THE SMALL SATELLITES of PLUTO. S. B. Porter1, M. R. Showalter2, H

Total Page:16

File Type:pdf, Size:1020Kb

THE SMALL SATELLITES of PLUTO. S. B. Porter1, M. R. Showalter2, H 47th Lunar and Planetary Science Conference (2016) 2390.pdf THE SMALL SATELLITES OF PLUTO. S. B. Porter1, M. R. Showalter2, H. A. Weaver3, J. R. Spencer1, R. P. Binzel4, D. P. Hamilton5, T. R. Lauer6, T. Stryk7, M. W. Buie1, B. Buratti8, A. J. Verbiscer9, A. H. Parker1, K. Sing- er1, W. McKinnon10, S. Robbins1, J. Moore11, W. Grundy12, S. A. Stern1, L. A. Young1, C. B. Olkin1, K. Ennico11 and the New Horizons Geology and Geophysics Imaging Team 1Southwest Research Institute (por- [email protected]), 2SETI Institute, 3Johns Hopkins APL, 4MIT, 5U. Maryland, 6NOAO, 7Roane State Commu- nity College, 8JPL, 9U. Virginia, 10Washington U., 11NASA Ames, 12Lowell Observatory Introduction: The Pluto dwarf planetary system respective orbital poles [10]. The poles of Styx and consists of six bodies orbiting their common center of Kerberos are inclined 80-90° to their orbits. The pole mass; the large inner binary Pluto (2374±4 km diame- of Nix is inclined 120-130° to its orbit. At this high ter) and Charon (1212±3 km diameter) [1] is surround- inclination, Nix’s rotation should be more perturbed by ed by four much smaller (~10-50 km diameter) satel- Charon than Styx or Kerberos, and this may be ex- lites, Styx, Nix, Kerberos, and Hydra [1]. All four of pressed in the variations seen in Nix’s rotation period these satellites are on near-circular orbits with low [11]. The pole of Hydra is harder to determine, as it inclinations to the orbital plane of the inner binary [2]. was pointing towards the spacecraft at the time the Discovery and Exploration: The brighter two of highest resolution images were taken, however it can Pluto’s small satellites, Nix and Hydra, were discov- be constrained to within 90-120° of its orbital pole. ered in 2005 [3]. Subsequent observations discovered Surfaces and Composition: The encounter face of Kerberos in 2011 [4] and Styx in 2012 [5]. NASA’s Nix appears to show a cratered surface of mostly New Horizons spacecraft was launched to the Pluto uniform composition. There is a large crater on the system in January 2006 and arrived in July 2015 [1]. encounter face, ~15 km diameter [12]. Around this Nix and Hydra were included in the science targeting crater is a region that is “redder” (larger Blue/NIR ra- schedule uploaded to the spacecraft shortly after tio) than the surrounding terrain. This may be evidence launch, but the late discovery of Styx and Kerberos of the crater excavating darker material from below, or only allowed limited imaging of those satellites. New of two compositionally distinct regions. A lower- Horizons flew closest to Nix, and on Nix’s day side, resolution color image of Hydra showed it to be a uni- allowing high quality imaging. The other three small form color similar to the light terrain on Nix. Numer- satellites were on the far side of the system (see Figure ous craters at the 1-2 km scale are apparent on both 1), and were imaged at lower resolution. Extensive Nix and Hydra [12]. Crater retention ages > 4 Gyr are searches for additional satellites by New Horizons on found for both Nix and Hydra. approach to Pluto did not detect any new satellites [1]. Relevance to the Proposed New Horizons Ex- Orbits and Stability: The Pluto system is a tended Mission: In October and November 2015, uniquely complex dynamical hierarchy in the solar New Horizons performed maneuvers to enable a pro- system. The small satellites orbit around the barycenter posed flyby of 2014 MU69 (formerly known as PT1). If of the central Pluto-Charon binary and are strongly NASA approves a New Horizons Extended Mission, perturbed by Charon [2]. Orbits interior to the 2:1 this flyby would occur on January 1, 2019 [13]. 