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Of Universal Gravitation and of the Theory of Relativity
ASTRONOMICAL APPLICATIONS OF THE LAW OF UNIVERSAL GRAVITATION AND OF THE THEORY OF RELATIVITY By HUGH OSCAR PEEBLES Bachelor of Science The University of Texas Austin, Texas 1955 Submitted to the faculty of the Graduate School of the Oklahoma State University in partial fulfillment of the requirements for the degree of MASTER OF SCIENCE August, 1960 ASTRONOMICAL APPLICATIONS OF THE LAW OF UNIVERSAL GRAVITATION AND OF THE THEORY OF RELATIVITY Report Approved: Dean of the Graduate School ii ACKNOWLEDGEMENT I express my deep appreciation to Dr. Leon w. Schroeder, Associate Professor of Physics, for his counsel, his criticisms, and his interest in the preparation of this study. My appre ciation is also extended to Dr. James H. Zant, Professor of Mathematics, for his guidance in the development of my graduate program. iii TABLE OF CONTENTS Chapter Page I. INTRODUCTION. 1 II. THE EARTH-MOON T"EST OF THE LAW OF GRAVITATION 4 III. DERIVATION OF KEPLER'S LAWS OF PLAN.ET.ARY MOTION FROM THE LAW OF UNIVERSAL GRAVITATION. • • • • • • • • • 9 The First Law-Law of Elliptical Paths • • • • • 10 The Second Law-Law of Equal Areas • • • • • • • 15 The Third Law-Harmonic Law • • • • • • • 19 IV. DETERMINATION OF THE MASSES OF ASTRONOMICAL BODIES. 20 V. ELEMENTARY THEORY OF TIDES. • • • • • • • • • • • • 26 VI. ELEMENTARY THEORY OF THE EQUATORIAL BULGE OF PLANETS 33 VII. THE DISCOVERY OF NEW PLANETS. • • • • • • • • • 36 VIII. ASTRONOMICAL TESTS OF THE THEORY OF RELATIVITY. 40 BIBLIOGRAPHY . 45 iv LIST OF FIGURES Figure Page 1. Fall of the Uoon Toward the Earth • • • • • • • • • • 6 2. Newton's Calculation of the Earth's Gravitational Ef- fect on the Moon. -
Constraints on the Habitability of Extrasolar Moons
Formation, Detection, and Characterization of Extrasolar Habitable Planets Proceedings IAU Symposium No. 293, 2012 c International Astronomical Union 2014 N. Haghighipour, ed. doi:10.1017/S1743921313012738 Constraints on the Habitability of Extrasolar Moons Ren´e Heller1 and Rory Barnes2,3 1 Leibniz Institute for Astrophysics Potsdam (AIP), An der Sternwarte 16, 14482 Potsdam email: [email protected] 2 University of Washington, Dept. of Astronomy, Seattle, WA 98195, USA 3 Virtual Planetary Laboratory, NASA, USA email: [email protected] Abstract. Detections of massive extrasolar moons are shown feasible with the Kepler space telescope. Kepler’s findings of about 50 exoplanets in the stellar habitable zone naturally make us wonder about the habitability of their hypothetical moons. Illumination from the planet, eclipses, tidal heating, and tidal locking distinguish remote characterization of exomoons from that of exoplanets. We show how evaluation of an exomoon’s habitability is possible based on the parameters accessible by current and near-future technology. Keywords. celestial mechanics – planets and satellites: general – astrobiology – eclipses 1. Introduction The possible discovery of inhabited exoplanets has motivated considerable efforts towards estimating planetary habitability. Effects of stellar radiation (Kasting et al. 1993; Selsis et al. 2007), planetary spin (Williams & Kasting 1997; Spiegel et al. 2009), tidal evolution (Jackson et al. 2008; Barnes et al. 2009; Heller et al. 2011), and composition (Raymond et al. 2006; Bond et al. 2010) have been studied. Meanwhile, Kepler’s high precision has opened the possibility of detecting extrasolar moons (Kipping et al. 2009; Tusnski & Valio 2011) and the first dedicated searches for moons in the Kepler data are underway (Kipping et al. -
Chapter 5 Water Levels and Flow
253 CHAPTER 5 WATER LEVELS AND FLOW 1. INTRODUCTION The purpose of this chapter is to provide the hydrographer and technical reader the fundamental information required to understand and apply water levels, derived water level products and datums, and water currents to carry out field operations in support of hydrographic surveying and mapping activities. The hydrographer is concerned not only with the elevation of the sea surface, which is affected significantly by tides, but also with the elevation of lake and river surfaces, where tidal phenomena may have little effect. The term ‘tide’ is traditionally accepted and widely used by hydrographers in connection with the instrumentation used to measure the elevation of the water surface, though the term ‘water level’ would be more technically correct. The term ‘current’ similarly is accepted in many areas in connection with tidal currents; however water currents are greatly affected by much more than the tide producing forces. The term ‘flow’ is often used instead of currents. Tidal forces play such a significant role in completing most hydrographic surveys that tide producing forces and fundamental tidal variations are only described in general with appropriate technical references in this chapter. It is important for the hydrographer to understand why tide, water level and water current characteristics vary both over time and spatially so that they are taken fully into account for survey planning and operations which will lead to successful production of accurate surveys and charts. Because procedures and approaches to measuring and applying water levels, tides and currents vary depending upon the country, this chapter covers general principles using documented examples as appropriate for illustration. -
