A Model of the Rotation of Venus Based on 5 Parameters. J.Souchay, L.Cottereau (SYRTE, observatoire de Paris)
|
|
- Edward Ward
- 7 years ago
- Views:
Transcription
1 A Model of the Rotation of Venus Based on 5 Parameters J.Souchay, L.Cottereau (SYRTE, observatoire de Paris)
2 Plan General Remarks on Venus and its rotation How to model the Venus rotation The «polar motion» (polhody) The precession-nutation motion The l.o.d. (Length of Day) Conclusion
3 General Remarks on Venus and its rotation
4 Vénus
5 Les passages de Vénus Next Venus transit : June 6, 2012
6 Les passages de Vénus Next Venus transit : June 6, 2012
7 Magellan probe (1991)
8 Vénus : résultats de Magellan
9 Vénus : résultats de Magellan
10 Vénus : le planisphère Venus planisphere
11 Comparisons Venus % Earth
12 Precession rate
13 is taller The Earth Venus
14 Solar time and sideral time Eccentricity Reduction at equator
15 Equation du temps
16 Solar day on Venus T ~ 116 d
17 Rotation of Venus / Previous studies Peculiar spin rate (Smith,1963; Goldstein, 1964, Carpenter,1964) Balance gravitational vs. thermical tides (Gold and Soter,1969) Friction at core-mantle boundary (Goldreich and Peale,1970) Various scenarios starting from tidal dissipation (Lago and Cazenave,1979;Dobrovolskis,1980, Shen and Zhang,1989, ) Wide set of possible spin rates explaining chaotic variations of obliquity (Laskar and Robutel,1993) Tilt of the spin axis from any initial value to 180 (Néron de Surgy,1996; Yoder,1997; Correia and Laskar,2001) Variations in the rotation rate due to orbital eccentricity modulation of solar tidal torques (Bills, 2005) Etc.
18 Solid tides exerted by the Sun on Venus
19 Tidal thermal atmospheric friction of the Sun on Venus
20 4 Scenarii (Correia and Laskar, 2001)
21 How to model Venus rotation
22 A model of rotation based on 5 parameters Polhody ( X,Y) (Orlov, 1895) Precession & Nutation (Δψ, Δε) (Bradley,1749) l.o.d /UT1/φ (De Sitter, 1923, Stoyko, 1937)
23 M = M 1 (X,Y) * M 2 (φ) * M 3 (ψ,ε, Δψ, Δε) [TRF] = M [CRF] Polhody ( X,Y) (Orlov, 1895) Precession & Nutation (Δψ, Δε) (Bradley,1749) l.o.d /UT1/φ (De Sitter, 1923, Stoyko, 1937)
24 Euler angles Woolard s theory (1953)
25 Parametrization with Andoyer variables Andoyer canonical variables l, g, h => angle variables L,G,H => action variables Kinoshita s theory (1972,1977)
26 Venus precession & nutation
27 Precession-nutation of Venus precession nutation J I=2 63 Inertial axis of Venus If Angular momentum axis Figure axis : coincides with the axis of the largest moment of inertia Inertial plane : the orbit of Venus at J The reference point is the intersection between the orbital plane and the mean equator of Venus at J2000.0
28 Yoder (1995)
29 Motion of Venus due to an external disturbing body 1 F 0 : free rotation E, E : moving reference orbit plane U 1 : disturbing potential
30 Canonical equations (Kinoshita,1977)
31 λ longitude along the orbit β inclination (here β = 0 )
32 Developments for the potential
33 Precession. ψ venus = 4474".35 ± 66.5 / cy. ψ terre = 1583".99 / cy (Sun only). ψ terre = 5000".3/ cy (Sun + Moon) L.Cottereau and J.Souchay Rotation of rigid Venus : a complete precession-nutation model A&A-2009
34 Nutation depending on the triaxiality
35 Calculation of Oppolzer terms Difference of nutation [ Figure axis Angular Momentum axis ]
36 Indirect planetary effect on nutation nutation in longitude arcsecond temps days
37 Indirect planetary effect on nutation
38 Comparison between the nutations of the figure axis and of the angular momentum axis Longitude Obliquity nutation in longitude arcsecond nutation in obliquity arcsecond times days times days ---- angular momentum axis ---- figure axis L.Cottereau et Al. A&A (2010)
39 Long time scale evolution of the motion of rotation of Venus Longitude Obliquity variation h degre 0 10 Variation of I degre times thousand of years times thousand of years
40 Motion of venus axis of figure in space 2,6328 Coordinate Y of pole of Venus (degree) 2,6326 2,6324 2,6322-0,06-0,05-0,04-0,03-0,02-0,01 0 Coordinate X of pole of Venus (degree)
41 Conclusion The precession in longitude due to the Sun is more than two times larger than the corresponding term for the Earth and slightly smaller than the combined effect of the Moon and of the Sun for the Earth. The nutation of the figure axis (calculated for the first time) is significantly different than the nutation of the angular momentum axis (smaller and dominated by three sinusoids) The evolution of Venus obliquity on a long time scale (~ y) is small as it is the case for the Earth The periodic variations of the speed of rotation of Venus due to the solid tides, atmospheric pressure, and core have been modeled => effects above the detection threshold (Venus Express) Possibility to represent Venus rotation with 5 parameters X,Y (polar motion), (ε + Δε, ψ + Δψ), VT (l.o.d.)
