this orbit? Solution: When e = 0. This is a circular orbit. 2. Create an orbit with a = 20 AU and e = 0. Drag the planet first to the far left of the ellipse and then to the far right. What are the values of r 1 and r 2 at these locations? r 1 (AU) r 2 (AU) Far Left Far Right Create an orbit with a = 20 AU and e = 0.5. Drag the planet first to the far left of the ellipse and then to the far right. What are the values of r 1 and r 2 at these locations? r 1 (AU) r 2 (AU) Far Left Far Right For the ellipse with a = 20 AU and e = 0.5, can you find a point in the orbit where r 1 and r 2 are equal? Sketch and label the ellipse, the location of this point, and r 1 and r 2 in the space below. 5. What is the value of the sum of r 1 and r 2 and how does it relate to the ellipse properties? Is this true for all ellipses? Solution: r 1 + r 2 = 2a = 40 AU. This is true for all ellipses regardless of eccentricity or semi-major axis. 4.2 Kepler s Second Law Use the clear optional features button to remove the First Law features. Open the Kepler s Second Law tab. 4 / 7

5 Press the start sweeping button. Adjust the semimajor axis and animation rate so that the planet moves at a reasonable speed. Adjust the size of the sweep using the adjust size slider. Click and drag the sweep segment around. Note how the shape of the sweep segment changes, but the area does not. Add more sweeps. Erase all sweeps with the erase sweeps button. The sweep continuously check box will cause sweeps to be created continuously when sweeping. Test this option. 1. Erase all sweeps and create an ellipse with a = 1 AU and e = 0. Set the fractional sweep size to one-twelfth of the period. Drag the sweep segment around. Does its size or shape change? Solution: It s a circle, so neither the shape nor the size change as the sweep segment is dragged around the orbit. 2. Leave the semi-major axis at a = 1 AU and change the eccentricity to e = 0.5. Drag the sweep segment around and note that its size and shape change. Where is the sweep segment the skinniest? Where is it the fattest? Where is the planet when it is sweeping out each of these segments? (What names do astronomers use for these positions?) Solution: Skinniest is when the planet is farthest from the star: aphelion. Fattest is when the planet is closest to the star: perihelion. 3. Halley s comet has a semimajor axis of about 18.5 AU, a period of 76 years, and an eccentricity of about 0.97 (so Halleys orbit cannot be shown in this simulator). The orbit of Halleys Comet, the Earths Orbit, and the Sun are shown in Figure 3 (not exactly to scale). Based upon what you know about Kepler s Second Law, explain why we can only see the comet for about 6 months every orbit (76 years)? Solution: For the six months when it s swinging through perihelion, it s moving at its fastest in the inner portion of the solar system. We can see it just fine. But when it moves out of the inner solar system, it gets harder to see, but it also slows down. So it spends the largest amount of its orbital period far away from us, moving very slowly, where we can t see it too well. Figure 3: The orbit of Halley s Comet, the Earth s orbit, and the sun. 4.3 Kepler s Third Law Use the clear optional features button to remove the Second Law features. Open the Kepler s Third Law tab. 1. Use the simulator to complete Table As the size of a planet s orbit increases, what happens to its period? Solution: Its period increases: a = 3 P Start with the Earth s orbit and change the eccentricity to 0.6. Does changing the eccentricity change the period of the planet? 5 / 7

6 Object P (years) a (AU) e P 2 a 3 Earth Mars Ceres Charon Table 1: Orbital period and distance for selected objects. Solution: No. 4.4 Newtonian Features Important: Use the clear optional features button to remove other features. Open the Newtonian features tab. Click both show vector boxes to show both the velocity and the acceleration of the planet. Observe the direction and length of the arrows. The length is proportional to the values of the vector in the plot. 1. The acceleration vector is always pointing towards what object in the simulator? Solution: The star. 2. Create an ellipse with a = 5 AU and e = 0.5. For each marked location on the plot in Figure 4 indicate a) whether the velocity is increasing or decreasing at the point in the orbit (by circling the appropriate arrow) and b) the angle θ between the velocity and acceleration vectors (you may have to eyeball the value). Note that one is completed for you. Figure 4: The orbit of Halley s Comet, the Earth s orbit, and the sun. 6 / 7

7 3. Where do the maximum and minimum values of velocity occur in the orbit? Solution: Maximum velocity is at perihelion. Minimum velocity is at aphelion. 4. Can you describe a general rule which identifies where in the orbit velocity is increasing and where it is decreasing? What is the angle between the velocity and acceleration vectors at these times? Solution: Orbital velocity increases when acceleration increases: from aphelion to perihelion, and the angle between the velocity and acceleration vectors is 45 < θ < 90. Orbital velocity decreases when acceleration decreases: from perihelion to aphelion, and the angle between the velocity and acceleration vectors is 90 < θ < 135. (The max value of θ depends on how eccentric the orbit is, but the rules above hold for all ellipses.) 7 / 7

Planetary Orbit Simulator Student Guide

Planetary Orbit Simulator Student Guide Name: Planetary Orbit Simulator Student Guide Background Material Answer the following questions after reviewing the Kepler's Laws and Planetary Motion and Newton and Planetary Motion background pages.

