DOCSLIB.ORG

Lecture 4 Simple Observations of the Moon

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Lecture 4 Simple Observations of the Moon Lecture 4 Motion of the Moon - phases of the Moon - Solar and Lunar eclipses David Haworth - tides Time & Calendar sunlight Properties of the Earth and Moon Koupelis - chapters 1 & 6 1 4 Phases are caused by the illumination by the Sun Third quarter Simple observations of the Moon David Haworth • displays phases with a period of 29.5 days waning • full Moon always opposite to the Sun • half Moon at 90 degrees from the Sun New Moon Full Moon • always displays the same hemisphere to the Earth • path along the sky deviates from the ecliptic waxing • Lunar eclipses always at full Moon, but not every month! • Solar eclipses at new Moon are less frequent First quarter 2 5 Sidereal en Synodic periodes orbital period and rotation period are synchronised Sidereal month: Moon reaches the same position wrt the stars (27.3 days) Synodic month: Moon reaches the same position wrt the Sun (29.5 days) A second Full Moon in the same month: ‘Blue Moon’ 3 6 A Lunar eclipse does not occur every month! Lunar eclipses The Moon traverses the shadow cone of the Earth Umbra : area of the shadow cone from which the Sun is totally invisible. The orbit of the Moon around the Earth is inclined by 5 degrees with respect to the orbit of the Earth around the Sun (ecliptic). Penumbra : area of the shadow cone from which the Sun is partially visible. What is the maximum declination the Moon can reach? 7 10 The eclipsed Moon (composite) A Lunar eclipse does not occur every month! Visible from anywhere on Earth where the Sun is below the horizon. 3 kinds of Lunar eclipses A : eclipse in the Penumbra B : total eclipse of the Moon The orbit of the Moon around the Earth is inclined by 5 degrees C : partial eclipse of the Moon with respect to the orbit of the Earth around the Sun (ecliptic). What is the maximum declination the Moon can reach? 8 11 The Earth atmosphere bends (refracts) the sunlight like a lens, and filters out the blue light. Solar eclipses The shadow of the Moon moves across the Earth The Moon displays a dark red/copper glow during a total Lunar eclipse: ‘Blood Moon’ A total solar eclipse is only visible from a narrow strip on Earth. 9 12 By the way, the orbit of the Moon is also elliptical. Libration ‘Super Moon’ analemma of the Moon 31 January 2018: a Super Blue Blood Moon 13 16 Total Solar eclipse: The Corona of the Sun the umbra of the Moon’s shadow ‘touches’ the Earth becomes visible for a few minutes. Annular Solar eclipse: the umbra of the Moon’s shadow does not ‘touch’ the Earth The shadow of the Moon seen from space. 14 17 тoтAL solАFl ЕCLIPSЕS: 1997_2o20 60'N з0"N Ф .= 00 з0.s Total solar eclipse sequence 60"s Predicted paths of total and annular Solar eclipses. 0' 60.Е 120.Е \ 1 Longitude Тhese dark b trаоkof the Ul тoтAL solАFl ЕCLIPSЕS: 1997_2o20 ANNULAR soLAR ЕCL|PSЕS: 1997-202o 60'N 60'N з0"N з0.N Ф Ф э .= 00 0" --(б з0.s з0.S 60"s 60"s 0' 60.Е 120.Е \ 1180.W 120'W 60"W 0" 60"Е 12o.Е 180" Е Longitude Тhese dark b Longitude trаоkof the Ul ANNULAR soLAR ЕCL|PSЕS: 1997-202o 60'N 15 18 з0.N Ф э 0" --(б з0.S 60"s 180.W 120'W 60"W 0" 60"Е 12o.Е 180" Е Longitude Total solar eclipse sequence Tides ‘Diamond ring’ Baily’s Beads Totality caused by differential gravity Because the Earth rotates faster than a Lunar period, the ocean’s waters are dragged forward by the Earth. Due to friction, the Earth rotation slows down while the Moon moves further away from the Earth. 19 22 Compared to the Moon, the Sun’s gravity ‘pulls’ 180x harder on the Earth, but the Sun is also 390x more distant. The differential gravity from the Moon is 2.2x stronger than that from the Sun. spring tide neap tide 20 23 Eclipse seasons Time & Calendar Eclipses only happen when line-of-nodes points toward the Sun. Eclipse pattern repeats every 11 months, not every 12 months. This is a consequence of the precession of the Moon’s orbit with a period of 18.6 years: The line-of-nodes rotates over 19.4 degrees every year. 21 24 Seasons & constellations Note that the Earth is further from the Sun in July than in January. Therefore, a Solar day in January lasts longer than a Solar day in July. concept of a year ⇒ ➙ equation of time! Planets Analemma ⇒ concept of a week The result of: Sun - obliquity of the Earth axis of rotation ⇒ concept of a day - elliptical orbit of the Earth B.t.w. Leap year