Gravity Field and Dynamics of the Earth
Milan Bursa Karel Pec Gravity Field and Dynamics of the Earth With 89 Figures Springer-Verlag Berlin Heidelberg New York London Paris Tokyo HongKong Barcelona Budapest Preface v Introduction 1 1 Fundamentals
More informationCelestial Sphere. Celestial Coordinates. Lecture 3: Motions of the Sun and Moon. ecliptic (path of Sun) ecliptic (path of Sun)
Lecture 3: Motions of the and Moon ecliptic (path of ) ecliptic (path of ) The 23.5 degree tilt of Earth s spin axis relative to its orbital axis around the causes the seasons Celestial Sphere Celestial
More informationDynamics of Celestial Bodies, 103-107 PLANETARY PERTURBATIONS ON THE ROTATION OF MERCURY
Dynamics of Celestial Bodies, 103-107 Contributed paper PLANETARY PERTURBATIONS ON THE ROTATION OF MERCURY J. DUFEY 1, N. RAMBAUX 1,2, B. NOYELLES 1,2 and A. LEMAITRE 1 1 University of Namur, Rempart de
More informationROTATION AND LIBRATION OF CELESTIAL BODIES
ROTATION AND LIBRATION OF CELESTIAL BODIES Nicolas Rambaux 1,2, In collaboration with J. Castillo-Rogez 3, L. Cottereau 6, V. Dehant 4, O. Karatekin 4, A. Lemaitre 5, P. Robutel 2, J. Souchay 6, T. Van
More informationDynamics of Iain M. Banks Orbitals. Richard Kennaway. 12 October 2005
Dynamics of Iain M. Banks Orbitals Richard Kennaway 12 October 2005 Note This is a draft in progress, and as such may contain errors. Please do not cite this without permission. 1 The problem An Orbital
More informationEDMONDS COMMUNITY COLLEGE ASTRONOMY 100 Winter Quarter 2007 Sample Test # 1
Instructor: L. M. Khandro EDMONDS COMMUNITY COLLEGE ASTRONOMY 100 Winter Quarter 2007 Sample Test # 1 1. An arc second is a measure of a. time interval between oscillations of a standard clock b. time
More informationNewton s Law of Gravity
Gravitational Potential Energy On Earth, depends on: object s mass (m) strength of gravity (g) distance object could potentially fall Gravitational Potential Energy In space, an object or gas cloud has
More informationAstronomy. Astrophysics. The various contributions in Venus rotation rate and LOD. L. Cottereau 1, N. Rambaux 2,3, S. Lebonnois 4, and J.
A&A 53, A5 ) DOI:.5/-636/666 c ESO Astronomy & Astrophysics The various contributions in Venus rotation rate and LOD L. Cottereau, N. Rambaux,3, S. Lebonnois, and J. Souchay Observatoire de Paris, Systèmes
More information1-2. What is the name given to the path of the Sun as seen from Earth? a.) Equinox b.) Celestial equator c.) Solstice d.
Chapter 1 1-1. How long does it take the Earth to orbit the Sun? a.) one sidereal day b.) one month c.) one year X d.) one hour 1-2. What is the name given to the path of the Sun as seen from Earth? a.)
