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Appendix a Orbits
Appendix A Orbits As discussed in the Introduction, a good ¯rst approximation for satellite motion is obtained by assuming the spacecraft is a point mass or spherical body moving in the gravitational ¯eld of a spherical planet. This leads to the classical two-body problem. Since we use the term body to refer to a spacecraft of ¯nite size (as in rigid body), it may be more appropriate to call this the two-particle problem, but I will use the term two-body problem in its classical sense. The basic elements of orbital dynamics are captured in Kepler's three laws which he published in the 17th century. His laws were for the orbital motion of the planets about the Sun, but are also applicable to the motion of satellites about planets. The three laws are: 1. The orbit of each planet is an ellipse with the Sun at one focus. 2. The line joining the planet to the Sun sweeps out equal areas in equal times. 3. The square of the period of a planet is proportional to the cube of its mean distance to the sun. The ¯rst law applies to most spacecraft, but it is also possible for spacecraft to travel in parabolic and hyperbolic orbits, in which case the period is in¯nite and the 3rd law does not apply. However, the 2nd law applies to all two-body motion. Newton's 2nd law and his law of universal gravitation provide the tools for generalizing Kepler's laws to non-elliptical orbits, as well as for proving Kepler's laws. -
Ionizing Feedback from Massive Stars in Massive Clusters III: Disruption of Partially Unbound Clouds 3
Mon. Not. R. Astron. Soc. 000, 1–14 (2006) Printed 30 August 2021 (MN LATEX style file v2.2) Ionizing feedback from massive stars in massive clusters III: Disruption of partially unbound clouds J. E. Dale1⋆, B. Ercolano1, I. A. Bonnell2 1Excellence Cluster ‘Universe’, Boltzmannstr. 2, 85748 Garching, Germany. 2Department of Physics and Astronomy, University of St Andrews, North Haugh, St Andrews, Fife KY16 9SS 30 August 2021 ABSTRACT We extend our previous SPH parameter study of the effects of photoionization from O–stars on star–forming clouds to include initially unbound clouds. We generate a set 4 6 of model clouds in the mass range 10 -10 M⊙ with initial virial ratios Ekin/Epot=2.3, allow them to form stars, and study the impact of the photoionizing radiation pro- duced by the massive stars. We find that, on the 3Myr timescale before supernovae are expected to begin detonating, the fractions of mass expelled by ionizing feedback is a very strong function of the cloud escape velocities. High–mass clouds are largely unaf- fected dynamically, while lower–mass clouds have large fractions of their gas reserves expelled on this timescale. However, the fractions of stellar mass unbound are modest and significant portions of the unbound stars are so only because the clouds themselves are initially partially unbound. We find that ionization is much more able to create well–cleared bubbles in the unbound clouds, owing to their intrinsic expansion, but that the presence of such bubbles does not necessarily indicate that a given cloud has been strongly influenced by feedback. -
ESO's VLT Sphere and DAMIT
ESO’s VLT Sphere and DAMIT ESO’s VLT SPHERE (using adaptive optics) and Joseph Durech (DAMIT) have a program to observe asteroids and collect light curve data to develop rotating 3D models with respect to time. Up till now, due to the limitations of modelling software, only convex profiles were produced. The aim is to reconstruct reliable nonconvex models of about 40 asteroids. Below is a list of targets that will be observed by SPHERE, for which detailed nonconvex shapes will be constructed. Special request by Joseph Durech: “If some of these asteroids have in next let's say two years some favourable occultations, it would be nice to combine the occultation chords with AO and light curves to improve the models.” 2 Pallas, 7 Iris, 8 Flora, 10 Hygiea, 11 Parthenope, 13 Egeria, 15 Eunomia, 16 Psyche, 18 Melpomene, 19 Fortuna, 20 Massalia, 22 Kalliope, 24 Themis, 29 Amphitrite, 31 Euphrosyne, 40 Harmonia, 41 Daphne, 51 Nemausa, 52 Europa, 59 Elpis, 65 Cybele, 87 Sylvia, 88 Thisbe, 89 Julia, 96 Aegle, 105 Artemis, 128 Nemesis, 145 Adeona, 187 Lamberta, 211 Isolda, 324 Bamberga, 354 Eleonora, 451 Patientia, 476 Hedwig, 511 Davida, 532 Herculina, 596 Scheila, 704 Interamnia Occultation Event: Asteroid 10 Hygiea – Sun 26th Feb 16h37m UT The magnitude 11 asteroid 10 Hygiea is expected to occult the magnitude 12.5 star 2UCAC 21608371 on Sunday 26th Feb 16h37m UT (= Mon 3:37am). Magnitude drop of 0.24 will require video. DAMIT asteroid model of 10 Hygiea - Astronomy Institute of the Charles University: Josef Ďurech, Vojtěch Sidorin Hygiea is the fourth-largest asteroid (largest is Ceres ~ 945kms) in the Solar System by volume and mass, and it is located in the asteroid belt about 400 million kms away. -
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: -
An Overview of New Worlds, New Horizons in Astronomy and Astrophysics About the National Academies