More information

Introduction to Gravity and Orbits. Isaac Newton. Newton s Laws of Motion

Introduction to Gravity and Orbits. Isaac Newton. Newton s Laws of Motion Introduction to Gravity and Orbits Isaac Newton Born in England in 1642 Invented calculus in early twenties Finally published work in gravity in 1687 The Principia Newton s Laws of Motion 1: An object

More information

Kepler, Newton and Gravitation

Kepler, Newton and Gravitation Kepler, Newton and Gravitation Kepler, Newton and Gravity 1 Using the unit of distance 1 AU = Earth-Sun distance PLANETS COPERNICUS MODERN Mercury 0.38 0.387 Venus 0.72 0.723 Earth 1.00 1.00 Mars 1.52

More information

Astronomy 1140 Quiz 1 Review

Astronomy 1140 Quiz 1 Review Astronomy 1140 Quiz 1 Review Prof. Pradhan September 15, 2015 What is Science? 1. Explain the difference between astronomy and astrology. (a) Astrology: nonscience using zodiac sign to predict the future/personality

More information

Lecture 13. Gravity in the Solar System

Lecture 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 information

Lecture Outlines. Chapter 2. Astronomy Today 7th Edition Chaisson/McMillan Pearson Education, Inc.

Lecture Outlines. Chapter 2. Astronomy Today 7th Edition Chaisson/McMillan Pearson Education, Inc. Lecture Outlines Chapter 2 Astronomy Today 7th Edition Chaisson/McMillan Chapter 2 The Copernican Revolution Units of Chapter 2 2.1 Ancient Astronomy 2.2 The Geocentric Universe 2.3 The Heliocentric Model

More information

Name: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due in class Tuesday, Jan. 20, 2015

Name: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due in class Tuesday, Jan. 20, 2015 Name: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due in class Tuesday, Jan. 20, 2015 Why are celestial motions and forces important? They explain the world around

More information

Unit 8 Lesson 2 Gravity and the Solar System

Unit 8 Lesson 2 Gravity and the Solar System Unit 8 Lesson 2 Gravity and the Solar System Gravity What is gravity? Gravity is a force of attraction between objects that is due to their masses and the distances between them. Every object in the universe

More information

Kepler, Newton, and laws of motion

Kepler, Newton, and laws of motion Kepler, Newton, and laws of motion !! " The only history in this course:!!!geocentric vs. heliocentric model (sec. 2.2-2.4)" The important historical progression is the following:!! Ptolemy (~140 AD) Copernicus

More information

PHYS-1000 Chapter 3 Homework Solutions Due: September 9, 2012

PHYS-1000 Chapter 3 Homework Solutions Due: September 9, 2012 1. In the Greek geocentric model, the retrograde motion of a planet occurs when A. Earth is about to pass the planet in its orbit around the Sun. B. the planet actually goes backward in its orbit around

More information

Motion and Gravity in Space

Motion and Gravity in Space Motion and Gravity in Space Each planet spins on its axis. The spinning of a body, such a planet, on its axis is called rotation. The orbit is the path that a body follows as it travels around another

More information

USING MS EXCEL FOR DATA ANALYSIS AND SIMULATION

USING MS EXCEL FOR DATA ANALYSIS AND SIMULATION USING MS EXCEL FOR DATA ANALYSIS AND SIMULATION Ian Cooper School of Physics The University of Sydney i.cooper@physics.usyd.edu.au Introduction The numerical calculations performed by scientists and engineers

More information

From Aristotle to Newton

From Aristotle to Newton From Aristotle to Newton The history of the Solar System (and the universe to some extent) from ancient Greek times through to the beginnings of modern physics. The Geocentric Model Ancient Greek astronomers

More information

Chapter 13 - Gravity. David J. Starling Penn State Hazleton Fall Chapter 13 - Gravity. Objectives (Ch 13) Newton s Law of Gravitation

Chapter 13 - Gravity. David J. Starling Penn State Hazleton Fall Chapter 13 - Gravity. Objectives (Ch 13) Newton s Law of Gravitation The moon is essentially gray, no color. It looks like plaster of Paris, like dirty beach sand with lots of footprints in it. -James A. Lovell (from the Apollo 13 mission) David J. Starling Penn State Hazleton

More information

The Main Point. The Scientific Method. Laws of Planetary Motion. Lecture #3: Orbits and Gravity. Laws of Planetary Motion:

