DOCSLIB.ORG

Algebra Based Physics Gravitational Force

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Algebra Based Physics Gravitational Force Slide 1 / 57 Slide 2 / 57 Algebra Based Physics Newton's Law of Universal Gravitation 2015-11-30 www.njctl.org Slide 3 / 57 Slide 4 / 57 Newton's Law of Universal Gravitation Click on the topic to go to that section · Gravitational Force · Gravitational Field · Surface Gravity · Gravitational Field in Space Gravitational Force · Orbital Motion · Kepler's Third Law of Motion Return to Table of https://www.njctl.org/video/?v=IP_u0xQvP04 Contents Slide 5 / 57 Slide 6 / 57 Newton’s Law of Universal Gravitation Newton’s Law of Universal Gravitation Newton connected the idea that objects, like apples, fall towards the center of Earth with the idea that the moon It has been well orbits around Earth...it's known since ancient also falling towards the times that Earth is a center of Earth. sphere and objects that are near the The moon just stays in surface tend fall circular motion since it has down. a velocity perpendicular to its acceleration. https://www.njctl.org/video/?v=uhS8K4gFu4s Slide 7 / 57 Slide 8 / 57 Newton’s Law of Universal Gravitation Gravitational Constant Newton concluded that all objects attract one another with a G = 6.67 x 10-11 N-m2 /kg2 "gravitational force". The magnitude of the gravitational force decreases as the centers of the masses increases in distance. In 1798, Henry Cavendish MORE Gravitational attraction measured G using a torsion beam M1 M2 balance. He did not initially set out to measure G, he was instead trying r to measure the density of the Earth. M1 LESS Gravitational attraction M2 r https://www.njctl.org/video/?v=2PdiUoKa9Nw Slide 9 / 57 Slide 10 / 57 Newton’s Law of Universal Gravitation Newton’s Law of Universal Gravitation Mathematically, the magnitude of the gravitational force decreases with the inverse of the square of the distance The direction of the force is along the line connecting the between the centers of the masses and in proportion to the centers of the two masses. Each mass feels a force of product of the masses. attraction towards the other mass...along that line. r Slide 11 / 57 Slide 12 / 57 Newton’s Law of Universal Gravitation 1 What is the magnitude of the gravitational force between two 1 kg objects which are located 1.0 m apart? Newton's third law tells us that the force on each mass is A 3.3 x 10-11 N equal. B 1.7 x 10-11 N That means that if I drop a pen, the force of Earth pulling the C 2.7 x 10-10 N pen down is equal to the force of the pen pulling Earth up. D 6.7 x 10-11 N However, since the mass of Earth is so much larger, that force causes the pen to accelerate down, while the movement of Earth up is completely unmeasurable. https://www.njctl.org/video/?v=IP_u0xQvP04 Slide 12 (Answer) / 57 Slide 13 / 57 1 What is the magnitude of the gravitational 2 What is the magnitude of the gravitational force between two 1 kg objects which are force acting on a 4.0 kg object which is 1.0 m located 1.0 m apart? from a 1.0 kg object? -11 A 3.3 x 10-11 N A 3.3 x 10 N B 1.7 x 10-11 N B 1.7 x 10-11 N C 2.7 x 10-10 N C 2.7 x 10-10 N D 6.7 x 10-11 N D 6.7 x 10-11 N Answer D [This object is a pull tab] https://www.njctl.org/video/?v=IP_u0xQvP04 https://www.njctl.org/video/?v=dPFsPm5UYhg Slide 13 (Answer) / 57 Slide 14 / 57 2 What is the magnitude of the gravitational 3 What is the magnitude of the gravitational force acting on a 4.0 kg object which is 1.0 m force acting on a 1.0 kg object which is 1.0 m from a 1.0 kg object? from a 4.0 kg object? A 3.3 x 10-11 N A 3.3 x 10-11 N B 1.7 x 10-11 N B 1.7 x 10-11 N -10 C 2.7 x 10-10 N C 2.7 x 10 N D 6.7 x 10-11 N D 6.7 x 10-11 N Answer C [This object is a pull tab] https://www.njctl.org/video/?v=iOovJt1I8lc https://www.njctl.org/video/?v=dPFsPm5UYhg Slide 14 (Answer) / 57 Slide 15 / 57 3 What is the magnitude of the gravitational 4 What is the