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Geodesy Methods Over Time
Geodesy methods over time GISC3325 - Lecture 4 Astronomic Latitude/Longitude • Given knowledge of the positions of an astronomic body e.g. Sun or Polaris and our time we can determine our location in terms of astronomic latitude and longitude. US Meridian Triangulation This map shows the first project undertaken by the founding Superintendent of the Survey of the Coast Ferdinand Hassler. Triangulation • Method of indirect measurement. • Angles measured at all nodes. • Scaled provided by one or more precisely measured base lines. • First attributed to Gemma Frisius in the 16th century in the Netherlands. Early surveying instruments Left is a Quadrant for angle measurements, below is how baseline lengths were measured. A non-spherical Earth • Willebrod Snell van Royen (Snellius) did the first triangulation project for the purpose of determining the radius of the earth from measurement of a meridian arc. • Snellius was also credited with the law of refraction and incidence in optics. • He also devised the solution of the resection problem. At point P observations are made to known points A, B and C. We solve for P. Jean Picard’s Meridian Arc • Measured meridian arc through Paris between Malvoisine and Amiens using triangulation network. • First to use a telescope with cross hairs as part of the quadrant. • Value obtained used by Newton to verify his law of gravitation. Ellipsoid Earth Model • On an expedition J.D. Cassini discovered that a one-second pendulum regulated at Paris needed to be shortened to regain a one-second oscillation. • Pendulum measurements are effected by gravity! Newton • Newton used measurements of Picard and Halley and the laws of gravitation to postulate a rotational ellipsoid as the equilibrium figure for a homogeneous, fluid, rotating Earth. -
Up, Up, and Away by James J
www.astrosociety.org/uitc No. 34 - Spring 1996 © 1996, Astronomical Society of the Pacific, 390 Ashton Avenue, San Francisco, CA 94112. Up, Up, and Away by James J. Secosky, Bloomfield Central School and George Musser, Astronomical Society of the Pacific Want to take a tour of space? Then just flip around the channels on cable TV. Weather Channel forecasts, CNN newscasts, ESPN sportscasts: They all depend on satellites in Earth orbit. Or call your friends on Mauritius, Madagascar, or Maui: A satellite will relay your voice. Worried about the ozone hole over Antarctica or mass graves in Bosnia? Orbital outposts are keeping watch. The challenge these days is finding something that doesn't involve satellites in one way or other. And satellites are just one perk of the Space Age. Farther afield, robotic space probes have examined all the planets except Pluto, leading to a revolution in the Earth sciences -- from studies of plate tectonics to models of global warming -- now that scientists can compare our world to its planetary siblings. Over 300 people from 26 countries have gone into space, including the 24 astronauts who went on or near the Moon. Who knows how many will go in the next hundred years? In short, space travel has become a part of our lives. But what goes on behind the scenes? It turns out that satellites and spaceships depend on some of the most basic concepts of physics. So space travel isn't just fun to think about; it is a firm grounding in many of the principles that govern our world and our universe. -
Surface Gravity and Interstellar Settlement (Version 3.0 September 2016)
Surface Gravity and Interstellar Settlement (version 3.0 September 2016) by Gerald D. Nordley 1238 Prescott Avenue Sunnyvale, CA 94089-2334 [email protected] Abstract. Gravity determines the scale of many physical Jupiter's inner satellites melts the ice of Europa and drives phenomena on and above a world's surface. Assuming that tool- volcanoes on Io, and that Mars in the past has had rain and using intelligences come from, and would settle, worlds with solid floods serves notice that worlds that are significantly less surfaces and gravities equal or less than that of their origin, we massive than Earth and have significantly less surface gravity note that such worlds in the Solar System have surface gravities can still have the deep atmospheres and liquid water significantly lower than that of Earth. The distribution of these temperatures needed to sustain life. surface gravities clumps around factors of about 2.5 and favors worlds with about one-sixth Earth gravity, conventionally 2. Surface Gravity Basics considered too small to retain atmospheres. Titan, however, Mass is, roughly, a measure of the amount of substance. shows that low surface gravity does not, in itself, preclude the Weight is the force by which that substance is attracted to presence a substantial atmosphere. Where small worlds have another mass. This force is directly proportional to the product of low exobase temperatures,and protection from stellar winds, both masses and inversely proportional to the square of the substantial atmospheres may be retained. distance between them. A spherically symmetric planet can be Significantly lower surface gravity affects a number of physical treated as if all the mass were at the center, so the relevant phenomena that affect environment and technological evolution-- distance is the radius from the center to the object. -