The Main Point. The Scientific Method. Laws of Planetary Motion. Lecture #3: Orbits and Gravity. Laws of Planetary Motion: Lecture #3: Orbits and Gravity Laws of Planetary Motion: Kepler's Laws. Newton's Laws. Gravity. Planetary Orbits. Spacecraft Orbits. The Main Point Motions of planets, moons, and asteroids can be very

More information

In Orbit. Overview. Venn Diagram Positioning. Time Required. Materials Required. Newton s Laws of Motion: In Orbit [ 1 ]

In Orbit. Overview. Venn Diagram Positioning. Time Required. Materials Required. Newton s Laws of Motion: In Orbit [ 1 ] In Orbit Overview The celestial bodies of our solar system move according to rules governed by gravity, Newton s Laws of Motion, and mathematics. In this computer-based simulation developed by the University

More information

Gravitation. Physics 1425 Lecture 11. Michael Fowler, UVa

Gravitation. Physics 1425 Lecture 11. Michael Fowler, UVa Gravitation Physics 1425 Lecture 11 Michael Fowler, UVa The Inverse Square Law Newton s idea: the centripetal force keeping the Moon circling the Earth is the same gravitational force that pulls us to

More information

Orbital Mechanics. Angular Momentum

Orbital Mechanics. Angular Momentum Orbital Mechanics The objects that orbit earth have only a few forces acting on them, the largest being the gravitational pull from the earth. The trajectories that satellites or rockets follow are largely

More information

Building Planetary Orbits (the Feynman way)

Building Planetary Orbits (the Feynman way) Building Planetary Orbits (the Feynman way) Using a method of computing known as finite differences we can quickly calculate the geometry of any planetary orbit. All we need are a starting position and

More information

5. Universal Laws of Motion

5. 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 (1642 1727) Physicist 5.1 Describing Motion: Examples from Daily

More information

Website: Reading: Homework: Discussion:

Website: Reading: Homework: Discussion: Reminders! Website: http://starsarestellar.blogspot.com/ Lectures 1-5 are available for download as study aids. Reading: You should have Chapters 1-4 read, Chapter 5 by the end of today, and Chapters 6

More information

Chapter 13. Gravitation

Chapter 13. Gravitation Chapter 13 Gravitation 13.2 Newton s Law of Gravitation In vector notation: Here m 1 and m 2 are the masses of the particles, r is the distance between them, and G is the gravitational constant. G = 6.67

More information

Physics 130 Astronomy Exam #1 July 19, 2004

Physics 130 Astronomy Exam #1 July 19, 2004 Physics 130 Astronomy Exam #1 July 19, 2004 Name Multiple Choice: 1. A scientist observes a new phenomenon that disagrees with his explanation or hypothesis. Following the scientific methods, he should

More information

tps Q: If the Earth were located at 0.5 AU instead of 1 AU, how would the Sun s gravitational force on Earth change?

tps Q: If the Earth were located at 0.5 AU instead of 1 AU, how would the Sun s gravitational force on Earth change? tps Q: If the Earth were located at 0.5 AU instead of 1 AU, how would the Sun s gravitational force on Earth change? A. It would be one-fourth as strong. B. It would be one-half as strong. C. It would

More information

PHY1 Review for Exam 5

PHY1 Review for Exam 5 Topics 1. Uniform circular Motion a. Centripetal acceleration b. Centripetal force c. Horizontal motion d. ertical motion e. Circular motion with an angle 2. Universal gravitation a. Gravitational force

More information

Understanding the motion of the Universe. Motion, Force, and Gravity

Understanding the motion of the Universe. Motion, Force, and Gravity Understanding the motion of the Universe Motion, Force, and Gravity Laws of Motion Stationary objects do not begin moving on their own. In the same way, moving objects don t change their movement spontaneously.

More information

Lab 6: Kepler's Laws. Introduction. Section 1: First Law

Lab 6: Kepler's Laws. Introduction. Section 1: First Law Lab 6: Kepler's Laws Purpose: to learn that orbit shapes are ellipses, gravity and orbital velocity are related, and force of gravity and orbital period are related. Materials: 2 thumbtacks, 1 pencil,

More information

DERIVING KEPLER S LAWS OF PLANETARY MOTION. By: Emily Davis

DERIVING KEPLER S LAWS OF PLANETARY MOTION. By: Emily Davis DERIVING KEPLER S LAWS OF PLANETARY MOTION By: Emily Davis WHO IS JOHANNES KEPLER? German mathematician, physicist, and astronomer Worked under Tycho Brahe Observation alone Founder of celestial mechanics

More information

Halliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton

Halliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton Halliday, Resnick & Walker Chapter 13 Gravitation Physics 1A PHYS1121 Professor Michael Burton II_A2: Planetary Orbits in the Solar System + Galaxy Interactions (You Tube) 21 seconds 13-1 Newton's Law

More information

Halliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton

Halliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton Halliday, Resnick & Walker Chapter 13 Gravitation Physics 1A PHYS1121 Professor Michael Burton II_A2: Planetary Orbits in the Solar System + Galaxy Interactions (You Tube) 21 seconds 13-1 Newton's Law