2014 Charon Mean Motion Resonance (MMR) are generally MU69 is a cold classical Kuiper Belt object similar in unstable [6], except for highly inclined orbits between size to the small satellites of Pluto (30-50 km across). Pluto and Charon [8]. The satellites orbit close to (but If approved, New Horizons will perform a day-side not perfectly at) the 3:1, 4:1, 5:1, and 6:1 Charon flyby that will permit spatial resolutions similar to MMRs [2]. This very close packing and the strong those achieved on Pluto. perturbation by Charon severely limits where stable References: [1] Stern S.A. et al. (2015) Science, orbits lie between Styx and Hydra [7]. New Horizons 350, 292–300. [2] Brozović M. et al. (2015) Icarus, performed a deep search for new satellites in the Pluto 246, 317–329. [3] Weaver, H.A., et al. (2006) Nature, system, but none were detected [1]. 439, 943–945. [4] Showalter, M.R. et al. (2011) CBAT, Rotational Rates and Poles: All four small satel- 2769. [5] Showalter, M.R. et al. (2012) IAU Circ., lites exhibited brightness variations in pre-flyby obser- 9253. [6] Stern, S.A. et al. (1994) Icarus, 108, 2. [7] vations by the Hubble Space Telescope. This was in- Youdin, A.N. et al. (2012) ApJ 755, 17. [8] Giuliatti terpreted by [9] to mean that they were rotating chaoti- Winter et al. (2010) MNRAS 404, 1. [9] Showalter, cally at a rate close to their orbital period. However, M.R. and Hamilton, D.P. (2015) Nature, 522, 7554. photometry taken by New Horizons on approach to [10] Porter, S.B. et al. (2015) DPS 47, #102.10. [11] Pluto showed that all four small satellites were rotating Showalter, M.R. et al. (2015) DPS 47, #102.09. [12] much faster than their orbital periods. In addition, all Weaver, H.A. et al. 2015 DPS 47, #102.07. [13] Porter, four rotational poles are significantly inclined to their S.B. et al (2015) LPS XXXXVII, #1310. 47th Lunar and Planetary Science Conference (2016) 2390.pdf Figure 1: Diagram of the Pluto system at the time of the New Horizons flyby. The spacecraft trajectory crosses the Pluto-Charon plane from above the page and right to below the page and left and inclined at 43° to the plane. The flyby geometry favored observations of Nix and Styx, but Styx was discovered so late (2012) that only a single resolved observation could be scheduled. Figure 2: The highest-resolution images of the small satellites of Pluto, with the limb of Charon for scale. .
Recommended publications
  • DOUGLAS P. HAMILTON Career Summary Professor, University of Maryland, Astronomy Dept., 9/1995 – Present
    CURRICULUM VITAE: DOUGLAS P. HAMILTON Career Summary Professor, University of Maryland, Astronomy Dept., 9/1995 { Present. Postdoctoral Scholar, MPI Kernphysik, Heidelberg Germany, 12/1993 { 9/1995. Cornell University, M.S. and Ph.D. in Applied Physics, 8/1990 and 1/1994. Stanford University, B.S. in Physics with Distinction and Honors, 6/1988. Academic Honors NASA Group Achievement Award (New Horizons Team) 2016. U. Maryland Board of Regent's Faculty Award for Scholarship 2010. Dean's Award for Excellence in Teaching 1997, 2008. U. Maryland Parents Association, Outstanding Faculty Nominee 2003. Certificate of Teaching Excellence 2003. Asteroid 12494 DH11 renamed Doughamilton 2000. Harold C. Urey Prize for Outstanding Research in Planetary Science 1999. NSF CAREER Award \Orbital Dynamics of Solar System Dust" 1998-2003. Professional Activities Co-Investigator with NASA's Juno mission to Jupiter. Collaborator with NASA's New Horizons mission to Pluto. Co-Investigator with the Galileo Dust Detection System (DDS) Team. Reviewer on over 100 occasions for 18 scientific journals and 6 book publishers. Reviewer for 6 domestic and 3 foreign funding agencies. Member of IAU C-A4 Organizing Committee (2015-Present); DDA Vice Chair, Chair, Past Chair (2011-2014); DDA Student Participation Committee (2005-2007); AAS Shapley Lecturer (2006-Present); DDA Committee (2003-2005); DPS Prize Committee (2000-2003); AAS Millennium Speaker (2000-2003); Planetary Data System Rings Node Advisory Council (1997-Present); Icarus editorial board (1999- 2002); AAS, AGU, DDA, DPS and IAU societies. Research Interests Solar System Dynamics: Orbital Evolution; Celestial Mechanics; Resonances; Numerical Methods; Rotational Dynamics; Charged Particle Motion. Origins: Satellite and Ring Systems; The Solar System; Extrasolar Planets.