Geodetic Position Computations
GEODETIC POSITION COMPUTATIONS E. J. KRAKIWSKY D. B. THOMSON February 1974 TECHNICALLECTURE NOTES REPORT NO.NO. 21739 PREFACE In order to make our extensive series of lecture notes more readily available, we have scanned the old master copies and produced electronic versions in Portable Document Format. The quality of the images varies depending on the quality of the originals. The images have not been converted to searchable text. GEODETIC POSITION COMPUTATIONS E.J. Krakiwsky D.B. Thomson Department of Geodesy and Geomatics Engineering University of New Brunswick P.O. Box 4400 Fredericton. N .B. Canada E3B5A3 February 197 4 Latest Reprinting December 1995 PREFACE The purpose of these notes is to give the theory and use of some methods of computing the geodetic positions of points on a reference ellipsoid and on the terrain. Justification for the first three sections o{ these lecture notes, which are concerned with the classical problem of "cCDputation of geodetic positions on the surface of an ellipsoid" is not easy to come by. It can onl.y be stated that the attempt has been to produce a self contained package , cont8.i.ning the complete development of same representative methods that exist in the literature. The last section is an introduction to three dimensional computation methods , and is offered as an alternative to the classical approach. Several problems, and their respective solutions, are presented. The approach t~en herein is to perform complete derivations, thus stqing awrq f'rcm the practice of giving a list of for11111lae to use in the solution of' a problem. -
Models for Earth and Maps
Earth Models and Maps James R. Clynch, Naval Postgraduate School, 2002 I. Earth Models Maps are just a model of the world, or a small part of it. This is true if the model is a globe of the entire world, a paper chart of a harbor or a digital database of streets in San Francisco. A model of the earth is needed to convert measurements made on the curved earth to maps or databases. Each model has advantages and disadvantages. Each is usually in error at some level of accuracy. Some of these error are due to the nature of the model, not the measurements used to make the model. Three are three common models of the earth, the spherical (or globe) model, the ellipsoidal model, and the real earth model. The spherical model is the form encountered in elementary discussions. It is quite good for some approximations. The world is approximately a sphere. The sphere is the shape that minimizes the potential energy of the gravitational attraction of all the little mass elements for each other. The direction of gravity is toward the center of the earth. This is how we define down. It is the direction that a string takes when a weight is at one end - that is a plumb bob. A spirit level will define the horizontal which is perpendicular to up-down. The ellipsoidal model is a better representation of the earth because the earth rotates. This generates other forces on the mass elements and distorts the shape. The minimum energy form is now an ellipse rotated about the polar axis. -
World Geodetic System 1984
World Geodetic System 1984 Responsible Organization: National Geospatial-Intelligence Agency Abbreviated Frame Name: WGS 84 Associated TRS: WGS 84 Coverage of Frame: Global Type of Frame: 3-Dimensional Last Version: WGS 84 (G1674) Reference Epoch: 2005.0 Brief Description: WGS 84 is an Earth-centered, Earth-fixed terrestrial reference system and geodetic datum. WGS 84 is based on a consistent set of constants and model parameters that describe the Earth's size, shape, and gravity and geomagnetic fields. WGS 84 is the standard U.S. Department of Defense definition of a global reference system for geospatial information and is the reference system for the Global Positioning System (GPS). It is compatible with the International Terrestrial Reference System (ITRS). Definition of Frame • Origin: Earth’s center of mass being defined for the whole Earth including oceans and atmosphere • Axes: o Z-Axis = The direction of the IERS Reference Pole (IRP). This direction corresponds to the direction of the BIH Conventional Terrestrial Pole (CTP) (epoch 1984.0) with an uncertainty of 0.005″ o X-Axis = Intersection of the IERS Reference Meridian (IRM) and the plane passing through the origin and normal to the Z-axis. The IRM is coincident with the BIH Zero Meridian (epoch 1984.0) with an uncertainty of 0.005″ o Y-Axis = Completes a right-handed, Earth-Centered Earth-Fixed (ECEF) orthogonal coordinate system • Scale: Its scale is that of the local Earth frame, in the meaning of a relativistic theory of gravitation. Aligns with ITRS • Orientation: Given by the Bureau International de l’Heure (BIH) orientation of 1984.0 • Time Evolution: Its time evolution in orientation will create no residual global rotation with regards to the crust Coordinate System: Cartesian Coordinates (X, Y, Z). -