More information

Lecture 5: Newton s Laws. Astronomy 111

Lecture 5: Newton s Laws. Astronomy 111 Lecture 5: Newton s Laws Astronomy 111 Isaac Newton (1643-1727): English Discovered: three laws of motion, one law of universal gravitation. Newton s great book: Newton s laws are universal in scope,

More information

Understanding the motion of the Universe. Motion, Force, and Gravity

Understanding the motion of the Universe. Motion, Force, and Gravity Understanding the motion of the Universe Motion, Force, and Gravity Laws of Motion Stationary objects do not begin moving on their own. In the same way, moving objects don t change their movement spontaneously.

More information

The Motions of Celestial Bodies, and Newton s Laws of Motion

The Motions of Celestial Bodies, and Newton s Laws of Motion The Motions of Celestial Bodies, and Newton s Laws of Motion Announcements The results of Quiz 1 are posted in OWL Looking ahead: Homework 1 is on-going, and is due on Thu, Sept. 29 th ; Homework 2 will

More information

Vocabulary - Understanding Revolution in. our Solar System

Vocabulary - Understanding Revolution in. our Solar System Vocabulary - Understanding Revolution in Universe Galaxy Solar system Planet Moon Comet Asteroid Meteor(ite) Heliocentric Geocentric Satellite Terrestrial planets Jovian (gas) planets Gravity our Solar

More information

Chapter 13 Newton s Theory of Gravity

Chapter 13 Newton s Theory of Gravity Chapter 13 Newton s Theory of Gravity Chapter Goal: To use Newton s theory of gravity to understand the motion of satellites and planets. Slide 13-2 Chapter 13 Preview Slide 13-3 Chapter 13 Preview Slide

More information

Announcements. Eclipses 2/1/12. HW1 is due Thursday. You have to be registered at MasteringAstronomy to do the homework!

Announcements. Eclipses 2/1/12. HW1 is due Thursday. You have to be registered at MasteringAstronomy to do the homework! Announcements HW1 is due Thursday. You have to be registered at MasteringAstronomy to do the homework! TA Qufei Gu will be in RH111 4:00-5:00PM Wednesday to help with homework. Email: zyx88@unm.edu Feb

More information

Astro 1 Lab Exercise

Astro 1 Lab Exercise Summer 2014 Astro 1 Lab Exercise Lab #4: ExoPlanet Detection Wednesday Aug 7,8 and 11 Room 200 in Wilder Lab reports are due by 5 pm on Friday August 15, 2013 Put it in the large ASTRO 1 Lab Box just inside

More information

Gravitation and Newton s Synthesis

Gravitation and Newton s Synthesis Gravitation and Newton s Synthesis Vocabulary law of unviversal Kepler s laws of planetary perturbations casual laws gravitation motion casuality field graviational field inertial mass gravitational mass

More information

2. Orbits. FER-Zagreb, Satellite communication systems 2011/12

2. Orbits. FER-Zagreb, Satellite communication systems 2011/12 2. Orbits Topics Orbit types Kepler and Newton laws Coverage area Influence of Earth 1 Orbit types According to inclination angle Equatorial Polar Inclinational orbit According to shape Circular orbit

More information

ASTR 1010 Astronomy of the Solar System Professor Caillault Fall 2009 Semester Exam 1 Answers

ASTR 1010 Astronomy of the Solar System Professor Caillault Fall 2009 Semester Exam 1 Answers ASTR 1010 Astronomy of the Solar System Professor Caillault Fall 2009 Semester Exam 1 Answers 1. The number of degrees in a full circle is (c) 360 2. An arcsecond is a measure of (d) angle. 3. How many

More information

Penn State University Physics 211 ORBITAL MECHANICS 1

Penn State University Physics 211 ORBITAL MECHANICS 1 ORBITAL MECHANICS 1 PURPOSE The purpose of this laboratory project is to calculate, verify and then simulate various satellite orbit scenarios for an artificial satellite orbiting the earth. First, there

More information

Chapter 3: Force and Motion

Chapter 3: Force and Motion Force and Motion Cause and Effect Chapter 3 Chapter 3: Force and Motion Homework: All questions on the Multiple- Choice and the odd-numbered questions on Exercises sections at the end of the chapter. In

More information

What s going on during a solar eclipse. Solar Eclipses. Total Solar Eclipse on March 29, 2006 (viewed from Turkey) Partial, Total, and Annular

What s going on during a solar eclipse. Solar Eclipses. Total Solar Eclipse on March 29, 2006 (viewed from Turkey) Partial, Total, and Annular Solar Eclipses The Sun disappears behind the Moon The Moon is always in the New phase during a solar eclipse Can only be seen from certain places on Earth These events are even more rare than lunar eclipses