More informationLecture L29-3D Rigid Body Dynamics
J. Peraire, S. Widnall 16.07 Dynamics Fall 2009 Version 2.0 Lecture L29-3D Rigid Body Dynamics 3D Rigid Body Dynamics: Euler Angles The difficulty of describing the positions of the body-fixed axis of
More informationSOFA software support for IAU 2000
SOFA software support for IAU 2000 Patrick Wallace Rutherford Appleton Laboratory, UK ptw@star.rl.ac.uk Presentation outline Introduction to SOFA IAU 2000 and SOFA Software design choices Examples SOFA
More informationMeasures of basins of attraction in spin-orbit dynamics
Celest Mech Dyn Astr (2008) 101:159 170 DOI 10.1007/s10569-008-9142-9 ORIGINAL ARTICLE Measures of basins of attraction in spin-orbit dynamics Alessandra Celletti Luigi Chierchia Received: 10 November
More informationAstronomy 1140 Quiz 1 Review
Astronomy 1140 Quiz 1 Review Prof. Pradhan September 15, 2015 What is Science? 1. Explain the difference between astronomy and astrology. (a) Astrology: nonscience using zodiac sign to predict the future/personality
More informationCELESTIAL CLOCK - THE SUN, THE MOON, AND THE STARS
INTRODUCTION CELESTIAL CLOCK - THE SUN, THE MOON, AND THE STARS This is a scientific presentation to provide you with knowledge you can use to understand the sky above in relation to the earth. Before
More information8.012 Physics I: Classical Mechanics Fall 2008
MIT OpenCourseWare http://ocw.mit.edu 8.012 Physics I: Classical Mechanics Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms. MASSACHUSETTS INSTITUTE
More informationAstromechanics. 1 solar day = 1.002737909350795 sidereal days
Astromechanics 13. Time Considerations- Local Sidereal Time The time that is used by most people is that called the mean solar time. It is based on the idea that if the Earth revolved around the Sun at
More informationLecture L17 - Orbit Transfers and Interplanetary Trajectories
S. Widnall, J. Peraire 16.07 Dynamics Fall 008 Version.0 Lecture L17 - Orbit Transfers and Interplanetary Trajectories In this lecture, we will consider how to transfer from one orbit, to another or to
More informationToday FIRST HOMEWORK DUE NEXT TIME. Seasons/Precession Recap. Phases of the Moon. Eclipses. Lunar, Solar. Ancient Astronomy
Today FIRST HOMEWORK DUE NEXT TIME Seasons/Precession Recap Phases of the Moon Eclipses Lunar, Solar Ancient Astronomy How do we mark the progression of the seasons? We define four special points: summer
More informationSolar System. 1. The diagram below represents a simple geocentric model. Which object is represented by the letter X?
Solar System 1. The diagram below represents a simple geocentric model. Which object is represented by the letter X? A) Earth B) Sun C) Moon D) Polaris 2. Which object orbits Earth in both the Earth-centered
More informationSun Earth Relationships
1 ESCI-61 Introduction to Photovoltaic Technology Sun Earth Relationships Ridha Hamidi, Ph.D. Spring (sun aims directly at equator) Winter (northern hemisphere tilts away from sun) 23.5 2 Solar radiation
More informationCoordinate Systems. Orbits and Rotation
Coordinate Systems Orbits and Rotation Earth orbit. The earth s orbit around the sun is nearly circular but not quite. It s actually an ellipse whose average distance from the sun is one AU (150 million
More informationTidal Forces and their Effects in the Solar System
Tidal Forces and their Effects in the Solar System Richard McDonald September 10, 2005 Introduction For most residents of Earth, tides are synonymous with the daily rise and fall of sea levels, and there
More informationLecture L30-3D Rigid Body Dynamics: Tops and Gyroscopes
J. Peraire, S. Widnall 16.07 Dynamics Fall 2008 Version 2.0 Lecture L30-3D Rigid Body Dynamics: Tops and Gyroscopes 3D Rigid Body Dynamics: Euler Equations in Euler Angles In lecture 29, we introduced
More informationUse the following information to deduce that the gravitational field strength at the surface of the Earth is approximately 10 N kg 1.