Sunday The Julian kalender was Monday replaced in 1582 by the Mardi Gregorian calender. Mercredi This fixed the error due to Jeudi the definition of a Julian Vendredi More about time/calendar later on year as 365.25 days. Saturday 25 28 Sidereal time vs Solar time Distinguish sidereal time from (mean) Solar time. Months A sidereal day is shorter than The Moon revolves around the Earth in 29,5 days (synodic month). a Solar day! Consequently, 12 MONths almost make up a year, but not quite: 12 x 29.5 = 354 dagen Some 11 extra days are required to fit 12 months in 1 year. → distribute these extra days over the months. Note: the number of days in a month follows MAMJJASONDJF, with some interesting consequences… The mean Solar time in Greenwich (GMT) is the reference time (Universal Time: UT), which defines the time zones. 26 29 The Earth Mass and volume yield an average density <ρ> <ρ> = 5.52 gr/cm3 This is significantly more dense than the surface material (water and silicates): the Earth contains a core of iron and nickel 27 30 Almost unique to the Earth : a magnetic field Seismological research has revealed: There is a liquid outer core below the mantle; the inner core is solid. The crust ‘floats’ on the (convective) mantle. De magnetic poles do not coincide with the geographic poles. The Earth magnetic field directs charged particles from the Solar wind Furthermore, the Earth retains an atmosphere! to the magnetic poles. 31 34 Aurora Borealis - Northern Lights Unique to the Earth: plate tectonics Andreas Coсos; 53uц P|ate.: Paсifiс ')''^ Plate -'',i''t'"'^.,{i )," oouno",,( AntarсtiсP|a|e l www.youtube.com/watch?v=uLahVJNnoZ4 32 35 Almost unique to the Earth : a magnetic field The Earth magnetic field directs charged particles from the Solar wind to the magnetic poles. 33 36 The Moon The dual face of the Moon ‣ diameter is 27% of Earth ‣ phases due to illumination by the Sun ‣ impact craters and maria, dust seas (lava) ‣ from Earth, we always see the same side: synchronous rotation ‣ <ρ> = 3.34 gr/cm3: the core is small or absent ‣ no atmosphere ‣ no magnetic field Origin: likely composed from crust material from the Earth ‣ often Lunar eclipses (impact theory) but not every month! 37 40 The Lunar surface The gravity on the Moon is much less than on Earth (17%) There are many more craters and far less maria on the far-side of the Moon: an uneven distribution of mass inside the Moon. 38 41 The dual face of the Moon Internal structure of the Moon t,tron-riсh сore? 140 I кm, l 1740km Partially molten? Mantlе 39 42.
Load more

Recommended publications
  • 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.
    [Show full text]
  • 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
    [Show full text]
  • 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 .
    [Show full text]
  • 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.
    [Show full text]
  • The Moon and Eclipses
    Lecture 10 The Moon and Eclipses Jiong Qiu, MSU Physics Department Guiding Questions 1. Why does the Moon keep the same face to us? 2. Is the Moon completely covered with craters? What is the difference between highlands and maria? 3. Does the Moon’s interior have a similar structure to the interior of the Earth? 4. Why does the Moon go through phases? At a given phase, when does the Moon rise or set with respect to the Sun? 5. What is the difference between a lunar eclipse and a solar eclipse? During what phases do they occur? 6. How often do lunar eclipses happen? When one is taking place, where do you have to be to see it? 7. How often do solar eclipses happen? Why are they visible only from certain special locations on Earth? 10.1 Introduction The moon looks 14% bigger at perigee than at apogee. The Moon wobbles. 59% of its surface can be seen from the Earth. The Moon can not hold the atmosphere The Moon does NOT have an atmosphere and the Moon does NOT have liquid water. Q: what factors determine the presence of an atmosphere? The Moon probably formed from debris cast into space when a huge planetesimal struck the proto-Earth. 10.2 Exploration of the Moon Unmanned exploration: 1950, Lunas 1-3 -- 1960s, Ranger -- 1966-67, Lunar Orbiters -- 1966-68, Surveyors (first soft landing) -- 1966-76, Lunas 9-24 (soft landing) -- 1989-93, Galileo -- 1994, Clementine -- 1998, Lunar Prospector Achievement: high-resolution lunar surface images; surface composition; evidence of ice patches around the south pole.