More information

Newton s Law of Gravity and Kepler s Laws

Newton s Law of Gravity and Kepler s Laws Newton s Law of Gravity and Kepler s Laws Michael Fowler Phys 142E Lec 9 2/6/09. These notes are partly adapted from my Physics 152 lectures, where more mathematical details can be found. The Universal

More information

Lecture 6: Newton & Kepler. Tycho Brahe ( ) Johannes Kepler

Lecture 6: Newton & Kepler. Tycho Brahe ( ) Johannes Kepler Lecture 6: Newton & Kepler Johannes Kepler (1600) was employed by Tycho to develop a mathematical theory to explain the observations made by Tycho Kepler was a pure theorist; Tycho a pure observer Issac

More information

Universal Law of Gravitation Honors Physics

Universal Law of Gravitation Honors Physics Universal Law of Gravitation Honors Physics Newton s Law of Universal Gravitation The greatest moments in science are when two phenomena that were considered completely separate suddenly are seen as just

More information

A. 81 2 = 6561 times greater. B. 81 times greater. C. equally strong. D. 1/81 as great. E. (1/81) 2 = 1/6561 as great.

A. 81 2 = 6561 times greater. B. 81 times greater. C. equally strong. D. 1/81 as great. E. (1/81) 2 = 1/6561 as great. Q12.1 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 information

The Mass of Jupiter Student Guide

The Mass of Jupiter Student Guide The Mass of Jupiter Student Guide Introduction: In this lab, you will use astronomical observations of Jupiter and its satellites to measure the mass of Jupiter. We will use the program Stellarium to simulate

More information

EDMONDS COMMUNITY COLLEGE ASTRONOMY 100 Winter Quarter 2007 Sample Test # 1

EDMONDS COMMUNITY COLLEGE ASTRONOMY 100 Winter Quarter 2007 Sample Test # 1 Instructor: L. M. Khandro EDMONDS COMMUNITY COLLEGE ASTRONOMY 100 Winter Quarter 2007 Sample Test # 1 1. An arc second is a measure of a. time interval between oscillations of a standard clock b. time

More information

Constructing. Ellipses BEGIN

Constructing. Ellipses BEGIN Constructing Ellipses BEGIN In 1609, astronomer Johannes Kepler theorized that planets orbit the Sun along elliptical paths, rather than circular paths. But what exactly is an ellipse? But what exactly

More information

Lesson 5 Rotational and Projectile Motion

Lesson 5 Rotational and Projectile Motion Lesson 5 Rotational and Projectile Motion Introduction: Connecting Your Learning The previous lesson discussed momentum and energy. This lesson explores rotational and circular motion as well as the particular

More information

The orbit of Halley s Comet

The orbit of Halley s Comet The orbit of Halley s Comet Given this information Orbital period = 76 yrs Aphelion distance = 35.3 AU Observed comet in 1682 and predicted return 1758 Questions: How close does HC approach the Sun? What

More information

4.1 Describing Motion. How do we describe motion? Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity

4.1 Describing Motion. How do we describe motion? 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 Our goals for learning:! How do we describe motion?! How is mass different from weight? How do we

More information

Kepler s Laws of Planetary Motion and Newton s Law of Universal Gravitation

Kepler s Laws of Planetary Motion and Newton s Law of Universal Gravitation Kepler s Laws of lanetary Motion and Newton s Law of Universal Gravitation Abstract These notes were written with those students in mind having taken (or are taking) A Calculus and A hysics Newton s law

More information

M OTION. Chapter2 OUTLINE GOALS

M OTION. Chapter2 OUTLINE GOALS Chapter2 M OTION OUTLINE Describing Motion 2.1 Speed 2.2 Vectors 2.3 Acceleration 2.4 Distance, Time, and Acceleration Acceleration of Gravity 2.5 Free Fall 2.6 Air Resistence Force and Motion 2.7 First

More information

Chapter 4: Newton s Laws of Motion

Chapter 4: Newton s Laws of Motion Chapter 4: Newton s Laws of Motion Dynamics: Study of motion and its causes. orces cause changes in the motion of an object. orce and Interactions Definition ( loose ): A force is a push or pull exerted

More information

Kepler s Laws and our Solar System

Kepler s Laws and our Solar System Kepler s Laws and our Solar System The Astronomical Unit, AU Kepler s Empirical Laws of Planetary mo=on The mass of the Sun, M O. A very brief tour of the solar system Major planets Dwarf planets (defini=on)

More information

Name: x 2 + 4x + 4 = -6y p = -6 (opens down) p = -3/2 = (x + 2) 2 = -6y + 6. (x + 2) 2 = -6(y - 1) standard form: (-2, 1) Vertex:

Name: x 2 + 4x + 4 = -6y p = -6 (opens down) p = -3/2 = (x + 2) 2 = -6y + 6. (x + 2) 2 = -6(y - 1) standard form: (-2, 1) Vertex: Write the equation of the parabola in standard form and sketch the graph of the parabola, labeling all points, and using the focal width as a guide for the width of the parabola. Find the vertex, focus,

More information

Notes: Most of the material in this chapter is taken from Young and Freedman, Chap. 13.