2020 VISION An Overview of New Worlds, New Horizons in Astronomy and Astrophysics About the National Academies The National Academies—comprising the National Academy of Sciences, the National Academy of Engineering, the Institute of Medicine, and the National Research Council—work together to enlist the nation’s top scientists, engineers, health professionals, and other experts to study specific issues in science, technology, and medicine that underlie many questions of national importance. The results of their deliberations have inspired some of the nation’s most significant and lasting efforts to improve the health, education, and welfare of the United States and have provided independent advice on issues that affect people’s lives worldwide. To learn more about the Academies’ activities, check the website at www.nationalacademies.org. Copyright 2011 by the National Academy of Sciences. All rights reserved. Printed in the United States of America This study was supported by Contract NNX08AN97G between the National Academy of Sciences and the National Aeronautics and Space Administration, Contract AST-0743899 between the National Academy of Sciences and the National Science Foundation, and Contract DE-FG02-08ER41542 between the National Academy of Sciences and the U.S. Department of Energy. Support for this study was also provided by the Vesto Slipher Fund. Any opinions, findings, conclusions, or recommendations expressed in this publication are those of the authors and do not necessarily reflect the views of the agencies that provided support for the project. 2020 VISION An Overview of New Worlds, New Horizons in Astronomy and Astrophysics Committee for a Decadal Survey of Astronomy and Astrophysics ROGER D. -
Year XIX, Supplement Ethnographic Study And/Or a Theoretical Survey of a Their Position in the Article Should Be Clearly Indicated
III. TITLES OF ARTICLES DRU[TVO ANTROPOLOGOV SLOVENIJE The journal of the Slovene Anthropological Society Titles (in English and Slovene) must be short, informa- SLOVENE ANTHROPOLOGICAL SOCIETY Anthropological Notebooks welcomes the submis- tive, and understandable. The title should be followed sion of papers from the field of anthropology and by the name of the author(s), their position, institutional related disciplines. Submissions are considered for affiliation, and if possible, by e-mail address. publication on the understanding that the paper is not currently under consideration for publication IV. ABSTRACT AND KEYWORDS elsewhere. It is the responsibility of the author to The abstract must give concise information about the obtain permission for using any previously published objective, the method used, the results obtained, and material. Please submit your manuscript as an e-mail the conclusions. Authors are asked to enclose in English attachment on [email protected] and enclose your contact information: name, position, and Slovene an abstract of 100 – 200 words followed institutional affiliation, address, phone number, and by three to five keywords. They must reflect the field of e-mail address. research covered in the article. English abstract should be placed at the beginning of an article and the Slovene one after the references at the end. V. NOTES A N T H R O P O L O G I C A L INSTRUCTIONS Notes should also be double-spaced and used sparingly. They must be numbered consecutively throughout the text and assembled at the end of the article just before references. VI. QUOTATIONS Short quotations (less than 30 words) should be placed in single quotation marks with double marks for quotations within quotations. -
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. -
Interplanetary Trajectories in STK in a Few Hundred Easy Steps*
Interplanetary Trajectories in STK in a Few Hundred Easy Steps* (*and to think that last year’s students thought some guidance would be helpful!) Satellite ToolKit Interplanetary Tutorial STK Version 9 INITIAL SETUP 1) Open STK. Choose the “Create a New Scenario” button. 2) Name your scenario and, if you would like, enter a description for it. The scenario time is not too critical – it will be updated automatically as we add segments to our mission. 3) STK will give you the opportunity to insert a satellite. (If it does not, or you would like to add another satellite later, you can click on the Insert menu at the top and choose New…) The Orbit Wizard is an easy way to add satellites, but we will choose Define Properties instead. We choose Define Properties directly because we want to use a maneuver-based tool called the Astrogator, which will undo any initial orbit set using the Orbit Wizard. Make sure Satellite is selected in the left pane of the Insert window, then choose Define Properties in the right-hand pane and click the Insert…button. 4) The Properties window for the Satellite appears. You can access this window later by right-clicking or double-clicking on the satellite’s name in the Object Browser (the left side of the STK window). When you open the Properties window, it will default to the Basic Orbit screen, which happens to be where we want to be. The Basic Orbit screen allows you to choose what kind of numerical propagator STK should use to move the satellite. -
Positional Astronomy Coordinate Systems
