Orbital Mechanics
Total Page:16
File Type:pdf, Size:1020Kb
Load more
Recommended publications
-
Arxiv:1912.09192V2 [Astro-Ph.EP] 24 Feb 2020
Draft version February 25, 2020 Typeset using LATEX preprint style in AASTeX62 Photometric analyses of Saturn's small moons: Aegaeon, Methone and Pallene are dark; Helene and Calypso are bright. M. M. Hedman,1 P. Helfenstein,2 R. O. Chancia,1, 3 P. Thomas,2 E. Roussos,4 C. Paranicas,5 and A. J. Verbiscer6 1Department of Physics, University of Idaho, Moscow, ID 83844 2Cornell Center for Astrophysics and Planetary Science, Cornell University, Ithaca NY 14853 3Center for Imaging Science, Rochester Institute of Technology, Rochester NY 14623 4Max Planck Institute for Solar System Research, G¨ottingen,Germany 37077 5APL, John Hopkins University, Laurel MD 20723 6Department of Astronomy, University of Virginia, Charlottesville, VA 22904 ABSTRACT We examine the surface brightnesses of Saturn's smaller satellites using a photometric model that explicitly accounts for their elongated shapes and thus facilitates compar- isons among different moons. Analyses of Cassini imaging data with this model reveals that the moons Aegaeon, Methone and Pallene are darker than one would expect given trends previously observed among the nearby mid-sized satellites. On the other hand, the trojan moons Calypso and Helene have substantially brighter surfaces than their co-orbital companions Tethys and Dione. These observations are inconsistent with the moons' surface brightnesses being entirely controlled by the local flux of E-ring par- ticles, and therefore strongly imply that other phenomena are affecting their surface properties. The darkness of Aegaeon, Methone and Pallene is correlated with the fluxes of high-energy protons, implying that high-energy radiation is responsible for darkening these small moons. Meanwhile, Prometheus and Pandora appear to be brightened by their interactions with nearby dusty F ring, implying that enhanced dust fluxes are most likely responsible for Calypso's and Helene's excess brightness. -
Analysis of Perturbations and Station-Keeping Requirements in Highly-Inclined Geosynchronous Orbits
ANALYSIS OF PERTURBATIONS AND STATION-KEEPING REQUIREMENTS IN HIGHLY-INCLINED GEOSYNCHRONOUS ORBITS Elena Fantino(1), Roberto Flores(2), Alessio Di Salvo(3), and Marilena Di Carlo(4) (1)Space Studies Institute of Catalonia (IEEC), Polytechnic University of Catalonia (UPC), E.T.S.E.I.A.T., Colom 11, 08222 Terrassa (Spain), [email protected] (2)International Center for Numerical Methods in Engineering (CIMNE), Polytechnic University of Catalonia (UPC), Building C1, Campus Norte, UPC, Gran Capitan,´ s/n, 08034 Barcelona (Spain) (3)NEXT Ingegneria dei Sistemi S.p.A., Space Innovation System Unit, Via A. Noale 345/b, 00155 Roma (Italy), [email protected] (4)Department of Mechanical and Aerospace Engineering, University of Strathclyde, 75 Montrose Street, Glasgow G1 1XJ (United Kingdom), [email protected] Abstract: There is a demand for communications services at high latitudes that is not well served by conventional geostationary satellites. Alternatives using low-altitude orbits require too large constellations. Other options are the Molniya and Tundra families (critically-inclined, eccentric orbits with the apogee at high latitudes). In this work we have considered derivatives of the Tundra type with different inclinations and eccentricities. By means of a high-precision model of the terrestrial gravity field and the most relevant environmental perturbations, we have studied the evolution of these orbits during a period of two years. The effects of the different perturbations on the constellation ground track (which is more important for coverage than the orbital elements themselves) have been identified. We show that, in order to maintain the ground track unchanged, the most important parameters are the orbital period and the argument of the perigee. -
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. -
Cassini Update
