The Revolution of the Moons of Jupiter


 Cuthbert Collins
 1 years ago
 Views:
Transcription
1 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 by the Department of Physics at Gettysburg College. This program will simulate observations of the same four moons that Galileo saw through his telescope when he observed Jupiter back in the 1600 s. Using these observations and Kepler s Third Law, you will go about determining the mass of Jupiter. Hopefully, by the time you are finished, you will have learned something about how planets (and moons) behave in their orbits and how Kepler s Third Law can be used to gain valuable information. Background: You know that the Moon orbits the Earth and that the Earth orbits the Sun. Likewise you probably know that the other planets of our solar system orbit the Sun and have moons that orbit them. But, do you know what the geometry is of the orbits or any of the other orbital properties? Well, by the time you are finished with this lab, you should have a much better understanding of orbits. In the 1500 s, Nicholaus Copernicus hypothesized that the planets orbit in circles about the Sun. Later, in the early 1600 s, using observations of the planets and stars made by his mentor, Tycho Brahe, Johannes Kepler found that the orbits were really ellipses (see Figure 1). He then went on to deduce three mathematical laws concerning planetary orbits. These laws can also be applied to any one body orbiting another body. The first of Kepler s three laws of planetary motion concerns the overall geometry of an orbit. Put simply it states: The orbit of a planet about the Sun is an ellipse with the Sun located at one focus. Now what does that really mean? First it would be good to understand what an ellipse is. This is best explained with the help of a diagram (Figure 1). 1
2 Minor Axis F a F b c a Major Axis Figure 1 An ellipse is a closed curve where the sum of the distances of every point on the curve from the two foci (points F a and F b ) is the same. The dashed horizontal line that runs through the foci and the center is called the major axis. Half this distance is termed the semimajor axis and is labeled with the letter a. The semimajor axis will be important to you later. The dashed vertical line that runs through the center is called the minor axis and likewise half this distance is the semiminor axis. Another important quantity you should be familiar with is the eccentricity (denoted with the letter e). This is a measure of how elongated an ellipse is. Eccentricity is determined by dividing the value c in Figure 1 (the distance from the center to the focus of the ellipse) by the semimajor axis. As an ellipse becomes more circular the foci and the center get closer together. Therefore the distance c becomes smaller. As c becomes smaller, so does the eccentricity, which remember is e = c/a. From this you should be able to see that eccentricity ranges from 0 (a perfect circle) to It can never reach 1, however. Okay so now you can start to understand what Kepler s First Law is saying. Each planet s orbit is an ellipse, that is; it follows an elliptical path around the Sun. The orbit, 2
3 since it is elliptical, has two foci and the Sun is located at one of them while nothing is at the other focus. This tells you how the orbit is positioned relative to the Sun (Figure 2). Kepler s Second Law deals with the speed at which the planets orbit. He noticed that as the planets neared the Sun their speed increased and conversely when planets are farther away from the Sun they moved slower. At a planet s closest approach to the Sun, called perihelion, it moves fastest. When a planet is at its farthest distance from the Sun, called aphelion, it moves slowest. This led to Kepler s Second Law, which states: A line joining a planet and the Sun sweeps out equal areas in equal time intervals. Another diagram at this point will be helpful. Figure 2 is another drawing of an ellipse illustrating Kepler s Second Law. Figure 2 Imagine it takes a planet 5 days to go from point A to point B along the orbit. A line joining the Sun and the planet will sweep out a somewhat triangular area between A and B (shaded region). If it also takes 5 days to travel from point C to point D, then the other shaded triangular region swept out will have the same area as the region swept out from A to B. This has come to be known as the law of equal areas. 3
4 The last of Kepler s laws relates the size of the planet s orbit to the time it takes the planet to go around the Sun once or its period. This is the law that you will be most concerned with in this lab. Simply put it states: The squares of the sidereal periods of the planets are proportional to the cubes of their semimajor axes. It sounds mathematical, but it s not too difficult to understand. You ve already learned that the semimajor axis is half of the major axis, which was defined earlier. See Figure 1 if you have forgotten. The sidereal period is just the time it takes for one body to orbit another with respect to the stars. For example the Earth s sidereal period is days. Proportional just means that the two quantities are related via some constant. The fullblown form of Kepler s Third Law is somewhat complicated, so you will be using this much simpler form: P 2 = a 3 /M J In this case the proportionality constant is just 1 over the mass of Jupiter in units of the solar masses. This form of Kepler s Third Law does require, however, that you make measurements of the period in Earth years and measurements of the semimajor axis in astronomical units. One astronomical unit (AU) is the average distance between the Earth and the Sun. What you are going to do now is make simulated observations of the 4 Galilean moons of Jupiter. You will record data from the computer, which will allow you to deduce the period and semimajor axis for each moon. Then using the form of Kepler s Third Law above, you will calculate the mass of Jupiter. Introduction: The CLEA computer program provided for this lab will simulate optical telescope observations of Jupiter and the 4 moons Galileo observed. In order of increasing distance from Jupiter they are Io, Europa, Ganymede, and Callisto. 4