IB PHYSICS: Gravitational Forces Review 1. This question is about gravitation and ocean tides. (b) State Newton s law of universal gravitation. Use the following information to deduce that the gravitational
More informationLet s first see how precession works in quantitative detail. The system is illustrated below: ...
lecture 20 Topics: Precession of tops Nutation Vectors in the body frame The free symmetric top in the body frame Euler s equations The free symmetric top ala Euler s The tennis racket theorem As you know,
More informationSUPPLEMENT 2. ESTIMATING THE EPOCHS OF THE GCC AND GA
Crucifying the Earth on the Galactic Cross. upplement 2 1 UPPLEMENT 2. ETIMATING THE EPOCH OF THE GCC AND GA 2.1. OLAR YTEM AND GALACTIC PARAMETER Coordinate ystems. In the Equatorial and al coordinate
More informationChapter 9 Rigid Body Motion in 3D
Chapter 9 Rigid Body Motion in 3D Rigid body rotation in 3D is a complicated problem requiring the introduction of tensors. Upon completion of this chapter we will be able to describe such things as the
More informationAttitude and Orbit Dynamics of High Area-to-Mass Ratio (HAMR) Objects and
Attitude and Orbit Dynamics of High Area-to-Mass Ratio (HAMR) Objects and Carolin Früh National Research Council Postdoctoral Fellow, AFRL, cfrueh@unm.edu Orbital Evolution of Space Debris Objects Main
More informationOrbital Mechanics and Space Geometry
Orbital Mechanics and Space Geometry AERO4701 Space Engineering 3 Week 2 Overview First Hour Co-ordinate Systems and Frames of Reference (Review) Kepler s equations, Orbital Elements Second Hour Orbit
More informationNotes: Most of the material in this chapter is taken from Young and Freedman, Chap. 13.
Chapter 5. Gravitation Notes: Most of the material in this chapter is taken from Young and Freedman, Chap. 13. 5.1 Newton s Law of Gravitation We have already studied the effects of gravity through the
More informationChapter 2. Mission Analysis. 2.1 Mission Geometry
Chapter 2 Mission Analysis As noted in Chapter 1, orbital and attitude dynamics must be considered as coupled. That is to say, the orbital motion of a spacecraft affects the attitude motion, and the attitude
More informationCHAPTER 2 ORBITAL DYNAMICS
14 CHAPTER 2 ORBITAL DYNAMICS 2.1 INTRODUCTION This chapter presents definitions of coordinate systems that are used in the satellite, brief description about satellite equations of motion and relative
More informationPhysics 9e/Cutnell. correlated to the. College Board AP Physics 1 Course Objectives
Physics 9e/Cutnell correlated to the College Board AP Physics 1 Course Objectives Big Idea 1: Objects and systems have properties such as mass and charge. Systems may have internal structure. Enduring
More informationThe Four Seasons. A Warm Up Exercise. A Warm Up Exercise. A Warm Up Exercise. The Moon s Phases
The Four Seasons A Warm Up Exercise What fraction of the Moon s surface is illuminated by the Sun (except during a lunar eclipse)? a) Between zero and one-half b) The whole surface c) Always half d) Depends
More informationPenn State University Physics 211 ORBITAL MECHANICS 1
ORBITAL MECHANICS 1 PURPOSE The purpose of this laboratory project is to calculate, verify and then simulate various satellite orbit scenarios for an artificial satellite orbiting the earth. First, there
More informationThis paper is also taken for the relevant Examination for the Associateship. For Second Year Physics Students Wednesday, 4th June 2008: 14:00 to 16:00
Imperial College London BSc/MSci EXAMINATION June 2008 This paper is also taken for the relevant Examination for the Associateship SUN, STARS, PLANETS For Second Year Physics Students Wednesday, 4th June
More informationWhat causes Tides? If tidal forces were based only on mass, the Sun should have a tidegenerating
What are Tides? Tides are very long-period waves that move through the oceans as a result of the gravitational attraction of the Moon and the Sun for the water in the oceans of the Earth. Tides start in