Cassini Update Dr. Linda Spilker Cassini Project Scientist Outer Planets Assessment Group 22 February 2017 Sols%ce Mission Inclina%on Profile equator Saturn wrt Inclination 22 February 2017 LJS-3 Year 3 Key Flybys Since Aug. 2016 OPAG T124 – Titan flyby (1584 km) • November 13, 2016 • LAST Radio Science flyby • One of only two (cf. T106) ideal bistatic observations capturing Titan’s Northern Seas • First and only bistatic observation of Punga Mare • Western Kraken Mare not explored by RSS before T125 – Titan flyby (3158 km) • November 29, 2016 • LAST Optical Remote Sensing targeted flyby • VIMS high-resolution map of the North Pole looking for variations at and around the seas and lakes. • CIRS last opportunity for vertical profile determination of gases (e.g. water, aerosols) • UVIS limb viewing opportunity at the highest spatial resolution available outside of occultations 22 February 2017 4 Interior of Hexagon Turning “Less Blue” • Bluish to golden haze results from increased production of photochemical hazes as north pole approaches summer solstice. • Hexagon acts as a barrier that prevents haze particles outside hexagon from migrating inward. • 5 Refracting Atmosphere Saturn's• 22unlit February rings appear 2017 to bend as they pass behind the planet’s darkened limb due• 6 to refraction by Saturn's upper atmosphere. (Resolution 5 km/pixel) Dione Harbors A Subsurface Ocean Researchers at the Royal Observatory of Belgium reanalyzed Cassini RSS gravity data• 7 of Dione and predict a crust 100 km thick with a global ocean 10’s of km deep. Titan’s Summer Clouds Pose a Mystery Why would clouds on Titan be visible in VIMS images, but not in ISS images? ISS ISS VIMS High, thin cirrus clouds that are optically thicker than Titan’s atmospheric haze at longer VIMS wavelengths,• 22 February but optically 2017 thinner than the haze at shorter ISS wavelengths, could be• 8 detected by VIMS while simultaneously lost in the haze to ISS. -
Astrodynamics
Politecnico di Torino SEEDS SpacE Exploration and Development Systems Astrodynamics II Edition 2006 - 07 - Ver. 2.0.1 Author: Guido Colasurdo Dipartimento di Energetica Teacher: Giulio Avanzini Dipartimento di Ingegneria Aeronautica e Spaziale e-mail: [email protected] Contents 1 Two–Body Orbital Mechanics 1 1.1 BirthofAstrodynamics: Kepler’sLaws. ......... 1 1.2 Newton’sLawsofMotion ............................ ... 2 1.3 Newton’s Law of Universal Gravitation . ......... 3 1.4 The n–BodyProblem ................................. 4 1.5 Equation of Motion in the Two-Body Problem . ....... 5 1.6 PotentialEnergy ................................. ... 6 1.7 ConstantsoftheMotion . .. .. .. .. .. .. .. .. .... 7 1.8 TrajectoryEquation .............................. .... 8 1.9 ConicSections ................................... 8 1.10 Relating Energy and Semi-major Axis . ........ 9 2 Two-Dimensional Analysis of Motion 11 2.1 ReferenceFrames................................. 11 2.2 Velocity and acceleration components . ......... 12 2.3 First-Order Scalar Equations of Motion . ......... 12 2.4 PerifocalReferenceFrame . ...... 13 2.5 FlightPathAngle ................................. 14 2.6 EllipticalOrbits................................ ..... 15 2.6.1 Geometry of an Elliptical Orbit . ..... 15 2.6.2 Period of an Elliptical Orbit . ..... 16 2.7 Time–of–Flight on the Elliptical Orbit . .......... 16 2.8 Extensiontohyperbolaandparabola. ........ 18 2.9 Circular and Escape Velocity, Hyperbolic Excess Speed . .............. 18 2.10 CosmicVelocities -
Launch and Deployment Analysis for a Small, MEO, Technology Demonstration Satellite
46th AIAA Aerospace Sciences Meeting and Exhibit AIAA 2008-1131 7 – 10 January 20006, Reno, Nevada Launch and Deployment Analysis for a Small, MEO, Technology Demonstration Satellite Stephen A. Whitmore* and Tyson K. Smith† Utah State University, Logan, UT, 84322-4130 A trade study investigating the economics, mass budget, and concept of operations for delivery of a small technology-demonstration satellite to a medium-altitude earth orbit is presented. The mission requires payload deployment at a 19,000 km orbit altitude and an inclination of 55o. Because the payload is a technology demonstrator and not part of an operational mission, launch and deployment costs are a paramount consideration. The payload includes classified technologies; consequently a USA licensed launch system is mandated. A preliminary trade analysis is performed where all available options for FAA-licensed US launch systems are considered. The preliminary trade study selects the Orbital Sciences Minotaur V launch vehicle, derived from the decommissioned Peacekeeper missile system, as the most favorable option for payload delivery. To meet mission objectives the Minotaur V configuration is modified, replacing the baseline 5th stage ATK-37FM motor with the significantly smaller ATK Star 27. The proposed design change enables payload delivery to the required orbit without using a 6th stage kick motor. End-to-end mass budgets are calculated, and a concept of operations is presented. Monte-Carlo simulations are used to characterize the expected accuracy of the final orbit. -