    [Show full text]
  • L1 Lunar Lander Element Conceptual Design Report
    EX15-01-092 L1 Lunar Lander Element Conceptual Design Report Engineering Directorate November 2000 National Aeronautics and Space Administration Lyndon B. Johnson Space Center Houston, Texas 77058 Table Of Contents i List of Figures………………………………………………………………………….……………iv ii List of Tables……………………………………………………………………………….………. v iii Contact Information………………………………………………………………………………..vi iv Introduction……………...………………………………………………………………………….vii 1.0 Element Description……………………………………………………………………….………..1 1.1 Design Objectives, Constraints & Requirements……………………………….…………..1 1.2 Vehicle Configuration Trades………………………………………………….……………3 1.3 Operations Concept…………………………………………………………….……………5 1.4 Vehicle Mass Statement…………………………………………………..………………. 9 1.5 Power Profile………………………………………………………………..……………. 10 2.0 Propulsion System…………………………………………………………………..…………….. 12 2.1 Functional Description and Design Requirements…………………………..……………. 12 2.2 Trades Considered and Results……………………………………………..……………... 12 2.3 Reference Design Description………………………………………………..…………… 12 2.4 Technology Needs and Design Challenges…………………………………..…………….13 3.0 Structure..……………………………………………………………….………….……………….14 3.1 Functional Description and Design Requirements………………………………...……….14 3.2 Trades Considered and Results……………………………………………………………..15 3.3 Reference Design Description……………………………………………………...………15 3.4 Technology Needs and Design Challenges…………………………………………………16 4.0 Electrical Power System…………………………………………………………………………….17 4.1 Functional Description and Design Requirements………………………………………….17 4.2 Trades
    [Show full text]
  • Analytical Formulation of Lunar Cratering Asymmetries Nan Wang (王楠) and Ji-Lin Zhou (周济林)
    A&A 594, A52 (2016) Astronomy DOI: 10.1051/0004-6361/201628598 & c ESO 2016 Astrophysics Analytical formulation of lunar cratering asymmetries Nan Wang (王`) and Ji-Lin Zhou (hN林) School of Astronomy and Space Science and Key Laboratory of Modern Astronomy and Astrophysics in Ministry of Education, Nanjing University, 210046 Nanjing, PR China e-mail: [email protected] Received 28 March 2016 / Accepted 3 July 2016 ABSTRACT Context. The cratering asymmetry of a bombarded satellite is related to both its orbit and impactors. The inner solar system im- pactor populations, that is, the main-belt asteroids (MBAs) and the near-Earth objects (NEOs), have dominated during the late heavy bombardment (LHB) and ever since, respectively. Aims. We formulate the lunar cratering distribution and verify the cratering asymmetries generated by the MBAs as well as the NEOs. Methods. Based on a planar model that excludes the terrestrial and lunar gravitations on the impactors and assuming the impactor encounter speed with Earth venc is higher than the lunar orbital speed vM, we rigorously integrated the lunar cratering distribution, and derived its approximation to the first order of vM=venc. Numerical simulations of lunar bombardment by the MBAs during the LHB were performed with an Earth–Moon distance aM = 20−60 Earth radii in five cases. Results. The analytical model directly proves the existence of a leading/trailing asymmetry and the absence of near/far asymmetry. The approximate form of the leading/trailing asymmetry is (1+A1 cos β), which decreases as the apex distance β increases. The numer- ical simulations show evidence of a pole/equator asymmetry as well as the leading/trailing asymmetry, and the former is empirically described as (1 + A2 cos 2'), which decreases as the latitude modulus j'j increases.