5 The images displayed on the screen were actually taken by the Voyager spacecraft. The moons will appear lined up horizontally because the view is edgeon to the plane of their orbit. The orbits themselves have fairly small eccentricities; that is, they are roughly circular. Therefore for your purposes in this lab you will consider them to be circular, which means that the semimajor axis will be the same as the radius. Notice that, because your view is edgeon, you see only the apparent distance (R app ) from Jupiter and not the true distance or radius (R). Look at Figure 3, which is a top view of the system. Moon R θ Jupiter R app = Rsinθ To Observer Figure 3 From the computer you will be able to take measurements of R app over time. Because the motion in circular, the apparent position should form a sine curve if plotted versus time. You will measure the apparent position of each moon (in Jupiter diameters) for a number of time intervals and plot the data. Once you have the data plotted you will fit a sine curve to the data points from which you will ultimately deduce the period and semimajor axis. A sine curve is a smooth oscillating curve with a regular period and 5
6 amplitude. The period of your fitted sine curve will tell you the period of the orbit and the amplitude will tell you the radius of the orbit. (Remember you made the assumption that the orbit is circular, therefore, the radius is equal to the semimajor axis.) Hopefully Figure 4 will clarify this for you. If you are still having trouble, ask your instructor for help Days Figure 4 This is basically what your plots should look like. You then can draw a smooth sine curve through these points, which represents how the apparent position changes over time. Note that the negative values indicate that the moon is on the left side of Jupiter as we look at it, while positive values indicates its position to the right of Jupiter. For this example the amplitude (maximum height of the peaks) is roughly 11 Jupiter diameters (JD), which tells you that the radius, and thus, the semimajor axis is 11 JD. The period for this curve is roughly 20 days. The period is determined by measuring the time between one peak to the next on the graph. These values can now be converted to the appropriate units so you can use Kepler s Third Law to calculate the mass of Jupiter. 6
7 The Program: You should now be able to get started taking data. Doubleclick on the CLEA Jupiter icon with the mouse to start the program and login via the menu at the top of the screen. If you cannot find the appropriate icon or you have trouble logging in, please ask your instructor for assistance. Select START from the menu. This will bring up a window of parameters for your simulated observations. Enter the appropriate date and time. It asks for Universal time, which is the time in Greenwich, England. To convert Eastern Standard Time to Universal Time just add five hours (four if it is currently daylight savings time). The window also asks you to set the observation interval time. The default is 24 hours, but we do not want this. Set the interval to 12 hours. This will make it easier for you when it comes time to do your fits. Once you have entered everything, click OK. You should see an image of Jupiter and the 4 Galilean moons. At the bottom of the screen is the date, time, and buttons to change the magnification. Record the date, time, and day in your data table on the answer sheet. Your first observation should be day 1, second observation day 1.5, third observation day 2, and so on, because you are going by 12 hour intervals. Now measure the apparent positions of the moons and record them in your data table. To do this, hold down the left mouse button and move the cursor over the moons. When you are centered over a moon, the name of the moon and the apparent position is displayed in the low right side of the screen. You should see 4 numbers. The one you are concerned with is the X value on the bottom line next to the R value. Record that value for each moon. Remember if the moon is to the right of Jupiter, assign a positive sign to the apparent position and if it is to the left, assign a negative sign to it. Note: it is best to measure the apparent position on the moon using the largest magnification possible. Once you have recorded everything, move on to the next observation by clicking the NEXT button and repeat the procedure until you have 20 lines of data. Sometimes the moon is directly behind or in front of Jupiter. If it is behind, then you cannot get a measurement, so record the distance for that moon as zero. If it is in front of Jupiter, you can still make a measurement if you zoom in close enough. The program is also designed to randomly give you some cloudy days to make the simulation more real. For days were 7