Rare Astronomical Sights and Sounds
Jonathan Powell Rare Astronomical Sights and Sounds The Patrick Moore The Patrick Moore Practical Astronomy Series More information about this series at http://www.springer.com/series/3192 Rare Astronomical Sights and Sounds Jonathan Powell Jonathan Powell Ebbw Vale, United Kingdom ISSN 1431-9756 ISSN 2197-6562 (electronic) The Patrick Moore Practical Astronomy Series ISBN 978-3-319-97700-3 ISBN 978-3-319-97701-0 (eBook) https://doi.org/10.1007/978-3-319-97701-0 Library of Congress Control Number: 2018953700 © Springer Nature Switzerland AG 2018 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors, and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. -
18Th EANA Conference European Astrobiology Network Association
18th EANA Conference European Astrobiology Network Association Abstract book 24-28 September 2018 Freie Universität Berlin, Germany Sponsors: Detectability of biosignatures in martian sedimentary systems A. H. Stevens1, A. McDonald2, and C. S. Cockell1 (1) UK Centre for Astrobiology, University of Edinburgh, UK ([email protected]) (2) Bioimaging Facility, School of Engineering, University of Edinburgh, UK Presentation: Tuesday 12:45-13:00 Session: Traces of life, biosignatures, life detection Abstract: Some of the most promising potential sampling sites for astrobiology are the numerous sedimentary areas on Mars such as those explored by MSL. As sedimentary systems have a high relative likelihood to have been habitable in the past and are known on Earth to preserve biosignatures well, the remains of martian sedimentary systems are an attractive target for exploration, for example by sample return caching rovers [1]. To learn how best to look for evidence of life in these environments, we must carefully understand their context. While recent measurements have raised the upper limit for organic carbon measured in martian sediments [2], our exploration to date shows no evidence for a terrestrial-like biosphere on Mars. We used an analogue of a martian mudstone (Y-Mars[3]) to investigate how best to look for biosignatures in martian sedimentary environments. The mudstone was inoculated with a relevant microbial community and cultured over several months under martian conditions to select for the most Mars-relevant microbes. We sequenced the microbial community over a number of transfers to try and understand what types microbes might be expected to exist in these environments and assess whether they might leave behind any specific biosignatures. -
Pluto and Charon
National Aeronautics and Space Administration 0 300,000,000 900,000,000 1,500,000,000 2,100,000,000 2,700,000,000 3,300,000,000 3,900,000,000 4,500,000,000 5,100,000,000 5,700,000,000 kilometers Pluto and Charon www.nasa.gov Pluto is classified as a dwarf planet and is also a member of a Charon’s orbit around Pluto takes 6.4 Earth days, and one Pluto SIGNIFICANT DATES group of objects that orbit in a disc-like zone beyond the orbit of rotation (a Pluto day) takes 6.4 Earth days. Charon neither rises 1930 — Clyde Tombaugh discovers Pluto. Neptune called the Kuiper Belt. This distant realm is populated nor sets but “hovers” over the same spot on Pluto’s surface, 1977–1999 — Pluto’s lopsided orbit brings it slightly closer to with thousands of miniature icy worlds, which formed early in the and the same side of Charon always faces Pluto — this is called the Sun than Neptune. It will be at least 230 years before Pluto history of the solar system. These icy, rocky bodies are called tidal locking. Compared with most of the planets and moons, the moves inward of Neptune’s orbit for 20 years. Kuiper Belt objects or transneptunian objects. Pluto–Charon system is tipped on its side, like Uranus. Pluto’s 1978 — American astronomers James Christy and Robert Har- rotation is retrograde: it rotates “backwards,” from east to west Pluto’s 248-year-long elliptical orbit can take it as far as 49.3 as- rington discover Pluto’s unusually large moon, Charon. -
Solar System