    [Show full text]
  • Iaa-Pdc-15-04-17 from Sail to Soil – Getting Sailcraft out of the Harbour on a Visit to One of Earth’S Nearest Neighbours
    4th IAA Planetary Defense Conference – PDC 2015 13-17 April 2015, Frascati, Roma, Italy IAA-PDC-15-04-17 FROM SAIL TO SOIL – GETTING SAILCRAFT OUT OF THE HARBOUR ON A VISIT TO ONE OF EARTH’S NEAREST NEIGHBOURS Jan Thimo Grundmann(1,2), Waldemar Bauer(1,3), Jens Biele(8,9), Federico Cordero(11), Bernd Dachwald(12), Alexander Koncz(13,14), Christian Krause(8,10), Tobias Mikschl(16,17), Sergio Montenegro(16,18), Dominik Quantius(1,4), Michael Ruffer(16,19), Kaname Sasaki (1,5), Nicole Schmitz(13,15), Patric Seefeldt (1,6), Norbert Tóth(1,7), Elisabet Wejmo(1,8) (1)DLR Institute of Space Systems, Robert-Hooke-Strasse 7, 28359 Bremen (2)+49-(0)421-24420-1107, (3)+49-(0)421-24420-1197, (4)+49-(0)421-24420-1109, (5)+49-(0)421-24420-1150, (6)+49-(0)421-24420-1609, (7)+49-(0)421-24420-1186, (8)+49-(0)421-24420-1107, (11)DLR Space Operations and Astronaut Training – MUSC, 51147 Köln, Germany (9)+49-2203-601-4563, (10)+49-2203-601-3048, (11)Telespazio-VEGA, Darmstadt, Germany, [email protected] (12) Faculty of Aerospace Engineering, FH Aachen University of Applied Sciences, Hohenstaufenallee 6, 52064 Aachen, Germany, +49-241-6009-52343 / -52854, (13)DLR Institute of Planetary Research, Rutherfordstr. 2, 12489 Berlin (14)+49-(0)30 67055-575, (15)+49-(0)30 67055-456, (16)Informatik 8, Universität Würzburg, Am Hubland, 97074 Würzburg, Germany Keywords: small spacecraft, solar sail, GOSSAMER roadmap, MASCOT, co-orbital asteroid ABSTRACT The DLR-ESTEC GOSSAMER roadmap envisages the development of solar sailing by successive low-cost technology demonstrators towards first science missions.
    [Show full text]
  • Strategy for Optimal, Long-Term Stationkeeping of Libration Point Orbits in the Earth-Moon System
    Strategy for Optimal, Long-Term Stationkeeping of Libration Point Orbits in the Earth-Moon System Thomas A. Pavlak∗ and Kathleen C. Howelly Purdue University, West Lafayette, IN, 47907-2045, USA In an effort to design low-cost maneuvers that reliably maintain unstable libration point orbits in the Earth-Moon system for long durations, an existing long-term stationkeeping strategy is augmented to compute locally optimal maneuvers that satisfy end-of-mission constraints downstream. This approach reduces stationkeeping costs for planar and three- dimensional orbits in dynamical systems of varying degrees of fidelity and demonstrates the correlation between optimal maneuver direction and the stable mode observed during ARTEMIS mission operations. An optimally-constrained multiple shooting strategy is also introduced that is capable of computing near optimal maintenance maneuvers without formal optimization software. I. Introduction Most orbits in the vicinity of collinear libration points are inherently unstable and, consequently, sta- tionkeeping strategies are a critical component of mission design and operations in these chaotic dynamical regions. Stationkeeping is particularly important for libration point missions in the Earth-Moon system since fast time scales require that orbit maintenance maneuvers be implemented approximately once per week. Assuming that acceptable orbit determination solutions require 3-4 days to obtain, stationkeeping ∆V planning activities must be quick, efficient, and effective. Furthermore, the duration of a libration point mission is often dictated by the remaining propellant so a key capability is maintenance maneuvers that are low-cost. Thus, to accommodate a likely increase in future operations in the vicinity of the Earth-Moon libration points, fast, reliable algorithms capable of rapidly computing low-cost stationkeeping maneuvers, with little or no human interaction, are critical.
    [Show full text]
  • Trajectory Sensitivities for Sun-Mars Libration Point Missions
    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Calhoun, Institutional Archive of the Naval Postgraduate School Calhoun: The NPS Institutional Archive Faculty and Researcher Publications Faculty and Researcher Publications Collection 2016 Trajectory Sensitivities for Sun-Mars Libration Point Missions Kutrieb, Joshua M. http://hdl.handle.net/10945/48886 AAS 01-327 TRAJECTORY SENSITIVITIES FOR SUN-MARS LIBRATION POINT MISSIONS John P. Carrico*, Jon D. Strizzi‡, Joshua M. Kutrieb‡, and Paul E. Damphousse‡ Previous research has analyzed proposed missions utilizing spacecraft in Lissajous orbits about each of the co-linear, near-Mars, Sun-Mars libration points to form a communication relay with Earth. This current effort focuses on 2016 Earth-Mars transfers to these mission orbits with their trajectory characteristics and sensitivities. This includes further analysis of using a mid-course correction as well as a braking maneuver at close approach to Mars to control Lissajous orbit insertion and the critical parameter of the phasing of the two-vehicle relay system, with one spacecraft each in orbit about L1 and L2. Stationkeeping sensitivities are investigated via a monte carlo technique. Commercial, desktop simulation and analysis tools are used to provide numerical data; and on-going, successful collaboration between military and industry researchers in a virtual environment is demonstrated. The resulting data should provide new information on these trajectory sensitivities to future researchers and mission planners. INTRODUCTION “NASA is seeking innovation to attack the diversity of Mars…to change the vantage point from which we explore…” - CNN, 25 June 2001 The concept of using communication relay vehicles in orbit about colinear Lagrange points to support exploration of the secondary body is not entirely new, being first conceptualized in the case of the Earth-Moon system by R.