8 you have clouds you cannot take measurement and will have a gap in your data (Remember this when you go to do you plots). Fill out the date, time, and day, and then indicate that it was a cloudy day. Once you have 20 lines of data, you can quit the program by clicking QUIT on the menu line. If you have any questions or something seems wrong with the program, please ask your instructor. Data Analysis: Now that you have all your data, you can begin the process of analyzing it. On each of the 4 graphs (one for each moon) provided at the back of this lab you want to plot the apparent position you measured (yaxis) versus the day you observed it (xaxis). Your plots should end up looking something like the one in Figure 4. Remember to skip days for which you have no measurements due to clouds. Once you have all the data plotted for each moon, you will want to go back and draw in a sine curve through your data that best fits the points. Remember the curve should have a regular period and have the same amplitude throughout. If you are having trouble getting a good curve, please ask your instructor for assistance. The curves are important for the rest of your analysis. From your curve you can now obtain the parameters you need to use Kepler s Third Law to determine the mass of Jupiter. The period of the orbit is going to be the period of the sine curve you fitted to the data. To measure this, just determine from your graph the time interval between one peak to the next peak or one trough to the next trough. If your observations allowed you to see the moon through many cycles (you see multiple peaks and troughs), then you can get a more accurate period by determining the time it takes the moon to complete, say 3 cycles and then divide that time by 3. If your graph does not have two peaks or troughs (this may happen for Ganymede and Callisto) then measure the time interval between a peak and the first trough after it or a trough and the next peak after it. This will give you half of the period, which you can then just multiple by two. Record your period for each moon in the space provided on the answer sheet. Remember your units. Now that you have the period, you need to determine the semimajor axis. Remember you assumed the orbits to be circular, therefore, the amplitude of your curves 8
9 will tell you how long the semimajor is. Measure the amplitude for each moon and record it in the space provided. Again remember your units. The last thing you need to do before you can determine the mass of Jupiter is convert your period and semimajor axis to the correct units. The period you measured was in days. Convert that to years by dividing by the number of days in a year, The semimajor axis was measured in Jupiter diameters. There are 1050 JD in one AU, so divide your semimajor axis in JD by 1050 to convert it to AU. Record these values. Now you can compute the mass of Jupiter in solar masses by plugging your values into Kepler s Third Law. Calculation of Jupiter s Mass: Use Kepler s Third Law to calculate Jupiter s mass using the data for each moon and record the values in the spaces provided on your answer sheet. Once you have a value for Jupiter s mass from each moon, calculate the average value. M J = a 3 /P 2 Where M J = mass of Jupiter in solar masses a = semimajor axis of the orbit in AU P = period of the orbit in Earth years Remember to fill in all of the spaces on your answer sheet and answer all of the questions, which follow your calculations. 9
10 Name: Date: Session: Answer Sheet: The Revolution of the Moons of Jupiter Data Table: Date Time Day Io Europa Ganymede Callisto 10
11 Graphs: Moon I Io Moon II Europa 11
12 Moon III Ganymede Moon IV Callisto 12
13 Graph Measurements: Io: Period = days Period = years Europa: Period = days Period = years Ganymede: Period = days Period = years Callisto: Period = days Period = years a (semimajor axis) = JD a (semimajor axis) = AU a (semimajor axis) = JD a (semimajor axis) = AU a (semimajor axis) = JD a (semimajor axis) = AU a (semimajor axis) = JD a (semimajor axis) = AU Mass Calculations: From Io From Europa From Ganymede From Callisto M J = solar masses M J = solar masses M J = solar masses M J = solar masses Average M J = solar masses Questions and Discussion: 1. Are any of the values for the mass of Jupiter from each case significantly different? If yes, what might be some sources of error? Hint: Think about the data you took. 13
14 2. Express the mass of Jupiter in Earth masses. The Earth is 3.0 x 106 solar masses. 3. Jupiter has more moons beyond the orbit of Callisto. Do these moons have larger or smaller periods than Callisto? Why? 4. Which of the following do you think would cause a larger error in your calculation of Jupiter s mass, a ten percent error in the period or a ten percent error in the semimajor axis? Explain. 14
15 5. The orbit of the earth s moon has a period of 27.3 days and a semimajor axis of 2.56 x 103 AU. What is the mass of the Earth? Show all your work for credit and remember the units. 15
PHYS133 Lab 4 The Revolution of the Moons of Jupiter
PHYS133 Lab 4 Goals: Use a simulated remotely controlled telescope to observe iter and the position of its four largest moons. Plot their positions relative to the planet vs. time and fit a curve to them
