SS 3 MATHS NOTE WEEK 1
|
|
- John White
- 7 years ago
- Views:
Transcription
1 SS 3 MATHS NOTE WEEK 1 Longitude and Latitude Lines of latitude run East & West or horizontal but measure distance North & South of the Equator vertically. The equator is labeled as zero degrees latitude. The greatest amount of latitude is 90 degrees at the North or South poles. We can label our equator as 0 degree. Latitude are parallel to the equator and are even referred to as parallels or parallels of latitude. Moving to lines of longitude, they run perpendicular to lines of latitude. That is, longitude lines run North and South but measure East and West of zero degrees longitude which is a line called the Prime Meridian. This arbitrary north/south line was marked by the British in the 17th century and runs through a town just outside of London called Greenwich. Starting at the Prime Meridian, we measure the earth east or west with these north/south-running lines called meridians. We can measure halfway around the world till these meridians meet at 180 degrees. This meridian line at east or west is called the International Date Line. So unlike latitude, 180 at either the north or south where the greatest or maximum latitude is 90 halfway around the world from poles, the greatest amount of longitude is 180 the prime meridian. One other important way these longitude lines differ from parallel latitude lines is that lines of longitude are not parallel, and in fact converge at both the North and South poles. CLASS ACTIVITY: Teacher Write on a board or a sheet of chart paper the terms latitude and longitude. Let students share what they know about the terms. Write down information that students share. Correct any misconceptions they might share.
2 Explain that the lines of latitude and longitude (see sidebar for tricks to help students remember the difference) comprise an imaginary grid that has been placed over the globe. The lines that run across the grid -- the flat lines -- are lines of latitude. The Equator is an example of a line of latitude. The Equator is the latitude line that divides Earth into two hemispheres, the northern hemisphere and the southern hemisphere. The Equator is the 0 point of latitude. Latitude lines North of the Equator are referred to as North latitude; latitude lines South of the Equator are referred to as South latitude. The lines that run up and down on the grid -- the tall lines -- are lines of longitude. The lines of longitude are also called meridians. The Prime Meridian, which passes through Greenwich, England, is the longitude line that divides Earth into two hemispheres, the eastern hemisphere and the western hemisphere. The Prime Meridian is the 0 point of longitude. Longitude lines East of the Prime Meridian are referred to as East longitude; longitude lines West of the Prime Meridian are referred to as West longitude.
3 MEANING OF LATITUDE & LONGITUDE Latitude and longitude are measuring lines used for locating places on the surface of the Earth. They are angular measurements, expressed as degrees of a circle. A full circle contains 360. Each degree can be divided into 60 minutes, and each minute is divided into 60 seconds. The symbol for minutes is ( ) and for seconds is ("). Latitude lines (called parallels) circle the planet's surface in lines parallel to the equator, which lies halfway between the North and South poles. Latitude lines circle the planet from east and west, beginning at 0 at the equator and increasing to 90 North or 90 South. Longitude lines (called meridians) run north and south and circle the planet from pole to pole. Each line is identified by the number of degrees east or west from a starting point at Greenwich, England, known as the prime meridian. The longitude at the prime meridian is 0. Longitudes lines mark the distance westward, to 180 West, and eastward, to 180 East. Latitude and longitude measurements can be written in several ways. For example, 211 degrees, 22 minutes, and 30 seconds is written as ", or with spaces: ; or with a decimal after the degrees ", or with a decimal after the minutes One degree of latitude equals about 69 miles. One minute is just over a mile, and one second is about 100 feet. POINTS TO NOTE: 1.1. Rotation of the Earth The spinning of the earth on its imaginary axis is called rotation. Aside from the cultural influences of rotation, this spinning also has a physical influence. The spinning has led to the creation of a system to determine points and directions on the sphere.