    [Show full text]
  • New Horizons Pluto/KBO Mission Impact Hazard
    New Horizons Pluto/KBO Mission Impact Hazard Hal Weaver NH Project Scientist The Johns Hopkins University Applied Physics Laboratory Outline • Background on New Horizons mission • Description of Impact Hazard problem • Impact Hazard mitigation – Hubble Space Telescope plays a key role New Horizons: To Pluto and Beyond The Initial Reconnaissance of The Solar System’s “Third Zone” KBOs Pluto-Charon Jupiter System 2016-2020 July 2015 Feb-March 2007 Launch Jan 2006 PI: Alan Stern (SwRI) PM: JHU Applied Physics Lab New Horizons is NASA’s first New Frontiers Mission Frontier of Planetary Science Explore a whole new region of the Solar System we didn’t even know existed until the 1990s Pluto is no longer an outlier! Pluto System is prototype of KBOs New Horizons gives the first close-up view of these newly discovered worlds New Horizons Now (overhead view) NH Spacecraft & Instruments 2.1 meters Science Team: PI: Alan Stern Fran Bagenal Rick Binzel Bonnie Buratti Andy Cheng Dale Cruikshank Randy Gladstone Will Grundy Dave Hinson Mihaly Horanyi Don Jennings Ivan Linscott Jeff Moore Dave McComas Bill McKinnon Ralph McNutt Scott Murchie Cathy Olkin Carolyn Porco Harold Reitsema Dennis Reuter Dave Slater John Spencer Darrell Strobel Mike Summers Len Tyler Hal Weaver Leslie Young Pluto System Science Goals Specified by NASA or Added by New Horizons New Horizons Resolution on Pluto (Simulations of MVIC context imaging vs LORRI high-resolution "noodles”) 0.1 km/pix The Best We Can Do Now 0.6 km/pix HST/ACS-PC: 540 km/pix New Horizons Science Status •
    [Show full text]
  • A Deep Search for Additional Satellites Around the Dwarf Planet
    Search for Additional Satellites around Haumea A Preprint typeset using LTEX style emulateapj v. 01/23/15 A DEEP SEARCH FOR ADDITIONAL SATELLITES AROUND THE DWARF PLANET HAUMEA Luke D. Burkhart1,2, Darin Ragozzine1,3,4, Michael E. Brown5 Search for Additional Satellites around Haumea ABSTRACT Haumea is a dwarf planet with two known satellites, an unusually high spin rate, and a large collisional family, making it one of the most interesting objects in the outer solar system. A fully self-consistent formation scenario responsible for the satellite and family formation is still elusive, but some processes predict the initial formation of many small moons, similar to the small moons recently discovered around Pluto. Deep searches for regular satellites around KBOs are difficult due to observational limitations, but Haumea is one of the few for which sufficient data exist. We analyze Hubble Space Telescope (HST) observations, focusing on a ten-consecutive-orbit sequence obtained in July 2010, to search for new very small satellites. To maximize the search depth, we implement and validate a non-linear shift-and-stack method. No additional satellites of Haumea are found, but by implanting and recovering artificial sources, we characterize our sensitivity. At distances between 10,000 km and 350,000 km from Haumea, satellites with radii as small as 10 km are ruled out, assuming∼ an albedo∼ (p 0.7) similar to Haumea. We also rule out satellites larger∼ than &40 km in most of the Hill sphere using≃ other HST data. This search method rules out objects similar in size to the small moons of Pluto.