More informationName: Lab Partner: Department of Physics Gettysburg College Gettysburg, PA 17325
Name: Lab Partner: The Revolution of the Moons of Jupiter Student Manual A Manual to Accompany Software for the Introductory Astronomy Lab Exercise Edited by Lucy Kulbago, John Carroll University 11/24/2008
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 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 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 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 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 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 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 informationThe 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 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 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 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 informationAST101: Our Corner of the Universe Lab 8: Measuring the Mass of Jupiter
AST101: Our Corner of the Universe Lab 8: Measuring the Mass of Jupiter Name: Student number (SUID): Lab section number: 1 Introduction Objectives In a previous lab, we measured the mass of the Earth with
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 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 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 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 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 informationName: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due on Tuesday, Jan. 19, 2016
Name: Earth 110 Exploration of the Solar System Assignment 1: Celestial Motions and Forces Due on Tuesday, Jan. 19, 2016 Why are celestial motions and forces important? They explain the world around us.
More 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 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 informationAstronomy 104: Stellar Astronomy
Astronomy 104: Stellar Astronomy Lecture 5: Observing is the key... Brahe and Kepler Spring Semester 2013 Dr. Matt Craig 1 For next time: Read Slater and Freedman 35 and 36 if you haven't already. Focus
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 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 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 informationAST101: Our Corner of the Universe Lab 4: Planetary Orbits
AST101: Our Corner of the Universe Lab 4: Planetary Orbits Name: Partners: Student number (SUID): Lab section number: 1 Introduction Objectives The Planetary Orbits Lab reviews used the Planetary Orbit
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 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 informationUniversal Gravitation
Universal Gravitation Johannes Kepler Johannes Kepler was a German mathematician, astronomer and astrologer, and key figure in the 17th century Scientific revolution. He is best known for his laws of planetary
More 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 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 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 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 informationThe Sun.  this is the visible surface of the Sun. The gases here are very still hot, but much cooler than inside about 6,000 C.
Name: The Sun The Sun is an average sized. Earth, Mars, Jupiter and Uranus are. A star is the only object in space that makes its own. This includes and. The sun is about million miles from Earth. This
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 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 informationEarth Science Unit 6: Astronomy Period: Date: Elliptical Orbits
Earth Science Name: Unit 6: Astronomy Period: Date: Lab # 5 Elliptical Orbits Objective: To compare the shape of the earth s orbit (eccentricity) with the orbits of and with a circle. other planets Focus
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 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 informationPLANETARY TEMPERATURES
APS 1010 Astronomy Lab 97 Planetary Temperatures PLANETARY TEMPERATURES Mars is essentially in the same orbit. Mars is somewhat the same distance from the Sun, which is very important. We have seen pictures
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 informationAstronomy 101 Lab: Lunar Phases and Eclipses
Name: Astronomy 101 Lab: Lunar Phases and Eclipses PreLab Assignment: In this week's lab, you will be using a lamp, a globe, and a ball to simulate the Sun, Earth, and the Moon. You will be able to see
More information1 The Solar System. 1.1 a journey into our galaxy
1 The Solar System Though Pluto, and the farflung depths of the Solar System, is the focus of this book, it is essential that Pluto is placed in the context of the planetary system that it inhabits our
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 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 informationChapter 16 The Solar System
Chapter 16 The Solar System Finding the Standard Time and Date at Another Location Example When it is 12 noon in London, what is the standard time in Denver, Colorado (40 N, 105 W)? Section 15.3 Finding
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 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 informationYou should have finished reading Chapter 3, and started on chapter 4 for next week.