Notes: Most of the material in this chapter is taken from Young and Freedman, Chap. 13. Chapter 5. Gravitation Notes: Most of the material in this chapter is taken from Young and Freedman, Chap. 13. 5.1 Newton s Law of Gravitation We have already studied the effects of gravity through the

More information

Newton s Law of Gravity

Newton s Law of Gravity Newton s Law of Gravity Example 4: What is this persons weight on Earth? Earth s mass = 5.98 10 24 kg Mar s mass = 6.4191 10 23 kg Mar s radius = 3400 km Earth s radius = 6378 km Newton s Form of Kepler

More information

356 CHAPTER 12 Bob Daemmrich

356 CHAPTER 12 Bob Daemmrich Standard 7.3.17: Investigate that an unbalanced force, acting on an object, changes its speed or path of motion or both, and know that if the force always acts toward the same center as the object moves,

More information

1 Newton s Laws of Motion

1 Newton s Laws of Motion Exam 1 Ast 4 - Chapter 2 - Newton s Laws Exam 1 is scheduled for the week of Feb 19th Bring Pencil Scantron 882-E (available in the Bookstore) A scientific calculator (you will not be allowed to use you

More information

Gravitation. Gravitation

Gravitation. Gravitation 1 Gravitation Newton s observations A constant center seeking force is required to keep an object moving along a circular path. You know that the moon orbits the earth and hence there should be a force

More information

Chapter 13: Universal Gravitation

Chapter 13: Universal Gravitation Chapter 13: Universal Gravitation I. The Falling Apple (13.1) A. Isaac Newton (1642-1727) 1. Formulated ideas based on earlier work by Galileo (concept of inertia) 2. Concept if object undergoes change

More information

PHYS 1901 Assignment 1

PHYS 1901 Assignment 1 PHYS 1901 Assignment 1 Due: Tuesday, October 18, 2016 DON T PANIC Seriously, don t panic. With a bit of effort, everyone in this class can succeed on this assignment. The bark is far worse than the bite.

More information

Background Information

Background Information Background Information The Second Law of Motion and The Law of Gravitation Student Activities 1. Round and Round They Go! 2. onic Sections - Movement in Newton s Gravitational orce Notes to Teachers Teacher

More information

Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity

Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity Chapter 4 Making Sense of the Universe: Understanding Motion, Energy, and Gravity How do we describe motion? Precise definitions to describe motion: Speed: Rate at which object moves sp e e d = d ista

More information

Making Sense of the Universe: Understanding Motion, Energy, and Gravity

Making Sense of the Universe: Understanding Motion, Energy, and Gravity Making Sense of the Universe: Understanding Motion, Energy, and Gravity 1. Newton s Laws 2. Conservation Laws Energy Angular momentum 3. Gravity Review from last time Ancient Greeks: Ptolemy; the geocentric

More information

The Cosmic Perspective Seventh Edition. Making Sense of the Universe: Understanding Motion, Energy, and Gravity. Chapter 4 Lecture

The 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 Making Sense of the Universe: Understanding Motion, Energy, and Gravity

More information

7.2 Calculate force of gravity at a given distance given the force of gravity at another distance (making use of the inverse square relationship).

7.2 Calculate force of gravity at a given distance given the force of gravity at another distance (making use of the inverse square relationship). Chapter 7 Circular Motion and Gravitation 7.1 Calculate force of gravity using Newton s Law of Universal Gravitation. 5. What is the gravitational force between the Earth and the Sun? (Mass of Earth: 5.98

More information

Orbital Dynamics with Maple (sll --- v1.0, February 2012)

Orbital Dynamics with Maple (sll --- v1.0, February 2012) Orbital Dynamics with Maple (sll --- v1.0, February 2012) Kepler s Laws of Orbital Motion Orbital theory is one of the great triumphs mathematical astronomy. The first understanding of orbits was published

More information

Unification of the laws of the Earth and the Universe Why do planets appear to wander slowly across the sky?

Unification of the laws of the Earth and the Universe Why do planets appear to wander slowly across the sky? October 19, 2015 Unification of the laws of the Earth and the Universe Why do planets appear to wander slowly across the sky? Key Words Newton s Laws of motion, and Newton s law of universal gravitation:

More information

6. What is the approximate angular diameter of the Sun in arcseconds? (d) 1860

6. What is the approximate angular diameter of the Sun in arcseconds? (d) 1860 ASTR 1020 Stellar and Galactic Astronomy Professor Caillault Fall 2009 Semester Exam 1 Multiple Choice Answers (Each multiple choice question is worth 1.5 points) 1. The number of degrees in a full circle

More information

Astro 101 F15 Test 2. Name: Multiple Choice Identify the choice that best completes the statement or answers the question.