magnitude of the gravitational force acting on a 1.0 kg object which is 1.0 m force acting on a 1.0 kg object which is 2.0 m from a 4.0 kg object? from a 4.0 kg object? A 3.3 x 10-11 N A 3.3 x 10-11 N B 1.7 x 10-11 N B 1.7 x 10-11 N C 2.7 x 10-10 N C 2.7 x 10-10 N D 6.7 x 10-11 N D 6.7 x 10-11 N Answer C [This object is a pull tab] https://www.njctl.org/video/?v=tjkf5sqwLT0 https://www.njctl.org/video/?v=iOovJt1I8lc Slide 15 (Answer) / 57 Slide 16 / 57 4 What is the magnitude of the gravitational 5 What is the magnitude of the gravitational force force acting on a 1.0 kg object which is 2.0 m between Earth and its moon? from a 4.0 kg object? r = 3.8 x 108m 24 mEarth = 6.0 x 10 kg -11 22 A 3.3 x 10 N mmoon = 7.3 x 10 kg B 1.7 x 10-11 N A 2.0 x 10 18 N C 2.7 x 10-10 N 19 D 6.7 x 10-11 N B 2.0 x 10 N C 2.0 x 1020 N Answer D D 2.0 x 1021 N [This object is a pull tab] https://www.njctl.org/video/?v=tjkf5sqwLT0 https://www.njctl.org/video/?v=4MieN1BT4Yc Slide 16 (Answer) / 57 Slide 17 / 57 5 What is the magnitude of the gravitational force 6 What is the magnitude of the gravitational between Earth and its moon? force between Earth and its sun? 11 r = 3.8 x 108m r = 1.5 x 10 m 24 24 mEarth = 6.0 x 10 kg mEarth = 6.0 x 10 kg 30 22 msun = 2.0 x 10 kg mmoon = 7.3 x 10 kg -18 A 2.0 x 10 18 N A 3.6 x 10 N B 3.6 x 1019 N B 2.0 x 1019 N C 3.6 x 1021 N 20 Answer C C 2.0 x 10 N D 3.6 x 1022 N D 2.0 x 1021 N [This object is a pull tab] https://www.njctl.org/video/?v=mAC5GoXjJGE https://www.njctl.org/video/?v=4MieN1BT4Yc Slide 17 (Answer) / 57 Slide 18 / 57 6 What is the magnitude of the gravitational force between Earth and its sun? r = 1.5 x 1011 m 24 mEarth = 6.0 x 10 kg 30 msun = 2.0 x 10 kg A 3.6 x 10-18 N B 3.6 x 1019 N C 3.6 x 1021 N * 22 D 3.6 x 10 N Answer D Gravitational Field [This object is a pull tab] Return to Table of https://www.njctl.org/video/?v=mAC5GoXjJGE https://www.njctl.org/video/?v=p_OteaRhSsk Contents Slide 19 / 57 Slide 20 / 57 *Gravitational Field *Gravitational Field While the force between two objects can always be computed The magnitude of the gravitational field created by an object varies from location to location in space; it depends on the distance from by using the formula for FG ; it's sometimes convenient to consider one mass as creating a gravitational field and the the object and the object's mass. other mass responding to that field. Gravitational field, g, is a vector. It's direction is always towards the object creating the field. That's the direction of the force that a test mass would experience if placed at that location. In fact, g is the acceleration that a mass would experience if placed at that location in space. Slide 21 / 57 Slide 21 (Answer) / 57 *Gravitational Field *Gravitational Field 7 Where is the gravitational field the strongest? 7 Where is the gravitational field the strongest? E E B B D D A A A Answer C C [This object is a pull tab] Slide 22 / 57 Slide 22 (Answer) / 57 8* What happens to the gravitational field if the 8* What happens to the gravitational field if the distance from the center of an object doubles? distance from the center of an object doubles? A It doubles A It doubles B It quadruples B It quadruples C It is cut to one half C It is cut to one half Answer D D It is cut to one fourth D It is cut to one fourth [This object is a pull tab] Slide 23 / 57 Slide 23 (Answer) / 57 9* What happens to the gravitational field if the 9* What happens to the gravitational field if the mass of an object doubles? mass of an object doubles? A It doubles A It doubles B It quadruples B It quadruples C It is cut to one half C It is cut to one half D It is cut to one fourth D It is cut to one fourth Answer A [This object is a pull tab] https://www.njctl.org/video/?v=E1KR_75YClA https://www.njctl.org/video/?v=E1KR_75YClA Slide 24 / 57 Slide 25 / 57 * Surface Gravity Planets, stars, moons, all have a gravitational field...since they all have mass.