More informationGEOPHYSICAL EFFECTS ON SITE DISPLACEMENTS FOR PERMANENT GPS TRACKING STATIONS IN TAIWAN
GEOPHYSICAL EFFECTS ON SITE DISPLACEMENTS FOR PERMANENT GPS TRACKING STATIONS IN TAIWAN C. C. Chang Department of Surveying and Mapping Engineering Chung Cheng Institute of Technology Tahsi, Taoyuan 335,
More informationOrbital-Scale Climate Change
Orbital-Scale Climate Change Climate Needed for Ice Age Warm winter and non-frozen oceans so lots of evaporation and snowfall Cool summer so that ice does not melt Ice Age Model When ice growing ocean
More informationarxiv:1003.0626v1 [astro-ph.ep] 2 Mar 2010
Astronomy & Astrophysics manuscript no. article deux4 c ESO 04 January 5, 04 Accurate free and forced rotational motions of rigid Venus L. Cottereau, J. Souchay,, S Aljbaae 3, arxiv:003.066v [astro-ph.ep
More information2. Orbits. FER-Zagreb, Satellite communication systems 2011/12
2. Orbits Topics Orbit types Kepler and Newton laws Coverage area Influence of Earth 1 Orbit types According to inclination angle Equatorial Polar Inclinational orbit According to shape Circular orbit
More informationAccurate spin axes and solar system dynamics: Climatic variations for the Earth and Mars
A&A 38, 689 71 () DOI: 1.151/-6361:9 c ESO Astronomy & Astrophysics Accurate spin axes and solar system dynamics: Climatic variations for the Earth and Mars S. Edvardsson, K. G. Karlsson, and M. Engholm
More informationExam # 1 Thu 10/06/2010 Astronomy 100/190Y Exploring the Universe Fall 11 Instructor: Daniela Calzetti
Exam # 1 Thu 10/06/2010 Astronomy 100/190Y Exploring the Universe Fall 11 Instructor: Daniela Calzetti INSTRUCTIONS: Please, use the `bubble sheet and a pencil # 2 to answer the exam questions, by marking
More informationEarth In Space Chapter 3
Earth In Space Chapter 3 Shape of the Earth Ancient Greeks Earth casts a circular shadow on the moon during a lunar eclipse Shape of the Earth Ancient Greeks Ships were observed to disappear below the
More informationThe ecliptic - Earth s orbital plane
The ecliptic - Earth s orbital plane The line of nodes descending node The Moon s orbital plane Moon s orbit inclination 5.45º ascending node celestial declination Zero longitude in the ecliptic The orbit
More informationTidal forces in the Solar System
Tidal forces in the Solar System Introduction As anywhere else in the Universe, gravity is the basic and fundamental principle that rules the shape and permanent motion of all the celestial bodies inside
More informationMotions of Earth, Moon, and Sun
Motions of Earth, Moon, and Sun Apparent Motions of Celestial Objects An apparent motion is a motion that an object appears to make. Apparent motions can be real or illusions. When you see a person spinning
More informationHalliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton
Halliday, Resnick & Walker Chapter 13 Gravitation Physics 1A PHYS1121 Professor Michael Burton II_A2: Planetary Orbits in the Solar System + Galaxy Interactions (You Tube) 21 seconds 13-1 Newton's Law
More informationCenter of Gravity. We touched on this briefly in chapter 7! x 2
Center of Gravity We touched on this briefly in chapter 7! x 1 x 2 cm m 1 m 2 This was for what is known as discrete objects. Discrete refers to the fact that the two objects separated and individual.
More informationarxiv:1104.4009v1 [astro-ph.ep] 20 Apr 2011
Astronomy & Astrophysics manuscript no. LOD Venus c ESO April, About the various contributions in Venus rotation rate and LOD L. Cottereau, N. Rambaux,, S. Lebonnois 4, J. Souchay arxiv:4.49v astro-ph.ep
More informationHalliday, Resnick & Walker Chapter 13. Gravitation. Physics 1A PHYS1121 Professor Michael Burton
Halliday, Resnick & Walker Chapter 13 Gravitation Physics 1A PHYS1121 Professor Michael Burton II_A2: Planetary Orbits in the Solar System + Galaxy Interactions (You Tube) 21 seconds 13-1 Newton's Law
More informationChapter 11. h = 5m. = mgh + 1 2 mv 2 + 1 2 Iω 2. E f. = E i. v = 4 3 g(h h) = 4 3 9.8m / s2 (8m 5m) = 6.26m / s. ω = v r = 6.