Astro 101 F15 Test 2. Name: Multiple Choice Identify the choice that best completes the statement or answers the question. Name: Astro 101 Test 2 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. The Moon undergoes synchronous rotation, and as a consequence the: a. Moon does

More information

Determination of the Orbit of Mars Using Kepler s Triangulation Technique. Abstract

Determination of the Orbit of Mars Using Kepler s Triangulation Technique. Abstract APS Determination of the Orbit of Mars Using Kepler s Triangulation Technique N. Copernicus University of Central Arkansas (Dated: August 25, 2008) Abstract The eccentricity (ɛ), semi-major axis (a), and

More information

Chapter 4 Dynamics: Newton s Laws of Motion. Copyright 2009 Pearson Education, Inc.

Chapter 4 Dynamics: Newton s Laws of Motion. Copyright 2009 Pearson Education, Inc. Chapter 4 Dynamics: Newton s Laws of Motion Force Units of Chapter 4 Newton s First Law of Motion Mass Newton s Second Law of Motion Newton s Third Law of Motion Weight the Force of Gravity; and the Normal

More information

Section 4: The Basics of Satellite Orbits

Section 4: The Basics of Satellite Orbits Section 4: The Basics of Satellite Orbits MOTION IN SPACE VS. MOTION IN THE ATMOSPHERE The motion of objects in the atmosphere differs in three important ways from the motion of objects in space. First,

More information

12/3/10. Copyright 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

12/3/10. Copyright 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley. The beautiful rings of Saturn consist of countless centimeter-sized ice crystals, all orbiting the planet under the influence of gravity. Chapter Goal: To use Newton s theory of gravity to understand the

More information

Q: Who established the law of universal gravitation? A: Newton. Q: What is a spring scale used for? A: To measure weight

Q: Who established the law of universal gravitation? A: Newton. Q: What is a spring scale used for? A: To measure weight Q: Who established the law of universal gravitation? A: Newton Q: What is a spring scale used for? A: To measure weight Q: What is the Law of Universal Gravitation? A: Everything in the universe has gravity.

More information

Astronomy 114 Summary of Important Concepts #1 1

Astronomy 114 Summary of Important Concepts #1 1 Astronomy 114 Summary of Important Concepts #1 1 1 Kepler s Third Law Kepler discovered that the size of a planet s orbit (the semi-major axis of the ellipse) is simply related to sidereal period of the

More information

Today. Galileo. Planetary Motion. Tycho Brahe s Observations. Kepler s Laws

Today. Galileo. Planetary Motion. Tycho Brahe s Observations. Kepler s Laws Today Galileo Planetary Motion Tycho Brahe s Observations Kepler s Laws 1 Galileo c. 1564-1642 First telescopic astronomical observations 2 First use of telescope for astronomy in 1609 400 years ago! 3

More information

Black holes 101(beyond science fiction)

Black holes 101(beyond science fiction) Chapter 13: Gravitation Newton s Law of Gravitation Why is gravity important? Revisit the following: gravitational force, weight, and gravitational energy Stellar motions: the orbits of satellites and

More information

Introduction Newton s law of gravitation. Copyright Kinetic Books Co. Chapter 13

Introduction Newton s law of gravitation. Copyright Kinetic Books Co. Chapter 13 13.0 - Introduction The topic of gravity has had a starring role in some of the most famous tales in the history of physics. Galileo Galilei was studying the acceleration due to the Earth s gravity when

More information

Newton's Laws. Before Isaac Newton

Newton's Laws. Before Isaac Newton Newton's Laws Before Isaac Newton Newton's Laws There were facts and laws about the way the physical world worked, but no explanations After Newton There was a unified system that explained those facts

More information

Clicker Question: Clicker Question: Gravitational Force. Newton's Law of Gravity. Inverse Square law Demo

Clicker Question: Clicker Question: Gravitational Force. Newton's Law of Gravity. Inverse Square law Demo Test results Last day to drop without a grade is Oct. 3 Grades posted in cabinet and online F D C B A A bullet is fired from a gun. Complete the following sentance to form a true statement. The speed of

More information

QUESTION BANK UNIT-6 CHAPTER-8 GRAVITATION

QUESTION BANK UNIT-6 CHAPTER-8 GRAVITATION QUESTION BANK UNIT-6 CHAPTER-8 GRAVITATION I. One mark Questions: 1. State Kepler s law of orbits. 2. State Kepler s law of areas. 3. State Kepler s law of periods. 4. Which physical quantity is conserved

More information

THE NATURE OF FORCES Forces can be divided into two categories: contact forces and non-contact forces.