Lecture 2 Solar system Beibei Liu (刘倍⻉) Introduction to Astrophysics, 2019 What is planet? Definition of planet 1. It orbits the sun (central star) 2. It has sufficient mass to have its self-gravity to overcome rigid bodies force, so that in a hydrostatic equilibrium (near round and stable shape) 3. Its perturbations have cleared away other objects in the neighbourhood of its orbit. asteroid, comet, moon, pluto? Moon-Earth system: Tidal force Tidal locking (tidal synchronisation): spin period of the moon is equal to the orbital period of the Earth-Moon system (~28 days). Moon-Earth system: Tidal force Earth rotation is only 24 hours Earth slowly decreases its rotation, and moon’s orbital distance gradually increases Lunar and solar eclipse Blood moon, sun’s light refracted by earth’s atmosphere. Due to Rayleigh scattering, red color is easy to remain Solar system Terrestrial planets Gas giant planets ice giant planets Heat source of the planet 1. Gravitational contraction: release potential energy 2. Decay of radioactive isotope,such as potassium, uranium 3. Giant impacts, planetesimal accretion Melting and differentiation of planet interior Originally homogeneous material begin to segregate into layers of different chemical composition. Heavy elements sink into the centre. Interior of planets Relative core size Interior of planets Metallic hydrogen: high pressure, H2 dissociate into atoms and become electronic conducting. Magnetic field is generated in this layer. Earth interior layers Crust (rigid): granite and basalt Silicate mantle: flow and convection Fe-Ni core: T~4000-9000K Magnetic field is generated by electric currents due to large convective motion of molten metal in outer core and mantle Earth interior layers Tectonics motion Large scale movement of plates in Earth’s lithosphere. -
Tellurium Tellurium N
Experiment Description/Manual Tellurium Tellurium N Table of contents General remarks ............................................................................................................................3 Important parts of the Tellurium and their operation .....................................................................4 Teaching units for working with the Tellurium: Introduction: From one´s own shadow to the shadow-figure on the globe of the Tellurium ...........6 1. The earth, a gyroscope in space ............................................................................................8 2. Day and night ..................................................................................................................... 10 3. Midday line and division of hours ....................................................................................... 13 4. Polar day and polar night .................................................................................................... 16 5. The Tropic of Cancer and Capricorn and the tropics ........................................................... 17 6. The seasons ........................................................................................................................ 19 7. Lengths of day and night in various latitudes ......................................................................22 Working sheet “Lengths of day in various seasons” ............................................................ 24 8. The times of day .................................................................................................................25 -
Equilibrium Model of Tides Highly Idealized, but Very Instructive, View of Tides
Tides Outline • Equilibrium Theory of Tides — diurnal, semidiurnal and mixed semidiurnal tides — spring and neap tides • Dynamic Theory of Tides — rotary tidal motion — larger tidal ranges in coastal versus open-ocean regions • Special Cases — Forcing ocean water into a narrow embayment — Tidal forcing that is in resonance with the tide wave Equilibrium Model of Tides Highly Idealized, but very instructive, View of Tides • Tide wave treated as a deep-water wave in equilibrium with lunar/solar forcing • No interference of tide wave propagation by continents Tidal Patterns for Various Locations 1 Looking Down on Top of the Earth The Earth’s Rotation Under the Tidal Bulge Produces the Rise moon and Fall of Tides over an Approximately 24h hour period Note: This is describing the ‘hypothetical’ condition of a 100% water planet Tidal Day = 24h + 50min It takes 50 minutes for the earth to rotate 12 degrees of longitude Earth & Moon Orbit Around Sun 2 R b a P Fa = Gravity Force on a small mass m at point a from the gravitational attraction between the small mass and the moon of mass M Fa = Centrifugal Force on a due to rotation about the center of mass of the two mass system using similar arguments The Main Point: Force at and point a and b are equal and opposite. It can be shown that the upward (normal the the earth’s surface) tidal force on a parcel of water produced by the moon’s gravitational attraction is small (1 part in 9 million) compared to the downward gravitation force on that parcel of water caused by earth’s on gravitational attraction. -
Lunar Laser Ranging: the Millimeter Challenge