Load more

Recommended publications
  • Introduction to Astronomy from Darkness to Blazing Glory
    Introduction to Astronomy From Darkness to Blazing Glory Published by JAS Educational Publications Copyright Pending 2010 JAS Educational Publications All rights reserved. Including the right of reproduction in whole or in part in any form. Second Edition Author: Jeffrey Wright Scott Photographs and Diagrams: Credit NASA, Jet Propulsion Laboratory, USGS, NOAA, Aames Research Center JAS Educational Publications 2601 Oakdale Road, H2 P.O. Box 197 Modesto California 95355 1-888-586-6252 Website: http://.Introastro.com Printing by Minuteman Press, Berkley, California ISBN 978-0-9827200-0-4 1 Introduction to Astronomy From Darkness to Blazing Glory The moon Titan is in the forefront with the moon Tethys behind it. These are two of many of Saturn’s moons Credit: Cassini Imaging Team, ISS, JPL, ESA, NASA 2 Introduction to Astronomy Contents in Brief Chapter 1: Astronomy Basics: Pages 1 – 6 Workbook Pages 1 - 2 Chapter 2: Time: Pages 7 - 10 Workbook Pages 3 - 4 Chapter 3: Solar System Overview: Pages 11 - 14 Workbook Pages 5 - 8 Chapter 4: Our Sun: Pages 15 - 20 Workbook Pages 9 - 16 Chapter 5: The Terrestrial Planets: Page 21 - 39 Workbook Pages 17 - 36 Mercury: Pages 22 - 23 Venus: Pages 24 - 25 Earth: Pages 25 - 34 Mars: Pages 34 - 39 Chapter 6: Outer, Dwarf and Exoplanets Pages: 41-54 Workbook Pages 37 - 48 Jupiter: Pages 41 - 42 Saturn: Pages 42 - 44 Uranus: Pages 44 - 45 Neptune: Pages 45 - 46 Dwarf Planets, Plutoids and Exoplanets: Pages 47 -54 3 Chapter 7: The Moons: Pages: 55 - 66 Workbook Pages 49 - 56 Chapter 8: Rocks and Ice:
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 1. Two Objects Attract Each Other Gravitationally. If the Distance Between Their Centers Is Cut in Half, the Gravitational Force A) Is Cut to One Fourth
    MULTIPLE CHOICE REVIEW – GRAVITATION (Dynamics Part 3) 1. Two objects attract each other gravitationally. If the distance between their centers is cut in half, the gravitational force A) is cut to one fourth. B) is cut in half. C) doubles. D) quadruples 2. Two objects, with masses m1 and m2, are originally a distance r apart. The magnitude of the gravitational force between them is F. The masses are changed to 2m1 and 2m2, and the distance is changed to 4r. What is the magnitude of the new gravitational force? A) F/16 B) F/4 C) 16F D) 4F 3. As a rocket moves away from the Earth's surface, the rocket's weight A) increases. B) decreases. C) remains the same. D) depends on how fast it is moving. 4. A hypothetical planet has a mass of half that of the Earth and a radius of twice that of the Earth. What is the acceleration due to gravity on the planet in terms of g, the acceleration due to gravity at the Earth? A) g B) g/2 C) g/4 D) g/8 5. Two planets have the same surface gravity, but planet B has twice the mass of planet A. If planet A has radius r, what is the radius of planet B? A) 0.707r B) r C) 1.41r D) 4r 6. A planet is discovered to orbit around a star in the galaxy Andromeda, with the same orbital diameter as the Earth around our Sun. If that star has 4 times the mass of our Sun, what will the period of revolution of that new planet be, compared to the Earth's orbital period? A) one-fourth as much B) one-half as much C) twice as much D) four times as much 7.