Chapter 11 11.7 A solid cylinder of radius 10cm and mass 1kg starts from rest and rolls without slipping a distance of 6m down a house roof that is inclined at 30 degrees (a) What is the angular speed
More informationMidterm Solutions. mvr = ω f (I wheel + I bullet ) = ω f 2 MR2 + mr 2 ) ω f = v R. 1 + M 2m
Midterm Solutions I) A bullet of mass m moving at horizontal velocity v strikes and sticks to the rim of a wheel a solid disc) of mass M, radius R, anchored at its center but free to rotate i) Which of
More informationToday. Solstices & Equinoxes Precession Phases of the Moon Eclipses. Ancient Astronomy. Lunar, Solar FIRST HOMEWORK DUE NEXT TIME
Today Solstices & Equinoxes Precession Phases of the Moon Eclipses Lunar, Solar Ancient Astronomy FIRST HOMEWORK DUE NEXT TIME The Reason for Seasons Hypothesis check: How would seasons in the northern
More informationPlanets beyond the solar system
Planets beyond the solar system Review of our solar system Why search How to search Eclipses Motion of parent star Doppler Effect Extrasolar planet discoveries A star is 5 parsecs away, what is its parallax?
More informationSo if ω 0 increases 3-fold, the stopping angle increases 3 2 = 9-fold.
Name: MULTIPLE CHOICE: Questions 1-11 are 5 points each. 1. A safety device brings the blade of a power mower from an angular speed of ω 1 to rest in 1.00 revolution. At the same constant angular acceleration,
More informationStudy Guide: Sun, Earth and Moon Relationship Assessment
I can 1. Define rotation, revolution, solstice and equinox. *Rotation and Revolution Review Worksheet 2. Describe why we experience days and years due to the rotation and r evolution of the Earth around
More informationThe Moon. Nicola Loaring, SAAO
The Moon Nicola Loaring, SAAO Vital Statistics Mean distance from Earth Orbital Period Rotational Period Diameter 384,400 km 27.322 days 27.322 days 3476 km (0.272 x Earth) Mass 7.3477 10 22 kg (0.0123
More informationPhysics 1A Lecture 10C
Physics 1A Lecture 10C "If you neglect to recharge a battery, it dies. And if you run full speed ahead without stopping for water, you lose momentum to finish the race. --Oprah Winfrey Static Equilibrium
More informationTropical Horticulture: Lecture 2
Lecture 2 Theory of the Tropics Earth & Solar Geometry, Celestial Mechanics The geometrical relationship between the earth and sun is responsible for the earth s climates. The two principal movements of
More informationExample application of the IAU 2000 resolutions concerning Earth orientation and rotation
Example application of the IAU 2000 resolutions concerning Earth orientation and rotation Patrick Wallace 1 (Original version 20 July 2004, revised 29 July 2004; this reformatted and corrected version
More informationA. 81 2 = 6561 times greater. B. 81 times greater. C. equally strong. D. 1/81 as great. E. (1/81) 2 = 1/6561 as great.
Q12.1 The mass of the Moon is 1/81 of the mass of the Earth. Compared to the gravitational force that the Earth exerts on the Moon, the gravitational force that the Moon exerts on the Earth is A. 81 2
More informationTIDES. 1. Tides are the regular rise and fall of sea level that occurs either once a day (every 24.8 hours) or twice a day (every 12.4 hours).
TIDES What causes tides? How are tides predicted? 1. Tides are the regular rise and fall of sea level that occurs either once a day (every 24.8 hours) or twice a day (every 12.4 hours). Tides are waves
More informationPHSC 3033: Meteorology Seasons
PHSC 3033: Meteorology Seasons Changing Aspect Angle Direct Sunlight is more intense and concentrated. Solar Incidence Angle is Latitude and Time/Date Dependent Daily and Seasonal Variation Zenith There
More informationLesson 1: Phases of the Moon
Lesson 1: Phases of the Moon The moon takes 29.5 days to revolve around the earth. During this time, the moon you see in the sky appears to change shape. These apparent changes, which are called phases,
More informationDynamics of Rotational Motion
Chapter 10 Dynamics of Rotational Motion PowerPoint Lectures for University Physics, Twelfth Edition Hugh D. Young and Roger A. Freedman Lectures by James Pazun Modified by P. Lam 5_31_2012 Goals for Chapter
More informationAstronomy 110 Homework #04 Assigned: 02/06/2007 Due: 02/13/2007. Name:
Astronomy 110 Homework #04 Assigned: 02/06/2007 Due: 02/13/2007 Name: Directions: Listed below are twenty (20) multiple-choice questions based on the material covered by the lectures this past week. Choose
More informationNote S1: Eclipses & Predictions
The Moon's Orbit The first part of this note gives reference information and definitions about eclipses [14], much of which would have been familiar to ancient Greek astronomers, though not necessarily
More information1. In the diagram below, the direct rays of the Sun are striking the Earth's surface at 23 º N. What is the date shown in the diagram?