    [Show full text]
  • CHORUS: Let's Go Meet the Dwarf Planets There Are Five in Our Solar
    Meet the Dwarf Planet Lyrics: CHORUS: Let’s go meet the dwarf planets There are five in our solar system Let’s go meet the dwarf planets Now I’ll go ahead and list them I’ll name them again in case you missed one There’s Pluto, Ceres, Eris, Makemake and Haumea They haven’t broken free from all the space debris There’s Pluto, Ceres, Eris, Makemake and Haumea They’re smaller than Earth’s moon and they like to roam free I’m the famous Pluto – as many of you know My orbit’s on a different path in the shape of an oval I used to be planet number 9, But I break the rules; I’m one of a kind I take my time orbiting the sun It’s a long, long trip, but I’m having fun! Five moons keep me company On our epic journey Charon’s the biggest, and then there’s Nix Kerberos, Hydra and the last one’s Styx 248 years we travel out Beyond the other planet’s regular rout We hang out in the Kuiper Belt Where the ice debris will never melt CHORUS My name is Ceres, and I’m closest to the sun They found me in the Asteroid Belt in 1801 I’m the only known dwarf planet between Jupiter and Mars They thought I was an asteroid, but I’m too round and large! I’m Eris the biggest dwarf planet, and the slowest one… It takes me 557 years to travel around the sun I have one moon, Dysnomia, to orbit along with me We go way out past the Kuiper Belt, there’s so much more to see! CHORUS My name is Makemake, and everyone thought I was alone But my tiny moon, MK2, has been with me all along It takes 310 years for us to orbit ‘round the sun But out here in the Kuiper Belt… our adventures just begun Hello my name’s Haumea, I’m not round shaped like my friends I rotate fast, every 4 hours, which stretched out both my ends! Namaka and Hi’iaka are my moons, I have just 2 And we live way out past Neptune in the Kuiper Belt it’s true! CHORUS Now you’ve met the dwarf planets, there are 5 of them it’s true But the Solar System is a great big place, with more exploring left to do Keep watching the skies above us with a telescope you look through Because the next person to discover one… could be me or you… .
    [Show full text]
  • Anticipated Scientific Investigations at the Pluto System
    Space Sci Rev (2008) 140: 93–127 DOI 10.1007/s11214-008-9462-9 New Horizons: Anticipated Scientific Investigations at the Pluto System Leslie A. Young · S. Alan Stern · Harold A. Weaver · Fran Bagenal · Richard P. Binzel · Bonnie Buratti · Andrew F. Cheng · Dale Cruikshank · G. Randall Gladstone · William M. Grundy · David P. Hinson · Mihaly Horanyi · Donald E. Jennings · Ivan R. Linscott · David J. McComas · William B. McKinnon · Ralph McNutt · Jeffery M. Moore · Scott Murchie · Catherine B. Olkin · Carolyn C. Porco · Harold Reitsema · Dennis C. Reuter · John R. Spencer · David C. Slater · Darrell Strobel · Michael E. Summers · G. Leonard Tyler Received: 5 January 2007 / Accepted: 28 October 2008 / Published online: 3 December 2008 © Springer Science+Business Media B.V. 2008 L.A. Young () · S.A. Stern · C.B. Olkin · J.R. Spencer Southwest Research Institute, Boulder, CO, USA e-mail: [email protected] H.A. Weaver · A.F. Cheng · R. McNutt · S. Murchie Johns Hopkins University Applied Physics Lab., Laurel, MD, USA F. Bagenal · M. Horanyi University of Colorado, Boulder, CO, USA R.P. Binzel Massachusetts Institute of Technology, Cambridge, MA, USA B. Buratti Jet Propulsion Laboratory, Pasadena, CA, USA D. Cruikshank · J.M. Moore NASA Ames Research Center, Moffett Field, CA, USA G.R. Gladstone · D.J. McComas · D.C. Slater Southwest Research Institute, San Antonio, TX, USA W.M. Grundy Lowell Observatory, Flagstaff, AZ, USA D.P. Hinson · I.R. Linscott · G.L. Tyler Stanford University, Stanford, CA, USA D.E. Jennings · D.C. Reuter NASA Goddard Space Flight Center, Greenbelt, MD, USA 94 L.A. Young et al.