REVIEW ARTICLE Lunar Laser Ranging: The Millimeter Challenge T. W. Murphy, Jr. Center for Astrophysics and Space Sciences, University of California, San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0424, USA E-mail: [email protected] Abstract. Lunar laser ranging has provided many of the best tests of gravitation since the first Apollo astronauts landed on the Moon. The march to higher precision continues to this day, now entering the millimeter regime, and promising continued improvement in scientific results. This review introduces key aspects of the technique, details the motivations, observables, and results for a variety of science objectives, summarizes the current state of the art, highlights new developments in the field, describes the modeling challenges, and looks to the future of the enterprise. PACS numbers: 95.30.Sf, 04.80.-y, 04.80.Cc, 91.4g.Bg arXiv:1309.6294v1 [gr-qc] 24 Sep 2013 CONTENTS 2 Contents 1 The LLR concept 3 1.1 Current Science Results . 4 1.2 A Quantitative Introduction . 5 1.3 Reflectors and Divergence-Imposed Requirements . 5 1.4 Fundamental Measurement and World Lines . 10 2 Science from LLR 12 2.1 Relativity and Gravity . 12 2.1.1 Equivalence Principle . 13 2.1.2 Time-rate-of-change of G ....................... 14 2.1.3 Gravitomagnetism, Geodetic Precession, and other PPN Tests . 14 2.1.4 Inverse Square Law, Extra Dimensions, and other Frontiers . 16 2.2 Lunar and Earth Physics . 16 2.2.1 The Lunar Interior . 16 2.2.2 Earth Orientation, Precession, and Coordinate Frames . 18 3 LLR Capability across Time 20 3.1 Brief LLR History . -
Moon-Earth-Sun: the Oldest Three-Body Problem
Moon-Earth-Sun: The oldest three-body problem Martin C. Gutzwiller IBM Research Center, Yorktown Heights, New York 10598 The daily motion of the Moon through the sky has many unusual features that a careful observer can discover without the help of instruments. The three different frequencies for the three degrees of freedom have been known very accurately for 3000 years, and the geometric explanation of the Greek astronomers was basically correct. Whereas Kepler’s laws are sufficient for describing the motion of the planets around the Sun, even the most obvious facts about the lunar motion cannot be understood without the gravitational attraction of both the Earth and the Sun. Newton discussed this problem at great length, and with mixed success; it was the only testing ground for his Universal Gravitation. This background for today’s many-body theory is discussed in some detail because all the guiding principles for our understanding can be traced to the earliest developments of astronomy. They are the oldest results of scientific inquiry, and they were the first ones to be confirmed by the great physicist-mathematicians of the 18th century. By a variety of methods, Laplace was able to claim complete agreement of celestial mechanics with the astronomical observations. Lagrange initiated a new trend wherein the mathematical problems of mechanics could all be solved by the same uniform process; canonical transformations eventually won the field. They were used for the first time on a large scale by Delaunay to find the ultimate solution of the lunar problem by perturbing the solution of the two-body Earth-Moon problem. -
Jupitor's Great Red Spot
GREAT RED SPOT appears somewhat orange in this remarkably ly ranged from '.'full gray" and "pinkish" to "brick red" and "car· detailed photograph made at the Lunar and Planetary Laboratory mine." The photograph was made on December 23, 1966, by Alika of the University of Arizona. During the century or so that Jupiter's Herring and John Fountain, who used a 61·inch reflecting tele· great red spot bas been closely observed its color has reported. scope. The exposure was one second on High Speed Ektachrome. © 1968 SCIENTIFIC AMERICAN, INC JUPITER'S GREAT RED SPOT There is evidence to suggest that this peculiar Inarking is the top of a "Taylor cohunn": a stagnant region above a bll111p 01' depression at the botton1 of a circulating fluid by Haymond Hide he surface markings of the plan To explain the fluctuations in the red tals suspended in an atmosphere that is Tets have always had a special fas spot's period of rotation one must assume mainly hydrogen admixed with water cination, and no single marking that there are forces acting on the solid and perhaps methane and helium. Other has been more fascinating and puzzling planet capable of causing an equivalent lines of evidence, particularly the fact than the great red spot of Jupiter. Un change in its rotation period. In other that Jupiter's density is only 1.3 times like the elusive "canals" of Mars, the red words, the fluctuations in the rotation the density of water, suggest that the spot unmistakably exists. Although it has period of the red spot are to be regarded main constituents of the planet are hy been known to fade and change color, it as a true reflection of the rotation period drogen and helium.