THE NATURE OF FORCES Forces can be divided into two categories: contact forces and non-contact forces. SESSION 2: NEWTON S LAWS Key Concepts In this session we Examine different types of forces Review and apply Newton's Laws of motion Use Newton's Law of Universal Gravitation to solve problems X-planation

More information

Newton s Laws. Newton s Imaginary Cannon. Michael Fowler Physics 142E Lec 6 Jan 22, 2009

Newton s Laws. Newton s Imaginary Cannon. Michael Fowler Physics 142E Lec 6 Jan 22, 2009 Newton s Laws Michael Fowler Physics 142E Lec 6 Jan 22, 2009 Newton s Imaginary Cannon Newton was familiar with Galileo s analysis of projectile motion, and decided to take it one step further. He imagined

More information

AST 101 Lecture 7. Newton s Laws and the Nature of Matter

AST 101 Lecture 7. Newton s Laws and the Nature of Matter AST 101 Lecture 7 Newton s Laws and the Nature of Matter The Nature of Matter Democritus (c. 470-380 BCE) posited that matter was composed of atoms Atoms: particles that can not be further subdivided 4

More information

Today. Laws of Motion Conservation Laws Gravity tides. What is the phase of the moon?

Today. Laws of Motion Conservation Laws Gravity tides. What is the phase of the moon? Today Laws of Motion Conservation Laws Gravity tides What is the phase of the moon? How is mass different from weight? Mass the amount of matter in an object Weight the force that acts upon an object You

More information

The Gravitational Field

The Gravitational Field The Gravitational Field The use of multimedia in teaching physics Texts to multimedia presentation Jan Hrnčíř jan.hrncir@gfxs.cz Martin Klejch martin.klejch@gfxs.cz F. X. Šalda Grammar School, Liberec

More information

Astron 100 Sample Exam 1 1. Solar eclipses occur only at (A) New moon (B) 1 st quarter moon (C) Full moon (D) 3 rd quarter moon (E) The equinoxes 2.

Astron 100 Sample Exam 1 1. Solar eclipses occur only at (A) New moon (B) 1 st quarter moon (C) Full moon (D) 3 rd quarter moon (E) The equinoxes 2. Astron 100 Sample Exam 1 1. Solar eclipses occur only at (A) New moon (B) 1 st quarter moon (C) Full moon (D) 3 rd quarter moon (E) The equinoxes 2. If the Moon is at first quarter tonight in Amherst,

More information

Concept Review. Physics 1

Concept Review. Physics 1 Concept Review Physics 1 Speed and Velocity Speed is a measure of how much distance is covered divided by the time it takes. Sometimes it is referred to as the rate of motion. Common units for speed or

More information

Solar System. 1. The diagram below represents a simple geocentric model. Which object is represented by the letter X?

Solar System. 1. The diagram below represents a simple geocentric model. Which object is represented by the letter X? Solar System 1. The diagram below represents a simple geocentric model. Which object is represented by the letter X? A) Earth B) Sun C) Moon D) Polaris 2. Which object orbits Earth in both the Earth-centered

More information

PHY131H1F - Class 13. Today: Gravitational Potential Energy. Newton s Law of Universal Gravitation. The Gravitational Field.

PHY131H1F - Class 13. Today: Gravitational Potential Energy. Newton s Law of Universal Gravitation. The Gravitational Field. PHY131H1F - Class 13 Today: Gravitational Potential Energy Newton s Law of Universal Gravitation The Gravitational Field Orbital Motion Two balls are launched along a pair of tracks with equal velocities,

More information

Exercise: Estimating the Mass of Jupiter Difficulty: Medium

Exercise: Estimating the Mass of Jupiter Difficulty: Medium Exercise: Estimating the Mass of Jupiter Difficulty: Medium OBJECTIVE The July / August observing notes for 010 state that Jupiter rises at dusk. The great planet is now starting its grand showing for

More information

AE554 Applied Orbital Mechanics. Hafta 1 Egemen Đmre

AE554 Applied Orbital Mechanics. Hafta 1 Egemen Đmre AE554 Applied Orbital Mechanics Hafta 1 Egemen Đmre A bit of history the beginning Astronomy: Science of heavens. (Ancient Greeks). Astronomy existed several thousand years BC Perfect universe (like circles

More information

Section 3 Newton s Laws of Motion

Section 3 Newton s Laws of Motion Section 3 Newton s Laws of Motion Key Concept Newton s laws of motion describe the relationship between forces and the motion of an object. What You Will Learn Newton s first law of motion states that

More information

Chapter 4. Forces and Newton s Laws of Motion

Chapter 4. Forces and Newton s Laws of Motion Chapter 4 Forces and Newton s Laws of Motion 4.1 The Concepts of Force and Mass A force is a push or a pull. Contact forces arise from physical contact. Action-at-a-distance forces do not require contact

More information

Newton s Law of Universal Gravitation

Newton s Law of Universal Gravitation Newton s Law of Universal Gravitation The greatest moments in science are when two phenomena that were considered completely separate suddenly are seen as just two different versions of the same thing.

More information