Effect of Gravity on Current & Their Implications on Planets
Crimson Publishers Research Article Wings to the Research Effect of Gravity on Current & Their Implications on Planets Saifullah Khalid* IEEE, India Abstract ISSN: 2640-9739 any variations in the effect of gravity at the atomic level and macroscopic level. The effect of gravity has beenThis paper calculated presents for various the effect planets. of gravity Consequently, on the atomic suggestions level. Various have researchbeen made has for been the considered space equipment to find manufacturers to consider the variation in current density due to gravity for the planets. Keywords: Gravity; Current; Charge; Earth; Planets Introduction Anything that has mass has gravity too. Objects with greater mass have greater gravity. With distance also, gravity gets weaker. Therefore, the smaller the bodies are, the greater their gravitational force is [1-5]. The gravity of Earth originates from all of its mass. All its mass makes the whole mass in the body a combined gravitational pull on. If we are on a planet *1Corresponding author: Saifullah Khalid, Member, IEEE, India with less mass than Earth, we’d be weighing less than here. Gravity is a fundamental force of Nature, one we Earthlings prefer to take for granted. And you can’t blame us. Having evolved Submission: March 24, 2021 in Earth’s climate throughout billions of years, we are used to living with the tug of a steady Published: August 03, 2021 1g (or 9.8m/s2). Yet gravity is a very tenuous and precious thing for those who have gone into space or set foot on the Moon [6]. Isaac Newton and Albert Einstein’s works dominate the Volume 2 - Issue 2 development of the theory of gravity. -
PHYSICAL GEOLOGY (WITH LABORATORY) Syllabus EPS 3300 – PHYSICAL GEOLOGY (4 Crs
Kingsborough Community College The City University of New York Department of Physical Sciences EPS 3300 – PHYSICAL GEOLOGY (WITH LABORATORY) Syllabus EPS 3300 – PHYSICAL GEOLOGY (4 crs. 6 hrs.) Study of the nature of the Earth and its processes includes: mineral and rock classification, analysis of the agents of weathering and erosion, dynamics of the Earth’s crust as manifest in mountain building, volcanoes and earthquakes, recent data concerning the geology of other planets, field and laboratory techniques of the geologist. ----Prerequisites: Passed, exempt, or completed developmental course work for the CUNY Assessment Tests in Reading, Writing, and ACCUPLACER CUNY Assessment Test in Math or Department permission ----Required Core: Life and Physical Sciences----- Flexible Core: Scientific World (Group E) Section: SECTION NUMBER Time: LECTURE AND LABORATORY SCHEDULE FOR SECTION Room: ROOM (S) FOR SECTION Instructor: INSTRUCTOR FOR SECTION Email: EMAIL ADDRESS FOR INSTRUCTOR FOR SECTION Office Hours: OFFICE HOURS FOR INSTRUCTOR FOR SECTION Source materials: An Introduction to Physical Geology10th or 11th or latest edition, by Tarbuck, Lutgens & Tasa Student Learning Outcomes Students will: Differentiate between the three types of plate boundaries by noting common geologic features and processes. Classify common physical properties and differentiate minerals and rocks. Summarize the relationship between the chemical and physical properties of minerals. Analyze igneous, metamorphic, and sedimentary rocks to determine how they formed. Compare how different types of magma form and explain their relationship to the formation of intrusive and volcanic igneous features. Compare and contrast weathering among different rock types and different environments. Identify strata, faults, and folds in geologic sections and summarize the forces and tectonic settings that lead to their formation. -
Summary of Lesson
Energy Skate Park Name High School Student Activity Class Open the TI-Nspire document energy-skate-park.tns. In this simulation, you will observe the changing potential and kinetic energies of a skateboarder-celestial body system as she moves over a track with negligible friction. You will also explore the relationship between the system’s potential and kinetic energy, and how they affect the total energy of the system. Finally, you will explore the impact of friction on these potential and kinetic energies. Read the information on page 1.1. Move to page 1.2. To start the simulation, select and drag the skateboarder up to the top left side of the track. Then, release him. You will see the skateboarder moving up and down along the skateboarding track on Earth. The skater’s motion follows a predictable path: 1. The skater starts from a stationary position. 2. The skater’s direction of motion changes. 3. The downward motion of the skater momentarily becomes horizontal at the bottom of the skating ramp, and then changes direction in an upward direction. 4. The skater nears the top of the skating ramp on the other side, momentarily stops, then changes direction and starts moving again. 5. The downward motion of the skater momentarily becomes horizontal at the bottom of the skating ramp, and then changes direction in an upward direction. 6. The skater reaches the top of the skating ramp where he originally started, momentarily stops, then it resumes a new cycle of movement. Part 1: Exploring Potential Energy 1. Wait until the skateboarder reaches the top part of the ramp and select the Pause button . -