    [Show full text]
  • Multi-Body Trajectory Design Strategies Based on Periapsis Poincaré Maps
    MULTI-BODY TRAJECTORY DESIGN STRATEGIES BASED ON PERIAPSIS POINCARÉ MAPS A Dissertation Submitted to the Faculty of Purdue University by Diane Elizabeth Craig Davis In Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy August 2011 Purdue University West Lafayette, Indiana ii To my husband and children iii ACKNOWLEDGMENTS I would like to thank my advisor, Professor Kathleen Howell, for her support and guidance. She has been an invaluable source of knowledge and ideas throughout my studies at Purdue, and I have truly enjoyed our collaborations. She is an inspiration to me. I appreciate the insight and support from my committee members, Professor James Longuski, Professor Martin Corless, and Professor Daniel DeLaurentis. I would like to thank the members of my research group, past and present, for their friendship and collaboration, including Geoff Wawrzyniak, Chris Patterson, Lindsay Millard, Dan Grebow, Marty Ozimek, Lucia Irrgang, Masaki Kakoi, Raoul Rausch, Matt Vavrina, Todd Brown, Amanda Haapala, Cody Short, Mar Vaquero, Tom Pavlak, Wayne Schlei, Aurelie Heritier, Amanda Knutson, and Jeff Stuart. I thank my parents, David and Jeanne Craig, for their encouragement and love throughout my academic career. They have cheered me on through many years of studies. I am grateful for the love and encouragement of my husband, Jonathan. His never-ending patience and friendship have been a constant source of support. Finally, I owe thanks to the organizations that have provided the funding opportunities that have supported me through my studies, including the Clare Booth Luce Foundation, Zonta International, and Purdue University and the School of Aeronautics and Astronautics through the Graduate Assistance in Areas of National Need and the Purdue Forever Fellowships.
    [Show full text]
  • Sha'áłchíní Welcome to Science Class! What If… My Teacher Gets Kicked August 27, 2020 out of Zoom?
    April 26, 2021 Yá’át’ééh! sha'áłchíní Welcome to science class! What if… My teacher gets kicked August 27, 2020 out of Zoom? Then.. 1. If you get assigned as the host end the meeting. 2. Everyone immediately log out of Zoom. 3. Re-enter the class in 5 minutes. 4. If you do not get back into the meeting after continuous tries, class is cancelled. 5. Refer to agenda slides from website. In case Mrs. Yazzie loses internet connection: ● someone becomes host ● host monitors class until Mrs. Yazzie returns or four minutes have passed ● after 4 minutes host ends class ● everyone tries to re-enter class ● if Mrs. Yazzie doesn’t return after another 4 minutes, class is ended for the day Sun. Mon. Tues. Wed. Thurs. Fri. Sat. 1 Intervention 2 3 Science Project PTC 4-7PM Check-In 4 5 6 7 8 9 10 No school Intervention Science Project Check-In 11 12 13 14 15 16 17 Intervention Science Project Due 40 points 18 19 20 21 22 23 24 Intervention 25 26 27 28 29 30 Community Forum Last Intervention NO SCHOOL 5:30pm No School Sun. Mon. Tues. Wed. Thurs. Fri. Sat. 25 26 27 28 29 30 1 Community Forum Last Day of Intervention 5:30PM No School 2 3 4 5 6 7 8 Last Day of Science Zoom No School 9 10 11 12 13 14 15 Mother’s No Zoom No Zoom No Zoom Return school laptops Day NWEA- Math NWEA-RDG NWEA-LANG No School 16 17 18 19 20 21 22 ALL WORK DUE No School 23 24 25 26 27 28 29 30 31 Last Day of School 8th Grade Promotion Announcements ● April 28th-Community Forum ● Friday, April 30th-NO SCHOOL ● Thurs., May 27th- 8th Grade Promotion ● Thurs., May 27th - Last Day of School Agenda -Announcements and Calendar -Student Objective & Essential Question -Intro to Vocabulary -Dwarf Planets -Kahoot! On a scale from 1-10 with 10 being excellent, how was your weekend? UPDATE! ● INGENUITY-2nd Flight Success! ● Perseverance makes oxygen! Student Objective Day 1, Monday: I can describe the relationship of objects in the solar system.