4 The North and South poles represent the axis of spin and are fixed reference points. If the North Pole was extended, it would point to a fixed star, the North Star (Polaris). Any point on the earth's surface moves with the rotation and traces an imaginary curved line: Parallel of Latitude 1.2. The Equator If a plane bisected the earth midway between the axis of rotation and perpendicular to it, the intersection with the surface would form a circle. This unique circle is the equator. The equator is a fundamental reference line for measuring the position of points around the globe. The equator and the poles are the most important parts of the earth's coordinate system Parallels of Latitude Parallels of latitude are all small circles, except for the equator. True east-west lines Always parallel Any two are always equal distances apart An infinite number can be created Parallels are related to the horizontal x-axes of the cartesian coordinate system. Figure 4. Parallels of Latitude Meridians of Longitude Meridians of longitude are halves of great circles, connecting one pole to the other. All run in a true north-south direction Spaced farthest apart at the equator and converge to a point at the poles An infinite number can be created on a globe Meridians are similar to the vertical y-axes of the cartesian coordinate system Degrees, Minutes, and Seconds Angular measurement must be used in addition to simple plane geometry to specify location on the earth's surface.
5 This is based on a sexagesimal scale: A circle has 360 degrees, 60 minutes per degree, and 60 seconds per minute. There are 3,600 seconds per degree. Example: 45 33' 22" (45 degrees, 33 minutes, 22 seconds). It is often necessary to convert this conventional angular measurement into decimal degrees. To convert 45 33' 22", first multiply 33 minutes by 60, which equals 1,980 seconds. Next add 22 seconds to 1,980: 2,002 total seconds. Now compute the ratio: 2,002/3,600 = Adding this to 45 degrees, the answer is The earth rotates on its axis once every 24 hours, therefore: Any point moves through 360 a day, or 15 per hour Great and Small Circles A great circle is a circle formed by passing a plane though the exact center of a sphere. The largest circle that can be drawn on a sphere's surface. An infinite number of great circles can be drawn on a sphere. Great circles are used in the calculation of distance between two points on a sphere. A small circle is produced by passing a plane through any part of the sphere other than the center. 1.4 Latitude Authalic Latitude is based on a spherical earth: Measures the position of a point on the earth's surface in terms of the angular distance between the equator and the poles. Indicates how far north or south of the equator a particular point is situated. North latitude: all points north of the equator in the northern hemisphere South latitude: all points south of the equator in the southern hemisphere Latitude is measured in angular degrees from 0 at the equator to 90 at either of the poles. A point in the northern hemisphere 40 degrees north of the equator is labeled Lat. 40 N. Forty degrees south of the equator, the label changes to Lat. 40 S.
6 The north or south measurement of latitude is actually measured along the meridian which passes through that location It is known as an arc of the meridian Longitude Longitude measures the position of a point on the earth's surface east or west from a specific meridian, the prime meridian. The longitude of a place is the arc, measured in degrees along a parallel of latitude from the prime meridian. The most widely accepted prime meridian is based on the Bureau International de l'heure (BIH) Zero Meridian: Defined by the longitudes of many BIH stations around the world.. Passes through the old Royal Observatory in Greenwich, England. The prime meridian has the angular designation of 0 longitude. All other points are measured with respect to their position east or west of this meridian. Longitude ranges from 0 to 180, either east or west. Since the placement of a prime meridian is arbitrary, other countries have often used their own. For the purposes of measurement, no one prime meridian is better than another Having a widely accepted meridian allows comparison between maps published in different areas. The distance represented by a degree of longitude varies upon where it is measured. The length of a degree of longitude along a meridian is not constant because of polar flattening. At the equator, the approximate length is determined by dividing the earth's circumference (24,900 miles) by 360 degrees: kilometers (69 miles). The meridians converge at the poles, and the distance represented by one degree decreases. At 60 N latitude, one degree of longitude is equal to about kilometers (34.5 miles).
7 WEEK 2 DISTANCE ALONG PARALLELS OF LATITUDE: (radius of parallel of latitude) N C r P R O R E S Let r be the radius of the parallel of latitude through P, then In Δ PCO, CPO=θ OP =R Cos θ= r=rcosθ Example Find the distance, measured along the parallel of la tude, between two points whose la tude are both 56 N and whose la tudes are respec vely 23 E and 17 W. Solution ACB= = 40 C r B A Arc AB= θ ₓ 2πr 360 NB: Since r is radius of parallel of latitude, then r=rcosθ and 2πR= θ= 40 π= 22 7 Arc AB= θ ₓ 2πr 360
8 = 40 ₓ 2πR Cosθ 360 = 40 ₓ Cos = km = 2490km (3 s.f) Example 2 An aeroplane leaves a point P(21 N, 32 E) and flies due south at 850 km/h. Find its position Q after 4 hrs. (Assume that the earth is a sphere of radius 6400km). Solution P 6400km O θ Q Let POQ=θ Θ=21 + x PQ=850 ₓ 4 = 3400km Arc= PQ= θ ₓ 2πr = 40 ₓ 2 ₓ 22 ₓ = 7040θ 63 Θ= = 30 (2 s.f) The posi on of Q = x = = 9 S NB: Pls do yourself good by carrying out the activities in the project work and also attempt solving the questions given to you.