1. In the diagram below, the direct rays of the Sun are striking the Earth's surface at 23 º N. What is the date shown in the diagram? 5. During how many days of a calendar year is the Sun directly overhead
More informationAn Introduction to Astronomy and Cosmology. 1) Astronomy - an Observational Science
An Introduction to Astronomy and Cosmology 1) Astronomy - an Observational Science Why study Astronomy 1 A fascinating subject in its own right. The origin and Evolution of the universe The Big Bang formation
More informationRS platforms. Fabio Dell Acqua - Gruppo di Telerilevamento
RS platforms Platform vs. instrument Sensor Platform Instrument The remote sensor can be ideally represented as an instrument carried by a platform Platforms Remote Sensing: Ground-based air-borne space-borne
More informationNight Sky III Planetary Motion Lunar Phases
Night Sky III Planetary Motion Lunar Phases Astronomy 1 Elementary Astronomy LA Mission College Spring F2015 Quotes & Cartoon of the Day Everything has a natural explanation. The moon is not a god, but
More informationSittiporn Channumsin Co-authors
28 Oct 2014 Space Glasgow Research Conference Sittiporn Channumsin Sittiporn Channumsin Co-authors S. Channumsin Outline Background Objective The model Simulation Results Conclusion and Future work 2 Space
More informationFrom Aristotle to Newton
From Aristotle to Newton The history of the Solar System (and the universe to some extent) from ancient Greek times through to the beginnings of modern physics. The Geocentric Model Ancient Greek astronomers
More informationSection 2. Satellite Orbits
Section 2. Satellite Orbits References Kidder and Vonder Haar: chapter 2 Stephens: chapter 1, pp. 25-30 Rees: chapter 9, pp. 174-192 In order to understand satellites and the remote sounding data obtained
More informationName Class Date. true
Exercises 131 The Falling Apple (page 233) 1 Describe the legend of Newton s discovery that gravity extends throughout the universe According to legend, Newton saw an apple fall from a tree and realized
More informationPresentation of problem T1 (9 points): The Maribo Meteorite
Presentation of problem T1 (9 points): The Maribo Meteorite Definitions Meteoroid. A small particle (typically smaller than 1 m) from a comet or an asteroid. Meteorite: A meteoroid that impacts the ground
More informationLecture 7 Formation of the Solar System. Nebular Theory. Origin of the Solar System. Origin of the Solar System. The Solar Nebula
Origin of the Solar System Lecture 7 Formation of the Solar System Reading: Chapter 9 Quiz#2 Today: Lecture 60 minutes, then quiz 20 minutes. Homework#1 will be returned on Thursday. Our theory must explain
More informationEarth in the Solar System
Copyright 2011 Study Island - All rights reserved. Directions: Challenge yourself! Print out the quiz or get a pen/pencil and paper and record your answers to the questions below. Check your answers with
More informationOrbital Mechanics. Angular Momentum
Orbital Mechanics The objects that orbit earth have only a few forces acting on them, the largest being the gravitational pull from the earth. The trajectories that satellites or rockets follow are largely
More informationSolar energy and the Earth s seasons
Solar energy and the Earth s seasons Name: Tilt of the Earth s axis and the seasons We now understand that the tilt of Earth s axis makes it possible for different parts of the Earth to experience different
More informationExtra-solar massive planets with small semi-major axes?
Monografías de la Real Academia de Ciencias de Zaragoza. 25: 115 120, (2004). Extra-solar massive planets with small semi-major axes? S. Fernández, D. Giuliodori and M. A. Nicotra Observatorio Astronómico.