Announcements Homework due on Sunday at 11:45pm. Thank your classmate! You should have finished reading Chapter 3, and started on chapter 4 for next week. Don t forget your out of class planetarium show
More informationPractice Test DeAnza College Astronomy 04 Test 1 Spring Quarter 2009
Practice Test DeAnza College Astronomy 04 Test 1 Spring Quarter 2009 Multiple Choice Identify the letter of the choice that best completes the statement or answers the question. Mark answer on Scantron.
More informationDATA LAB. Data Lab Page 1
NOTE: This DataLab Activity Guide will be updated soon to reflect April 2015 changes DATA LAB PURPOSE. In this lab, students analyze and interpret quantitative features of their brightness graph to determine
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 informationDeAnza College Winter First Midterm Exam MAKE ALL MARKS DARK AND COMPLETE.
FAMILY NAME : (Please PRINT!) GIVEN NAME : (Please PRINT!) Signature: ASTRONOMY 4 DeAnza College Winter 2018 First Midterm Exam MAKE ALL MARKS DARK AND COMPLETE. Instructions: 1. On your Parscore sheet
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 informationKey Stage 3: Celestia Navigation Teacher s Notes
Key Stage 3: Celestia Navigation Teacher s Notes Curriculum Links: Sci7L The Solar System and Beyond, Sci9J Gravity and Space, Unit 6E Forces in action Celestia is a spaceflight simulator that allows you
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 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 informationTycho Brahe
Tycho Brahe 15461601 At the time of Shakespeare and Elizabeth I and Champlain Lost part of his nose in a duel over who was the best mathematician At 27 he measured the distance of a supernova and a comet
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 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 information2.7 Kepler s Laws of Planetary Motion
2.7 Kepler s Laws of Planetary Motion PRELECTURE READING 2.7 Astronomy Today, 8 th Edition Chaisson & McMillan) Astronomy Today, 7 th Edition Chaisson & McMillan) Astronomy Today, 6 th Edition Chaisson
More informationPlanet Detection. AST 105 Intro Astronomy The Solar System
Review AST 105 Intro Astronomy The Solar System MIDTERM III this THURSDAY 04/8 covering LECT. 17 through We ve talked about the Terrestrial Planets and the Jovian Planets  What about planets around other
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 informationExam #1 Study Guide (Note this is not all the information you need to know for the test, these are just SOME of the main points)
Exam #1 Study Guide (Note this is not all the information you need to know for the test, these are just SOME of the main points) Moon Phases Moon is always ½ illuminated by the Sun, and the sunlit side
More informationPhysics 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 informationThe Scientific Method
Chapter 1 The Scientific Method http://www.mhhe.com/physsci/physical/bookpage/ Chapter 1 Outline: Main Ideas Scientists make science work The Scientific Method Science is a process Exploring Nature An
More informationCoriolis Effect  the apparent curved paths of projectiles, winds, and ocean currents
Regents Earth Science Unit 5: Astronomy Models of the Universe Earliest models of the universe were based on the idea that the Sun, Moon, and planets all orbit the Earth models needed to explain how the
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 informationAssignment #13 Roemer s measurement of the speed of light
Name: Class: Date: Assignment #13 Roemer s measurement of the speed of light Part I: Purpose, Goals, and Objectives This assignment will give you some observational experience associated with what I consider
More informationKepler s Laws. Determining one point on Mars orbit
Kepler s Laws Hwk1: max is 28 If you want a question regraded, write a note on the front & give me the paper. Figure added to Homework 2 See link on syllabus Read pages in Galileo s Starry Messenger for
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 informationNext Homework Due. Feb. 20
This week: Chapter 2 Required: Guided Discovery (p.4447) Required: Astro. Toolbox 21 Optional: Astro. Toolbox 22, 23 Next Homework Due. Feb. 20 Office Hours: Monday, 34 Did you see the Lunar Eclipse?
More informationChapter 3 Lecture. The Cosmic Perspective Seventh Edition. The Science of Astronomy Pearson Education, Inc.