Coordinate Systems. Orbits and Rotation
Coordinate Systems Orbits and Rotation Earth orbit. The earth s orbit around the sun is nearly circular but not quite. It s actually an ellipse whose average distance from the sun is one AU (150 million
More informationSolar Angles and Latitude
Solar Angles and Latitude Objectives The student will understand that the sun is not directly overhead at noon in most latitudes. The student will research and discover the latitude ir classroom and calculate
More informationThe Globe Latitudes and Longitudes
INDIAN SCHOOL MUSCAT MIDDLE SECTION DEPARTMENT OF SOCIAL SCIENCE The Globe Latitudes and Longitudes NAME: CLASS VI SEC: ROLL NO: DATE:.04.2015 I NAME THE FOLLOWING: 1. A small spherical model of the Earth:
More informationThe Earth Really is Flat! The Globe and Coordinate Systems. Long History of Mapping. The Earth is Flat. Long History of Mapping
The Earth Really is Flat! The Globe and Coordinate Systems Intro to Mapping & GIS The Earth is Flat Day to day, we live life in a flat world sun rises in east, sets in west sky is above, ground is below
More informationLines on Maps and Globes. Cross Curricular Writing Activity Social Studies Grade 4
Lines on Maps and Globes Cross Curricular Writing Activity Social Studies Grade 4 Fourth Grade Social Studies Standard Map: Chart/Globe The learner will be able to use maps, charts, graphs, and globes
More information4 The Rhumb Line and the Great Circle in Navigation
4 The Rhumb Line and the Great Circle in Navigation 4.1 Details on Great Circles In fig. GN 4.1 two Great Circle/Rhumb Line cases are shown, one in each hemisphere. In each case the shorter distance between
More informationPre and post-visit activities - Navigating by the stars
Pre and post-visit activities - Navigating by the stars Vocabulary List Adult Education at Scienceworks Pre-visit Activity 1: What is longitude and latitude? Activity 2: Using the Southern Cross to find
More informationSECOND GRADE 1 WEEK LESSON PLANS AND ACTIVITIES
SECOND GRADE 1 WEEK LESSON PLANS AND ACTIVITIES UNIVERSE CYCLE OVERVIEW OF SECOND GRADE UNIVERSE WEEK 1. PRE: Discovering stars. LAB: Analyzing the geometric pattern of constellations. POST: Exploring
More informationWorld Map Lesson 4 - The Global Grid System - Grade 6+
World Map Lesson 4 - The Global Grid System - Grade 6+ Activity Goal To use the global grid system of latitude and longitude to find specific locations on a world map. Materials Needed: A pencil, a ruler,
More informationLines of Latitude and Longitude
ED 5661 Mathematics & Navigation Teacher Institute Keith Johnson Lesson Plan Lines of Latitude and Longitude Lesson Overview: This lesson plan will introduce students to latitude and longitude along with
More informationBasic Coordinates & Seasons Student Guide
Name: Basic Coordinates & Seasons Student Guide There are three main sections to this module: terrestrial coordinates, celestial equatorial coordinates, and understanding how the ecliptic is related to
More informationOBJECTIVES. Identify the means by which latitude and longitude were created and the science upon which they are based.