    [Show full text]
  • 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.
    [Show full text]
  • Study Points ⚫ Name a Dwarf Planet
    ⚫ What is the major difference between a planet and a dwarf planet? Study Points ⚫ Name a dwarf planet. ⚫ Where are the dwarf planets in our solar system? ⚫ Distinguish between a meteor, a meteorite, and a meteoroid. ⚫ What is a "shooting star"? Why do we see it? On average, how big is one? ⚫ Why do we study meteorites? ⚫ What is a comet? ⚫ Describe a comet including the nucleus, head and tail. Why do we see a comet? ⚫ Roughly, how big are comets? ⚫ What is the Asteroid Belt? the Oort Cloud? the Kuiper Belt? Where is each located? ⚫ Why study comets? ⚫ What is a meteor shower? What is the comet connection to a meteor shower? What’s in our solar system? Sun Planets Terrestrial Jovian Dwarf Small Solar System Bodies Meteoroids Comets Dust Sun (future lecture after Test 2 all about the Sun) a. Most of mass (>99%) of solar system b. Star – produces own energy by fusion c. Hot http://sohowww.nascom.nasa.gov/gallery/images/large/eit001_prev.jpg What’s in our solar system? Sun Planets Terrestrial Jovian http://www.techastronomy.com/UserFiles/2007/7/22/solar_system4(1).jpg From**KNOW Last THIS**Lecture: Terrestrial* Jovian* “Earth-like” “Jupiter-like” • Small, less massive • Large, massive • Close to Sun (warm) • Far from Sun (cold) • Rings • Big storms, turbulent atmosphere, belt rotation • Heavy elements • Hydrogen rich (light elements) • High density • Low density • Solid Surfaces • Gas and Liquid • Cratered • Few moons • Many moons • Thin atmospheres • Thick atmospheres • Weak magnetic fields • Large magnetic fields (some tilted) • Slow rotation
    [Show full text]
  • Perturbation Theory in Celestial Mechanics
    Perturbation Theory in Celestial Mechanics Alessandra Celletti Dipartimento di Matematica Universit`adi Roma Tor Vergata Via della Ricerca Scientifica 1, I-00133 Roma (Italy) ([email protected]) December 8, 2007 Contents 1 Glossary 2 2 Definition 2 3 Introduction 2 4 Classical perturbation theory 4 4.1 The classical theory . 4 4.2 The precession of the perihelion of Mercury . 6 4.2.1 Delaunay action–angle variables . 6 4.2.2 The restricted, planar, circular, three–body problem . 7 4.2.3 Expansion of the perturbing function . 7 4.2.4 Computation of the precession of the perihelion . 8 5 Resonant perturbation theory 9 5.1 The resonant theory . 9 5.2 Three–body resonance . 10 5.3 Degenerate perturbation theory . 11 5.4 The precession of the equinoxes . 12 6 Invariant tori 14 6.1 Invariant KAM surfaces . 14 6.2 Rotational tori for the spin–orbit problem . 15 6.3 Librational tori for the spin–orbit problem . 16 6.4 Rotational tori for the restricted three–body problem . 17 6.5 Planetary problem . 18 7 Periodic orbits 18 7.1 Construction of periodic orbits . 18 7.2 The libration in longitude of the Moon . 20 1 8 Future directions 20 9 Bibliography 21 9.1 Books and Reviews . 21 9.2 Primary Literature . 22 1 Glossary KAM theory: it provides the persistence of quasi–periodic motions under a small perturbation of an integrable system. KAM theory can be applied under quite general assumptions, i.e. a non– degeneracy of the integrable system and a diophantine condition of the frequency of motion.