More informationAnswers for the Study Guide: Sun, Earth and Moon Relationship Test
Answers for the Study Guide: Sun, Earth and Moon Relationship Test 1) It takes one day for the Earth to make one complete on its axis. a. Rotation 2) It takes one year for the Earth to make one around
More informationSpacecraft Dynamics and Control. An Introduction
Brochure More information from http://www.researchandmarkets.com/reports/2328050/ Spacecraft Dynamics and Control. An Introduction Description: Provides the basics of spacecraft orbital dynamics plus attitude
More informationAPPENDIX D: SOLAR RADIATION
APPENDIX D: SOLAR RADIATION The sun is the source of most energy on the earth and is a primary factor in determining the thermal environment of a locality. It is important for engineers to have a working
More informationThe following words and their definitions should be addressed before completion of the reading:
Seasons Vocabulary: The following words and their definitions should be addressed before completion of the reading: sphere any round object that has a surface that is the same distance from its center
More informationLecture L3 - Vectors, Matrices and Coordinate Transformations
S. Widnall 16.07 Dynamics Fall 2009 Lecture notes based on J. Peraire Version 2.0 Lecture L3 - Vectors, Matrices and Coordinate Transformations By using vectors and defining appropriate operations between
More informationLab 8: Ballistic Pendulum
Lab 8: Ballistic Pendulum Equipment: Ballistic pendulum apparatus, 2 meter ruler, 30 cm ruler, blank paper, carbon paper, masking tape, scale. Caution In this experiment a steel ball is projected horizontally
More informationα α λ α = = λ λ α ψ = = α α α λ λ ψ α = + β = > θ θ β > β β θ θ θ β θ β γ θ β = γ θ > β > γ θ β γ = θ β = θ β = θ β = β θ = β β θ = = = β β θ = + α α α α α = = λ λ λ λ λ λ λ = λ λ α α α α λ ψ + α =
More informationSatellite Posi+oning. Lecture 5: Satellite Orbits. Jan Johansson jan.johansson@chalmers.se Chalmers University of Technology, 2013
Lecture 5: Satellite Orbits Jan Johansson jan.johansson@chalmers.se Chalmers University of Technology, 2013 Geometry Satellite Plasma Posi+oning physics Antenna theory Geophysics Time and Frequency GNSS
More informationSimulation, prediction and analysis of Earth rotation parameters
Simulation, prediction and analysis of Earth rotation parameters with a dynamic Earth system model Florian Seitz Earth Oriented Space Science and Technology (ESPACE) 20.9.2011 Earth rotation parameters
More informationLocal Sidereal Time is the hour angle of the First Point of Aries, and is equal to the hour angle plus right ascension of any star.
1 CHAPTER 7 TIME In this chapter we briefly discuss the several time scales that are in use in astronomy, such as Universal Time, Mean Solar Time, Ephemeris Time, Terrestrial Dynamical Time, and the several
More informationScience Standard 4 Earth in Space Grade Level Expectations
Science Standard 4 Earth in Space Grade Level Expectations Science Standard 4 Earth in Space Our Solar System is a collection of gravitationally interacting bodies that include Earth and the Moon. Universal
More informationAngular Velocity vs. Linear Velocity
MATH 7 Angular Velocity vs. Linear Velocity Dr. Neal, WKU Given an object with a fixed speed that is moving in a circle with a fixed ius, we can define the angular velocity of the object. That is, we can
More informationPHY121 #8 Midterm I 3.06.2013
PHY11 #8 Midterm I 3.06.013 AP Physics- Newton s Laws AP Exam Multiple Choice Questions #1 #4 1. When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension
More informationLinear Motion vs. Rotational Motion
Linear Motion vs. Rotational Motion Linear motion involves an object moving from one point to another in a straight line. Rotational motion involves an object rotating about an axis. Examples include a
More informationNeutron stars as laboratories for exotic physics
Ian Jones Neutron stars as laboratories for exotic physics 1/20 Neutron stars as laboratories for exotic physics Ian Jones D.I.Jones@soton.ac.uk General Relativity Group, Southampton University Context
More informationPh\sics 2210 Fall 2012 - Novcmbcr 21 David Ailion
Ph\sics 2210 Fall 2012 - Novcmbcr 21 David Ailion Unid: Discussion T A: Bryant Justin Will Yuan 1 Place answers in box provided for each question. Specify units for each answer. Circle correct answer(s)
More informationRotation: Moment of Inertia and Torque
Rotation: Moment of Inertia and Torque Every time we push a door open or tighten a bolt using a wrench, we apply a force that results in a rotational motion about a fixed axis. Through experience we learn
More informationSection 4: The Basics of Satellite Orbits
Section 4: The Basics of Satellite Orbits MOTION IN SPACE VS. MOTION IN THE ATMOSPHERE The motion of objects in the atmosphere differs in three important ways from the motion of objects in space. First,
More information