Name: Key OBJECTIVES Correctly define: isolines, gradient, topographic map, contour interval, hachured lines, profile, latitude, longitude, hydrosphere, lithosphere, atmosphere, elevation, model EARTH
More informationCelestial Observations
Celestial Observations Earth experiences two basic motions: Rotation West-to-East spinning of Earth on its axis (v rot = 1770 km/hr) (v rot Revolution orbit of Earth around the Sun (v orb = 108,000 km/hr)
More informationAn Introduction to Coordinate Systems in South Africa
An Introduction to Coordinate Systems in South Africa Centuries ago people believed that the earth was flat and notwithstanding that if this had been true it would have produced serious problems for mariners
More informationSun Earth Relationships
1 ESCI-61 Introduction to Photovoltaic Technology Sun Earth Relationships Ridha Hamidi, Ph.D. Spring (sun aims directly at equator) Winter (northern hemisphere tilts away from sun) 23.5 2 Solar radiation
More informationExercise 5.0 LUNAR MOTION, ELONGATION, AND PHASES
Exercise 5.0 LUNAR MOTION, ELONGATION, AND PHASES I. Introduction The Moon's revolution in orbit around the center of gravity (barycenter) of the Earth- Moon System results in an apparent motion of the
More informationAstromechanics. 1 solar day = 1.002737909350795 sidereal days
Astromechanics 13. Time Considerations- Local Sidereal Time The time that is used by most people is that called the mean solar time. It is based on the idea that if the Earth revolved around the Sun at
More informationEarth-Sun Relationships. The Reasons for the Seasons
Earth-Sun Relationships The Reasons for the Seasons Solar Radiation The earth intercepts less than one two-billionth of the energy given off by the sun. However, the radiation is sufficient to provide
More informationNavigation: Latitude and Longitude
Sextants and Chronometers Help Sailors Find Their Position at Sea Latitude lines run horizontally across the globe and are used to measure distances north and south of the equator. Sailors used a sextant
More informationNumber Sense and Operations
Number Sense and Operations representing as they: 6.N.1 6.N.2 6.N.3 6.N.4 6.N.5 6.N.6 6.N.7 6.N.8 6.N.9 6.N.10 6.N.11 6.N.12 6.N.13. 6.N.14 6.N.15 Demonstrate an understanding of positive integer exponents
More informationEarth Coordinates & Grid Coordinate Systems
Earth Coordinates & Grid Coordinate Systems How do we model the earth? Datums Datums mathematically describe the surface of the Earth. Accounts for mean sea level, topography, and gravity models. Projections
More informationNewton s Law of Gravity
Gravitational Potential Energy On Earth, depends on: object s mass (m) strength of gravity (g) distance object could potentially fall Gravitational Potential Energy In space, an object or gas cloud has
More informationThe following words and their definitions should be addressed before completion of the reading:
Seasons Vocabulary: The following words and their definitions should be addressed before completion of the reading: sphere any round object that has a surface that is the same distance from its center
More informationMotion & The Global Positioning System (GPS)
Grade Level: K - 8 Subject: Motion Prep Time: < 10 minutes Duration: 30 minutes Objective: To learn how to analyze GPS data in order to track an object and derive its velocity from positions and times.
More informationStellarium a valuable resource for teaching astronomy in the classroom and beyond
Stellarium 1 Stellarium a valuable resource for teaching astronomy in the classroom and beyond Stephen Hughes Department of Physical and Chemical Sciences, Queensland University of Technology, Gardens
More informationCELESTIAL CLOCK - THE SUN, THE MOON, AND THE STARS
INTRODUCTION CELESTIAL CLOCK - THE SUN, THE MOON, AND THE STARS This is a scientific presentation to provide you with knowledge you can use to understand the sky above in relation to the earth. Before
More informationMeasuring the Earth Using a GPS M. Scott Wilkerson & M. Beth Wilkerson, DePauw University, May 10, 2007
Measuring the Earth Using a GPS M. Scott Wilkerson & M. Beth Wilkerson, DePauw University, May 10, 2007 Modified from: Kerski, J.J., 2007, Measuring the Earth s Circumference with GPS, Copyright ESRI,
More information6. The greatest atmospheric pressure occurs in the 1) troposphere 3) mesosphere 2) stratosphere 4) thermosphere
1. The best evidence of the Earth's nearly spherical shape is obtained through telescopic observations of other planets photographs of the Earth from an orbiting satellite observations of the Sun's altitude
More informationcompass Encyclopedic Entry
This website would like to remind you: Your browser (Apple Safari 7) is out of date. Update your browser for more security, comfort and the best experience on this site. Encyclopedic Entry compass For
More informationTopographic Maps Practice Questions and Answers Revised October 2007
Topographic Maps Practice Questions and Answers Revised October 2007 1. In the illustration shown below what navigational features are represented by A, B, and C? Note that A is a critical city in defining
More informationGeography I Pre Test #1
Geography I Pre Test #1 1. The sun is a star in the galaxy. a) Orion b) Milky Way c) Proxima Centauri d) Alpha Centauri e) Betelgeuse 2. The response to earth's rotation is a) an equatorial bulge b) polar
More informationThe Map Grid of Australia 1994 A Simplified Computational Manual
The Map Grid of Australia 1994 A Simplified Computational Manual The Map Grid of Australia 1994 A Simplified Computational Manual 'What's the good of Mercator's North Poles and Equators, Tropics, Zones
More informationDouglas Adams The Hitchhikers Guide to the Galaxy
There is a theory which states that if ever anybody discovers exactly what the Universe is for and why it is here, it will instantly disappear and be replaced by something even more bizarre and inexplicable.