Positional Astronomy Observational Astronomy 2019 Part 2 Prof. S.C. Trager Coordinate systems We need to know where the astronomical objects we want to study are located in order to study them! We need a system (well, many systems!) to describe the positions of astronomical objects. The Celestial Sphere First we need the concept of the celestial sphere. It would be nice if we knew the distance to every object we’re interested in — but we don’t. And it’s actually unnecessary in order to observe them! The Celestial Sphere Instead, we assume that all astronomical sources are infinitely far away and live on the surface of a sphere at infinite distance. This is the celestial sphere. If we define a coordinate system on this sphere, we know where to point! Furthermore, stars (and galaxies) move with respect to each other. The motion normal to the line of sight — i.e., on the celestial sphere — is called proper motion (which we’ll return to shortly) Astronomical coordinate systems A bit of terminology: great circle: a circle on the surface of a sphere intercepting a plane that intersects the origin of the sphere i.e., any circle on the surface of a sphere that divides that sphere into two equal hemispheres Horizon coordinates A natural coordinate system for an Earth- bound observer is the “horizon” or “Alt-Az” coordinate system The great circle of the horizon projected on the celestial sphere is the equator of this system. Horizon coordinates Altitude (or elevation) is the angle from the horizon up to our object — the zenith, the point directly above the observer, is at +90º Horizon coordinates We need another coordinate: define a great circle perpendicular to the equator (horizon) passing through the zenith and, for convenience, due north This line of constant longitude is called a meridian Horizon coordinates The azimuth is the angle measured along the horizon from north towards east to the great circle that intercepts our object (star) and the zenith. -
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. -
The Minor Planet Bulletin 37 (2010) 45 Classification for 244 Sita
THE MINOR PLANET BULLETIN OF THE MINOR PLANETS SECTION OF THE BULLETIN ASSOCIATION OF LUNAR AND PLANETARY OBSERVERS VOLUME 37, NUMBER 2, A.D. 2010 APRIL-JUNE 41. LIGHTCURVE AND PHASE CURVE OF 1130 SKULD Robinson (2009) from his data taken in 2002. There is no evidence of any change of (V-R) color with asteroid rotation. Robert K. Buchheim Altimira Observatory As a result of the relatively short period of this lightcurve, every 18 Altimira, Coto de Caza, CA 92679 (USA) night provided at least one minimum and maximum of the [email protected] lightcurve. The phase curve was determined by polling both the maximum and minimum points of each night’s lightcurve. Since (Received: 29 December) The lightcurve period of asteroid 1130 Skuld is confirmed to be P = 4.807 ± 0.002 h. Its phase curve is well-matched by a slope parameter G = 0.25 ±0.01 The 2009 October-November apparition of asteroid 1130 Skuld presented an excellent opportunity to measure its phase curve to very small solar phase angles. I devoted 13 nights over a two- month period to gathering photometric data on the object, over which time the solar phase angle ranged from α = 0.3 deg to α = 17.6 deg. All observations used Altimira Observatory’s 0.28-m Schmidt-Cassegrain telescope (SCT) working at f/6.3, SBIG ST- 8XE NABG CCD camera, and photometric V- and R-band filters. Exposure durations were 3 or 4 minutes with the SNR > 100 in all images, which were reduced with flat and dark frames. -
IRTF Spectra for 17 Asteroids from the C and X Complexes: a Discussion of Continuum Slopes and Their Relationships to C Chondrites and Phyllosilicates ⇑ Daniel R
Icarus 212 (2011) 682–696 Contents lists available at ScienceDirect Icarus journal homepage: www.elsevier.com/locate/icarus IRTF spectra for 17 asteroids from the C and X complexes: A discussion of continuum slopes and their relationships to C chondrites and phyllosilicates ⇑ Daniel R. Ostrowski a, Claud H.S. Lacy a,b, Katherine M. Gietzen a, Derek W.G. Sears a,c, a Arkansas Center for Space and Planetary Sciences, University of Arkansas, Fayetteville, AR 72701, United States b Department of Physics, University of Arkansas, Fayetteville, AR 72701, United States c Department of Chemistry and Biochemistry, University of Arkansas, Fayetteville, AR 72701, United States article info abstract Article history: In order to gain further insight into their surface compositions and relationships with meteorites, we Received 23 April 2009 have obtained spectra for 17 C and X complex asteroids using NASA’s Infrared Telescope Facility and SpeX Revised 20 January 2011 infrared spectrometer. We augment these spectra with data in the visible region taken from the on-line Accepted 25 January 2011 databases. Only one of the 17 asteroids showed the three features usually associated with water, the UV Available online 1 February 2011 slope, a 0.7 lm feature and a 3 lm feature, while five show no evidence for water and 11 had one or two of these features. According to DeMeo et al. (2009), whose asteroid classification scheme we use here, 88% Keywords: of the variance in asteroid spectra is explained by continuum slope so that asteroids can also be charac- Asteroids, composition terized by the slopes of their continua.