    [Show full text]
  • 2015 October
    TTSIQ #13 page 1 OCTOBER 2015 www.nasa.gov/press-release/nasa-confirms-evidence-that-liquid-water-flows-on-today-s-mars Flash! Sept. 28, 2015: www.space.com/30674-flowing-water-on-mars-discovery-pictures.html www.space.com/30673-water-flows-on-mars-discovery.html - “boosting odds for life!” These dark, narrow, 100 meter~yards long streaks called “recurring slope lineae” flowing downhill on Mars are inferred to have been formed by contemporary flowing water www.space.com/30683-mars-liquid-water-astronaut-exploration.html INDEX 2 Co-sponsoring Organizations NEWS SECTION pp. 3-56 3-13 Earth Orbit and Mission to Planet Earth 13-14 Space Tourism 15-20 Cislunar Space and the Moon 20-28 Mars 29-33 Asteroids & Comets 34-47 Other Planets & their moons 48-56 Starbound ARTICLES & ESSAY SECTION pp 56-84 56 Replace "Pluto the Dwarf Planet" with "Pluto-Charon Binary Planet" 61 Kepler Shipyards: an Innovative force that could reshape the future 64 Moon Fans + Mars Fans => Collaboration on Joint Project Areas 65 Editor’s List of Needed Science Missions 66 Skyfields 68 Alan Bean: from “Moonwalker” to Artist 69 Economic Assessment and Systems Analysis of an Evolvable Lunar Architecture that Leverages Commercial Space Capabilities and Public-Private-Partnerships 71 An Evolved Commercialized International Space Station 74 Remembrance of Dr. APJ Abdul Kalam 75 The Problem of Rational Investment of Capital in Sustainable Futures on Earth and in Space 75 Recommendations to Overcome Non-Technical Challenges to Cleaning Up Orbital Debris STUDENTS & TEACHERS pp 85-96 Past TTSIQ issues are online at: www.moonsociety.org/international/ttsiq/ and at: www.nss.org/tothestarsOO TTSIQ #13 page 2 OCTOBER 2015 TTSIQ Sponsor Organizations 1.
    [Show full text]
  • On Optimal Two-Impulse Earth–Moon Transfers in a Four-Body Model
    Noname manuscript No. (will be inserted by the editor) On Optimal Two-Impulse Earth–Moon Transfers in a Four-Body Model F. Topputo Received: date / Accepted: date Abstract In this paper two-impulse Earth–Moon transfers are treated in the restricted four-body problem with the Sun, the Earth, and the Moon as primaries. The problem is formulated with mathematical means and solved through direct transcription and multiple shooting strategy. Thousands of solutions are found, which make it possible to frame known cases as special points of a more general picture. Families of solutions are defined and characterized, and their features are discussed. The methodology described in this paper is useful to perform trade-off analyses, where many solutions have to be produced and assessed. Keywords Earth–Moon transfer low-energy transfer ballistic capture trajectory optimization · · · · restricted three-body problem restricted four-body problem · 1 Introduction The search for trajectories to transfer a spacecraft from the Earth to the Moon has been the subject of countless works. The Hohmann transfer represents the easiest way to perform an Earth–Moon transfer. This requires placing the spacecraft on an ellipse having the perigee on the Earth parking orbit and the apogee on the Moon orbit. By properly switching the gravitational attractions along the orbit, the spacecraft’s motion is governed by only the Earth for most of the transfer, and by only the Moon in the final part. More generally, the patched-conics approximation relies on a Keplerian decomposition of the solar system dynamics (Battin 1987). Although from a practical point of view it is desirable to deal with analytical solutions, the two-body problem being integrable, the patched-conics approximation inherently involves hyperbolic approaches upon arrival.
    [Show full text]