More informationOrientation to the Sky: Apparent Motions
Chapter 2 Orientation to the Sky: Apparent Motions 2.1 Purpose The main goal of this lab is for you to gain an understanding of how the sky changes during the night and over the course of a year. We will
More informationGeometric Optics Converging Lenses and Mirrors Physics Lab IV
Objective Geometric Optics Converging Lenses and Mirrors Physics Lab IV In this set of lab exercises, the basic properties geometric optics concerning converging lenses and mirrors will be explored. The
More informationTropical Horticulture: Lecture 2
Lecture 2 Theory of the Tropics Earth & Solar Geometry, Celestial Mechanics The geometrical relationship between the earth and sun is responsible for the earth s climates. The two principal movements of
More informationLecture 2. Map Projections and GIS Coordinate Systems. Tomislav Sapic GIS Technologist Faculty of Natural Resources Management Lakehead University
Lecture 2 Map Projections and GIS Coordinate Systems Tomislav Sapic GIS Technologist Faculty of Natural Resources Management Lakehead University Map Projections Map projections are mathematical formulas
More informationWhich month has larger and smaller day time?
ACTIVITY-1 Which month has larger and smaller day time? Problem: Which month has larger and smaller day time? Aim: Finding out which month has larger and smaller duration of day in the Year 2006. Format
More informationSolar 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 informationCelestial Sphere. Celestial Coordinates. Lecture 3: Motions of the Sun and Moon. ecliptic (path of Sun) ecliptic (path of Sun)
Lecture 3: Motions of the and Moon ecliptic (path of ) ecliptic (path of ) The 23.5 degree tilt of Earth s spin axis relative to its orbital axis around the causes the seasons Celestial Sphere Celestial
More informationStage 4. Geography. Blackline Masters. By Karen Devine
1 Devine Educational Consultancy Services Stage 4 Geography Blackline Masters By Karen Devine Updated January 2010 2 This book is intended for the exclusive use in NSW Secondary Schools. It is meant to
More informationEVERY DAY COUNTS CALENDAR MATH 2005 correlated to
EVERY DAY COUNTS CALENDAR MATH 2005 correlated to Illinois Mathematics Assessment Framework Grades 3-5 E D U C A T I O N G R O U P A Houghton Mifflin Company YOUR ILLINOIS GREAT SOURCE REPRESENTATIVES:
More informationActivity 10 - Universal Time
Activity 10 - Universal Time Teacher s Guide Scientists use the Universal Time reference to talk about data that is taken around the globe. Universal Time is the time kept in the time zone centered on
More informationObjectives After completing this section, you should be able to:
Chapter 5 Section 1 Lesson Angle Measure Objectives After completing this section, you should be able to: Use the most common conventions to position and measure angles on the plane. Demonstrate an understanding
More information11.1. Objectives. Component Form of a Vector. Component Form of a Vector. Component Form of a Vector. Vectors and the Geometry of Space
11 Vectors and the Geometry of Space 11.1 Vectors in the Plane Copyright Cengage Learning. All rights reserved. Copyright Cengage Learning. All rights reserved. 2 Objectives! Write the component form of
More informationFull credit for this chapter to Prof. Leonard Bachman of the University of Houston
Chapter 6: SOLAR GEOMETRY Full credit for this chapter to Prof. Leonard Bachman of the University of Houston SOLAR GEOMETRY AS A DETERMINING FACTOR OF HEAT GAIN, SHADING AND THE POTENTIAL OF DAYLIGHT PENETRATION...