    [Show full text]
  • Interaction Mechanism and Response of Tidal Effect on the Shallow Geology of Europa Yifei Wang 1 ABSTRACT 1. INTRODUCTION 2
    １ Interaction Mechanism and Response of Tidal Effect on the Shallow Geology of Europa Yifei Wang 1 Beijing University of Aeronautics and Astronautics Department of Materials Science and Engineering Undergraduate ABSTRACT Europa has been confirmed to have a multilayered structure and complex geological condition in last two decades whose detail and cause of formation remains unclear. In this work, we start from analyzing the mechanism of tidal effect on satellite’s surface and discuss if interaction like tidal locking and orbital resonance play an important role in tidal effect including heating, underground convection and eruption. During discussion we propose the main factors affecting Europa’s tidal heat and the formation mechanism of typical shallow geological features, and provide theoretical support for further exploration. Keywords: Europa, tidal heating, tidal locking, orbital resonance 1. INTRODUCTION According to existing observations by Galileo radio-tracking/gravity data and Galileo SSI images, Europa has a complex structure and distribution of different components including solid ice layer, warm liquid ocean, local convection and eruption between solid and liquid region, and hard brittle lithosphere. And for Jupiter’s three moon system--IO, Europa and Ganymede, these are in the rotation and revolution of synchronous pattern which called tidal locking. Besides, it is confirmed that IO, Jupiter and Ganymede are in the situation of orbital resonance, whose orbital period ratio is about 1:2:4 and the ratio remains constant with time. Their effect on the surface is periodic during revolution. From Ogilvie and Lin’s work2, a response to tidal force is separated in two parts: an equilibrium tide and a dynamic tide which is irrelevant with time and the angular position to Jupiter and other satellites because of periodic interaction to the subsurface structure.
    [Show full text]
  • 12 Lunar Libration Point - \ , Gpo Price $ - I I - Cfsti Price(S) $
    ~_________ - https://ntrs.nasa.gov/search.jsp?R=19670017256 2020-03-24T00:44:51+00:00Z View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by NASA Technical Reports Server . *‘ L. ---- ~ X-507-67-167 -- -. , \ A ‘“HUMMINGBIRD” ,-’ FOR THE . I 12 LUNAR LIBRATION POINT - \ , GPO PRICE $ - I I - CFSTI PRICE(S) $ - Hard copy - Microfiche ff 653 July 65 F. 0. VONBUN ,- / APRIL1967 , - GODDARD SPACE FLCGHT CENTER - i GREENBELT, MARYLAND , - - I .Y i \“ , .. Q - X-507-67-167 A "HUMMINGBIRD" FOR THE L, LUNAR LIBRATION POINT F. 0. Vonbun April 1967 Goddard Space Flight Center Greenbelt, Maryland TABLE OF CONTENTS ABSTRACT...................................... vi SUMMARY ...................................... vi 1. ACCELERATIONS EXPERIENCED BY THE "HUMMINGBIRD". 1 A. General .. .. .. .. .. .... .. 1 B. Accelerations Along the Earth-Moon Line . 4 C. TheSun'sInfluence . .. ... 7 II. NECESSARY SPECIFIC IMPULSE FOR ECONOMIC STATION KEEPING. 9 A. Fuel to Spacecraft Mass Ratio . 9 B. Needed Station Keeping and Attitude Engines. 10 III. REFERENCES ................................... 15 iii A tlHUMMINGBIRD1l FOR THE L, LUNAR LIBRATION POINT F. 0. Vonbun ABSTRACT Consider as an example a spacecraft, contrary to all previously published investigations, NOT in an orbit but in a more or less permanent position in the vicinity of the far-sided lunar libration point L, , as commonly called, Such a spacecraft would be very useful for a communications relay between the back side of the moon and an earth tracking station. It could be placed Icaboverrthe lunar libration point in such a fashion that it is never occulted, thus making the stated communication link a continuous one, independent of time.
    [Show full text]