8. Newton's Law Gravitation.Nb
2 8. Newton's Law Gravitation.nb 8. Newton's Law of Gravitation Introduction and Summary There is one other major law due to Newton that will be used in this course and this is his famous Law of Universal Gravitation. It deals with the force between any two massive objects. We will use the Law of Universal Gravitation together with Newton's Laws of Motion to discuss a variety of problems involving the motion of large objects like the Earth moving in orbit about the Sun as well as small objects like the famous apple falling from a tree. Also it will be shown that Newton's 3rd Law of Motion follows as a consequence of Newton's Law of Universal Gravitation. Some additional topics that related to Newton's 1st and 2nd Laws of Motion also will be discussed. In particular, the concept of the Non-Inertia Reference Frame will be introduced and why it is useful. Also it will be shown how Newton's 1st Law and 2nd Law are NOT valid in Non- Inertial Reference Frames. It will be shown what is necessary to "fix-up" Newton's 2nd Law so it works in Non-Inertial Reference Frames. In particular, the examples of accelerated cars and elevators are used to illustrate the concept of the Non-Inertial Frame. The Four Fundamental Forces of Nature: There are four basic or fundamental forces known in nature. These forces are gravity, electromagnetism, the weak nuclear force, and the strong nuclear force. The force of gravity is described by Newton's Law of gravitation and the more recent modification called General Relativity due to Einstein. -
Reduced Gravity: Effects on the Human Body an Educator Guide
Reduced Gravity: Effects on the Human Body An Educator Guide Reduced Gravity: Effects on the Human Body A Digital Learning Network Experience Designed To Share NASA's Space Exploration Program This publication is in the public domain and is not protected by copyright. Permission is not required for duplication. Reduced Gravity: Effects on the Human Body Page 2 of 38 DLN-08-01-2008- JSC Table of Contents Digital Learning Network Expedition....................................................... 4 Expedition Overview ................................................................................. 5 Grade Level Focus Question Instructional Objectives National Standards.................................................................................... 5 Pre-Conference Requirements.................................................................6 Online Pre-Assessment Pre-Conference Requirement Questions Answers to Questions Expedition Videoconference Guidelines.................................................10 Audience Guidelines Teacher Event Checklist Expedition Videoconference Outline.......................................................12 Pre-Classroom Activities..........................................................................11 The Water Mystery Bag of Bones Post Conference........................................................................................19 Online Post Assessment Post-conference Assessment Questions NASA Education Evaluation Information System ..................................20 Certificate of Completion..........................................................................21 -
Geological Survey
BULLETIN UNITED STATES GEOLOGICAL SURVEY 2STo. 48 WASHINGTON GOVERNMENT PRINTING OFFICE 1SSS UNITED STATES GEOLOGICAL SURVEY J. W. POWELL, DIRECTOR ON THE FORM AND POSITION OH' THE SEA LEVEL WITH SPECIAL UEKEIIENCE TO ITS DEPENDENCE OX SUPEKiriCIAL MASSES SYMMETRICALLY DISPOSED ABOUT A NOKMAL TO THE EAKTH'S SUKFACE ROBERT SIMPSON WOODWARD WASHINGTON . - GOVERNMENT PRINTING OFFICE 1888 CONTENTS. Page. Key to mathematical symbols ............................................... 9 Letter of transmittal........................................................ 13 I. Introduction..... .................................................... 15 1. Form and dimensions of sea-level surface of earth. Close approxi mation of oblate spheroid. Eolation of actual sea surface or geoid to spheroidal surface. A knowledge required of form of geoid by geodesy, of variations in form and position by geology. Difficulties in way of improved theory ......................... 15 2. Class of problems discussed in this paper........................... 16 3. R6sum6 of results attained......................................... 17 A. THEORY. II. Mathematical statement of problem ............ ...................... 18 4. Fundamental principle and equation............................... 18 5. Dimensions of earth's ellipsoid and sphere of equal volume.......... 19 6. Derivation of equation of disturbed surface ........................ 19 III. Evaluation of potential of disturbing mass of uniform thickness....... 21 7. Determination of potential iu terms of rectangular and