More informationCHAPTER 9 SURVEYING TERMS AND ABBREVIATIONS
CHAPTER 9 SURVEYING TERMS AND ABBREVIATIONS Surveying Terms 9-2 Standard Abbreviations 9-6 9-1 A) SURVEYING TERMS Accuracy - The degree of conformity with a standard, or the degree of perfection attained
More informationAPPENDIX D: SOLAR RADIATION
APPENDIX D: SOLAR RADIATION The sun is the source of most energy on the earth and is a primary factor in determining the thermal environment of a locality. It is important for engineers to have a working
More informationUTM Zones for the US UTM UTM. Uniform strips Scalable coordinates
UTM UTM Uniform strips Scalable coordinates Globally consistent, most popular projection/coordinate system for regional to global scale geospatial data (i.e. satellite images global scale datasets USGS/EDC)
More informationShadows, Angles, and the Seasons
Shadows, Angles, and the Seasons If it's cold in winter, why is Earth closer to the Sun? This activity shows the relationship between Earth-Sun positions and the seasons. From The WSU Fairmount Center
More informationSection 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 informationEarth In Space Chapter 3
Earth In Space Chapter 3 Shape of the Earth Ancient Greeks Earth casts a circular shadow on the moon during a lunar eclipse Shape of the Earth Ancient Greeks Ships were observed to disappear below the
More informationGeometry Notes PERIMETER AND AREA
Perimeter and Area Page 1 of 57 PERIMETER AND AREA Objectives: After completing this section, you should be able to do the following: Calculate the area of given geometric figures. Calculate the perimeter
More informationFIRST GRADE 1 WEEK LESSON PLANS AND ACTIVITIES
FIRST GRADE 1 WEEK LESSON PLANS AND ACTIVITIES UNIVERSE CYCLE OVERVIEW OF FIRST GRADE UNIVERSE WEEK 1. PRE: Describing the Universe. LAB: Comparing and contrasting bodies that reflect light. POST: Exploring
More informationUTM: Universal Transverse Mercator Coordinate System
Practical Cartographer s Reference #01 UTM: Universal Transverse Mercator Coordinate System 180 174w 168w 162w 156w 150w 144w 138w 132w 126w 120w 114w 108w 102w 96w 90w 84w 78w 72w 66w 60w 54w 48w 42w
More informationExam 1 Sample Question SOLUTIONS. y = 2x
Exam Sample Question SOLUTIONS. Eliminate the parameter to find a Cartesian equation for the curve: x e t, y e t. SOLUTION: You might look at the coordinates and notice that If you don t see it, we can
More informationIllinois State Standards Alignments Grades Three through Eleven
Illinois State Standards Alignments Grades Three through Eleven Trademark of Renaissance Learning, Inc., and its subsidiaries, registered, common law, or pending registration in the United States and other
More informationUse WITH Investigation 4, Part 2, Step 2
INVESTIGATION 4 : The Sundial Project Use WITH Investigation 4, Part 2, Step 2 EALR 4: Earth and Space Science Big Idea: Earth in Space (ES1) Projects: Tether Ball Pole Sundial Globe and a Light Indoors
More informationCIRCLE COORDINATE GEOMETRY
CIRCLE COORDINATE GEOMETRY (EXAM QUESTIONS) Question 1 (**) A circle has equation x + y = 2x + 8 Determine the radius and the coordinates of the centre of the circle. r = 3, ( 1,0 ) Question 2 (**) A circle
More informationLet s explore the content and skills assessed by Heart of Algebra questions.
Chapter 9 Heart of Algebra Heart of Algebra focuses on the mastery of linear equations, systems of linear equations, and linear functions. The ability to analyze and create linear equations, inequalities,
More informationAngles that are between parallel lines, but on opposite sides of a transversal.
GLOSSARY Appendix A Appendix A: Glossary Acute Angle An angle that measures less than 90. Acute Triangle Alternate Angles A triangle that has three acute angles. Angles that are between parallel lines,
More informationThe Celestial Sphere. Questions for Today. The Celestial Sphere 1/18/10
Lecture 3: Constellations and the Distances to the Stars Astro 2010 Prof. Tom Megeath Questions for Today How do the stars move in the sky? What causes the phases of the moon? What causes the seasons?