    [Show full text]
  • Tidal Tomography to Probe the Moon's Mantle Structure Using
    Tidal Tomography to Probe the Moon’s Mantle Structure Using Lunar Surface Gravimetry Kieran A. Carroll1, Harriet Lau2, 1: Gedex Systems Inc., [email protected] 2: Department of Earth and Planetary Sciences, Harvard University, [email protected] Lunar Tides Gravimetry of the Lunar Interior VEGA Instrument through the Moon's PulSE • Gedex has developed a low cost compact space gravimeter instrument , VEGA (Vector (GLIMPSE) Investigation Gravimeter/Accelerometer) Moon • Currently this is the only available gravimeter that is suitable for use in space Earth GLIMPSE Investigation: • Proposed under NASA’s Lunar Surface Instrument and Technology Payloads • ca. 1972 MIT developed a space gravimeter (LSITP) program. instrument for use on the Moon, for Apollo 17. That instrument is long-ago out of • To fly a VEGA instrument to the Moon on a commercial lunar lander, via NASA’s production and obsolete. Commercial Lunar Payload Services (CLPS) program. VEGA under test in thermal- GLIMPSE Objectives: VEGA Space Gravimeter Information vacuum chamber at Gedex • Prove the principle of measuring time-varying lunar surface gravity to probe the lunar • Measures absolute gravity vector, with no • Just as the Moon and the Sun exert tidal forces on the Earth, the Earth exerts tidal deep interior using the Tidal Tomography technique. bias forces on the Moon. • Determine constraints on parameters defining the Lunar mantle structure using time- • Accuracy on the Moon: • Tidal stresses in the Moon are proportional to the gravity gradient tensor field at the varying gravity measurements at a location on the surface of the Moon, over the • Magnitude: Effective noise of 8 micro- Moon’s centre, multiplies by the distance from the Moon’s centre.
    [Show full text]
  • 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.
    [Show full text]
  • 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.
    [Show full text]
  • 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 .
    [Show full text]
  • 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.
    [Show full text]
  • 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
    [Show full text]
  • 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
    [Show full text]
  • Chapter 3 Projects Test Monday Gravity
    Chapter 3 Celestial Sphere Movie Gravity and Motion Projects Test Monday Preview • I moved due-date for Part 1 to 10/21 Ch 1 Ch 2 • I added a descriptive webpage about the Galileo Movie projects. Essay 1: Backyard Astronomy Ch. 3 (just beginning) Northern Hemisphere sky: Big Dipper Little Dipper Cassiopeia Orion Polaris Gravity The Problem of Astronomical Motion • Gravity gives the Universe its structure • Astronomers of antiquity did – It is a universal force that not connect gravity and causes all objects to pull on astronomical motion all other objects • Galileo investigated this everywhere connection with experiments – It holds objects together using projectiles and balls – It is responsible for holding rolling down planks the Earth in its orbit around • He put science on a course to the Sun, the Sun in its orbit determine laws of motion and around the Milky Way, and to develop the scientific the Milky Way in its path method within the Local Group Inertia and Newton’s First Law Inertia • This concept was • Galileo established the idea of inertia incorporated in – A body at rest tends to remain at rest Newton’s First Law – A body in motion tends to remain in motion of Motion: – Through experiments with inclined planes, Galileo demonstrated the idea of inertia and the A body continues in a importance of forces (friction) state of rest or uniform motion in a straight line unless made to change that state by forces acting on it Newton’s First Law Astronomical Motion • As seen earlier, planets • Must there be a force at move along curved work? • Important ideas of (elliptical) paths, or Newton’s First Law – The law implies that if • Yes! an object is not moving orbits.
    [Show full text]