Chapter 3 Lecture The Cosmic Perspective Seventh Edition The Science of Astronomy 2014 Pearson Education, Inc. The Science of Astronomy 2014 Pearson Education, Inc. 3.1 The Ancient Roots of Science Our
More informationPhysics Lab #6:! Mercury!
Physics 10293 Lab #6: Mercury Introduction Today we will explore the motions in the sky of the innermost planet in our solar system: Mercury. Both Mercury and Venus were easily visible to the naked eye
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 informationAstronomy 101 Lab: Stellarium Tutorial
Name: Astronomy 101 Lab: Stellarium Tutorial Please install the Stellarium software on your computer using the instructions in the procedure. If you own a laptop, please bring it to class. You will submit
More informationEdmonds Community College ASTRONOMY 100 Sample Test #2 Fall Quarter 2006
Edmonds Community College ASTRONOMY 100 Sample Test #2 Fall Quarter 2006 Instructor: L. M. Khandro 10/19/06 Please Note: the following test derives from a course and text that covers the entire topic of
More informationAy 1 Lecture 2. Starting the Exploration
Ay 1 Lecture 2 Starting the Exploration 2.1 Distances and Scales Some Commonly Used Units Distance: Astronomical unit: the distance from the Earth to the Sun, 1 au = 1.496 10 13 cm ~ 1.5 10 13 cm Light
More informationTest Bank for Life in the Universe, Third Edition Chapter 2: The Science of Life in the Universe
1. The possibility of extraterrestrial life was first considered A) after the invention of the telescope B) only during the past few decades C) many thousands of years ago during ancient times D) at the
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 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 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 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 informationTest 1 Review Chapter 1 Our place in the universe
Test 1 Review Bring Gator 1 ID card Bring pencil #2 with eraser No use of calculator or any electronic device during the exam We provide the scantrons Formulas will be projected on the screen You can use
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 informationWhat was once so mysterious about planetary motion in our sky? We see apparent retrograde motion when we pass by a planet
What was once so mysterious about planetary motion in our sky? Planets usually move slightly eastward from night to night relative to the stars. You cannot see this motion on a single night. But sometimes
More information9 Reflectance Spectroscopy
Name: Date: 9 Reflectance Spectroscopy 9.1 Introduction With this lab, we will look at the wavelength dependence of the visible reflectance of various objects, and learn what this can tell us about the
More information3) During retrograde motion a planet appears to be A) dimmer than usual. B) the same brightness as usual C) brighter than usual.
Descriptive Astronomy (ASTR 108) Exam 1 B February 17, 2010 Name: In each of the following multiple choice questions, select the best possible answer. In the line on the scan sheet corresponding to the
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 informationSkyGlobe Planetarium
SkyGlobe Planetarium Introduction: This exercise will simulate the night sky and demonstrate a number of principles of the celestial sphere and the motions of the Earth and planets. Getting Started: 1.
More informationSearching for ExtraSolar Planets
Searching for ExtraSolar Planets Until 1996, astronomers only knew about planets orbiting our sun. Though other planetary systems were suspected to exist, none had been found. Now, thirteen years later,
More informationTOPIC 2.1: EXPLORATION OF SPACE
TOPIC 2.1: EXPLORATION OF SPACE S4P21 S4P22 S4P23 S4P24 S4P25 Identify and analyze issues pertaining to space exploration. Examples: scale of the universe, technological advancement, promotion
More informationLinear Motion with Constant Acceleration
Linear Motion 1 Linear Motion with Constant Acceleration Overview: First you will attempt to walk backward with a constant acceleration, monitoring your motion with the ultrasonic motion detector. Then
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 informationProjectile Motion. Conceptual Physics 11 th Edition. Projectile Motion. Projectile Motion. Projectile Motion. This lecture will help you understand:
Conceptual Physics 11 th Edition Projectile motion is a combination of a horizontal component, and Chapter 10: PROJECTILE AND SATELLITE MOTION a vertical component. This lecture will help you understand:
More informationAstronomy, PART 2. Vocabulary. A. Universe  Our Milky Way Galaxy is one of of galaxies in an expanding universe.
Astronomy, PART 2 Vocabulary Aphelion Asteroid Astronomical Unit Comet Constellation Crater Eccentricity Eclipse Equinox Geocentric model Gravitation Heliocentric model Inertia Jovian Perihelion Revolution
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 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 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 information