More informationPlotting Earthquake Epicenters an activity for seismic discovery
Plotting Earthquake Epicenters an activity for seismic discovery Tammy K Bravo Anne M Ortiz Plotting Activity adapted from: Larry Braile and Sheryl Braile Department of Earth and Atmospheric Sciences Purdue
More informationThe Four Seasons. A Warm Up Exercise. A Warm Up Exercise. A Warm Up Exercise. The Moon s Phases
The Four Seasons A Warm Up Exercise What fraction of the Moon s surface is illuminated by the Sun (except during a lunar eclipse)? a) Between zero and one-half b) The whole surface c) Always half d) Depends
More informationFor further information, and additional background on the American Meteorological Society s Education Program, please contact:
Project ATMOSPHERE This guide is one of a series produced by Project ATMOSPHERE, an initiative of the American Meteorological Society. Project ATMOSPHERE has created and trained a network of resource agents
More informationCabri Geometry Application User Guide
Cabri Geometry Application User Guide Preview of Geometry... 2 Learning the Basics... 3 Managing File Operations... 12 Setting Application Preferences... 14 Selecting and Moving Objects... 17 Deleting
More informationChapter 23. The Reflection of Light: Mirrors
Chapter 23 The Reflection of Light: Mirrors Wave Fronts and Rays Defining wave fronts and rays. Consider a sound wave since it is easier to visualize. Shown is a hemispherical view of a sound wave emitted
More informationLecture 8 : Coordinate Geometry. The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 20
Lecture 8 : Coordinate Geometry The coordinate plane The points on a line can be referenced if we choose an origin and a unit of 0 distance on the axis and give each point an identity on the corresponding
More informationReflection and Refraction
Equipment Reflection and Refraction Acrylic block set, plane-concave-convex universal mirror, cork board, cork board stand, pins, flashlight, protractor, ruler, mirror worksheet, rectangular block worksheet,
More informationFlight and Orbital Mechanics
Flight and Orbital Mechanics Lecture slides Challenge the future 1 Material for exam: this presentation (i.e., no material from text book). Sun-synchronous orbit: used for a variety of earth-observing
More informationEPSG. Coordinate Reference System Definition - Recommended Practice. Guidance Note Number 5
European Petroleum Survey Group EPSG Guidance Note Number 5 Coordinate Reference System Definition - Recommended Practice Revision history: Version Date Amendments 1.0 April 1997 First release. 1.1 June
More informationCalculating Astronomical Unit from Venus Transit
Calculating Astronomical Unit from Venus Transit A) Background 1) Parallaxes of the Sun (the horizontal parallaxes) By definition the parallaxes of the Sun is the angle β shown below: By trigonometry,
More informationChapter 19 Magnetic Forces and Fields
Chapter 19 Magnetic Forces and Fields Student: 3. The magnetism of the Earth acts approximately as if it originates from a huge bar magnet within the Earth. Which of the following statements are true?
More information2. 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 informationHigher Education Math Placement
Higher Education Math Placement Placement Assessment Problem Types 1. Whole Numbers, Fractions, and Decimals 1.1 Operations with Whole Numbers Addition with carry Subtraction with borrowing Multiplication
More informationCycles in the Sky. Teacher Guide: Cycles in the Sky Page 1 of 8 2008 Discovery Communications, LLC
Cycles in the Sky What is a Fun damental? Each Fun damental is designed to introduce your younger students to some of the basic ideas about one particular area of science. The activities in the Fun damental
More informationDrawing an Approximate Representation of an Involute Spur Gear Tooth Project Description
Drawing an Approximate Representation of an Involute Spur Gear Tooth Project Description Create a solid model and a working drawing of the 24 pitch gears specified below. It is only necessary to create
More informationWhat are map projections?
Page 1 of 155 What are map projections? ArcGIS 10 Within ArcGIS, every dataset has a coordinate system, which is used to integrate it with other geographic data layers within a common coordinate framework
More informationGeometry and Measurement
The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for
More informationArea and Arc Length in Polar Coordinates
Area and Arc Length in Polar Coordinates The Cartesian Coordinate System (rectangular coordinates) is not always the most convenient way to describe points, or relations in the plane. There are certainly
More informationGeometry Chapter 1. 1.1 Point (pt) 1.1 Coplanar (1.1) 1.1 Space (1.1) 1.2 Line Segment (seg) 1.2 Measure of a Segment
Geometry Chapter 1 Section Term 1.1 Point (pt) Definition A location. It is drawn as a dot, and named with a capital letter. It has no shape or size. undefined term 1.1 Line A line is made up of points
More informationShape Dictionary YR to Y6
Shape Dictionary YR to Y6 Guidance Notes The terms in this dictionary are taken from the booklet Mathematical Vocabulary produced by the National Numeracy Strategy. Children need to understand and use
More informationMeasuring Your Latitude from the Angle of the Sun at Noon
Measuring Your Latitude from the Angle of the Sun at Noon Background: You can measure your latitude in earth's northern hemisphere by finding out the altitude of the celestial equator from the southern
More informationUnit 5: Coordinate Geometry Practice Test
Unit 5: Coordinate Geometry Practice Test Math 10 Common Name: Block: Please initial this box to indicate you carefully read over your test and checked your work for simple mistakes. What I can do in this
More informationFirst published in 2013 by the University of Utah in association with the Utah State Office of Education.
First published in 201 by the University of Utah in association with the Utah State Office of Education. Copyright 201, Utah State Office of Education. Some rights reserved. This work is published under
More informationSearching Land Records thru the BLM General Land Office Records.
Searching Land Records thru the BLM General Land Office Records. Land Records can be an exciting addition to your family history search. The United States Government transferred ownership of land to millions
More informationLesson 26: Reflection & Mirror Diagrams
Lesson 26: Reflection & Mirror Diagrams The Law of Reflection There is nothing really mysterious about reflection, but some people try to make it more difficult than it really is. All EMR will reflect
More informationUSING MAPS AND GLOBES
USING MAPS AND GLOBES Grade Level or Special Area: 4 th Grade Written by: Krystal Kroeker, Colorado Springs Charter Academy, Colorado Springs, CO Length of Unit: Five lessons (approximately one week (five
More information56 questions (multiple choice, check all that apply, and fill in the blank) The exam is worth 224 points.
6.1.1 Review: Semester Review Study Sheet Geometry Core Sem 2 (S2495808) Semester Exam Preparation Look back at the unit quizzes and diagnostics. Use the unit quizzes and diagnostics to determine which
More informationASTR 1030 Astronomy Lab 65 Celestial Motions CELESTIAL MOTIONS
ASTR 1030 Astronomy Lab 65 Celestial Motions CELESTIAL MOTIONS SYNOPSIS: The objective of this lab is to become familiar with the apparent motions of the Sun, Moon, and stars in the Boulder sky. EQUIPMENT:
More informationME 111: Engineering Drawing
ME 111: Engineering Drawing Lecture 4 08-08-2011 Engineering Curves and Theory of Projection Indian Institute of Technology Guwahati Guwahati 781039 Eccentrici ty = Distance of the point from the focus
More informationQuick Reference ebook
This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed
More informationScope and Sequence KA KB 1A 1B 2A 2B 3A 3B 4A 4B 5A 5B 6A 6B
Scope and Sequence Earlybird Kindergarten, Standards Edition Primary Mathematics, Standards Edition Copyright 2008 [SingaporeMath.com Inc.] The check mark indicates where the topic is first introduced
More informationHow do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.
The verbal answers to all of the following questions should be memorized before completion of pre-algebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics
More informationLatitude, Longitude, and Time Zones
Latitude, Longitude, and Time Zones Typical Graph This is an example of a typical graph. It is made up of points that are connected by a line. Y axis Typical Graph Each point has two values: (4,7) An X
More informationCHAPTER 8 - LAND DESCRIPTIONS
CHAPTER 8 - LAND DESCRIPTIONS Notes: While the location of land is commonly referred to by street number and city, it is necessary to use the legal description in the preparation of those instruments relating
More informationThe Analemma for Latitudinally-Challenged People
The Analemma for Latitudinally-Challenged People Teo Shin Yeow An academic exercise presented in partial fulfillment for the degree of Bachelor of Science with Honours in Mathematics Supervisor : Associate
More informationThe purposes of this experiment are to test Faraday's Law qualitatively and to test Lenz's Law.
260 17-1 I. THEORY EXPERIMENT 17 QUALITATIVE STUDY OF INDUCED EMF Along the extended central axis of a bar magnet, the magnetic field vector B r, on the side nearer the North pole, points away from this
More informationEDMONDS 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