View and Print This Publication
@ SOUTHWEST FOREST SERVICE Forest and R U. S.DEPARTMENT OF AGRICULTURE P.0. BOX 245, BERKELEY, CALIFORNIA 94701 Experime Computation of times of sunrise, sunset, and twilight in or near mountainous terrain Bill 6. Ryan Times of sunrise and sunset at specific mountain- ous locations often are important influences on for- estry operations. The change of heating of slopes and terrain at sunrise and sunset affects temperature, air density, and wind. The times of the changes in heat- ing are related to the times of reversal of slope and valley flows, surfacing of strong winds aloft, and the USDA Forest Service penetration inland of the sea breeze. The times when Research NO& PSW- 322 these meteorological reactions occur must be known 1977 if we are to predict fire behavior, smolce dispersion and trajectory, fallout patterns of airborne seeding and spraying, and prescribed burn results. ICnowledge of times of different levels of illumination, such as the beginning and ending of twilight, is necessary for scheduling operations or recreational endeavors that require natural light. The times of sunrise, sunset, and twilight at any particular location depend on such factors as latitude, longitude, time of year, elevation, and heights of the surrounding terrain. Use of the tables (such as The 1 Air Almanac1) to determine times is inconvenient Ryan, Bill C. because each table is applicable to only one location. 1977. Computation of times of sunrise, sunset, and hvilight in or near mountainous tersain. USDA Different tables are needed for each location and Forest Serv. Res. Note PSW-322, 4 p. Pacific corrections must then be made to the tables to ac- Southwest Forest and Range Exp. -
Design of Low-Altitude Martian Orbits Using Frequency Analysis A
Design of Low-Altitude Martian Orbits using Frequency Analysis A. Noullez, K. Tsiganis To cite this version: A. Noullez, K. Tsiganis. Design of Low-Altitude Martian Orbits using Frequency Analysis. Advances in Space Research, Elsevier, 2021, 67, pp.477-495. 10.1016/j.asr.2020.10.032. hal-03007909 HAL Id: hal-03007909 https://hal.archives-ouvertes.fr/hal-03007909 Submitted on 16 Nov 2020 HAL is a multi-disciplinary open access L’archive ouverte pluridisciplinaire HAL, est archive for the deposit and dissemination of sci- destinée au dépôt et à la diffusion de documents entific research documents, whether they are pub- scientifiques de niveau recherche, publiés ou non, lished or not. The documents may come from émanant des établissements d’enseignement et de teaching and research institutions in France or recherche français ou étrangers, des laboratoires abroad, or from public or private research centers. publics ou privés. Design of Low-Altitude Martian Orbits using Frequency Analysis A. Noulleza,∗, K. Tsiganisb aUniversit´eC^oted'Azur, Observatoire de la C^oted'Azur, CNRS, Laboratoire Lagrange, bd. de l'Observatoire, C.S. 34229, 06304 Nice Cedex 4, France bSection of Astrophysics Astronomy & Mechanics, Department of Physics, Aristotle University of Thessaloniki, GR 541 24 Thessaloniki, Greece Abstract Nearly-circular Frozen Orbits (FOs) around axisymmetric bodies | or, quasi-circular Periodic Orbits (POs) around non-axisymmetric bodies | are of primary concern in the design of low-altitude survey missions. Here, we study very low-altitude orbits (down to 50 km) in a high-degree and order model of the Martian gravity field. We apply Prony's Frequency Analysis (FA) to characterize the time variation of their orbital elements by computing accurate quasi-periodic decompositions of the eccentricity and inclination vectors. -
Electric Propulsion System Scaling for Asteroid Capture-And-Return Missions
Electric propulsion system scaling for asteroid capture-and-return missions Justin M. Little⇤ and Edgar Y. Choueiri† Electric Propulsion and Plasma Dynamics Laboratory, Princeton University, Princeton, NJ, 08544 The requirements for an electric propulsion system needed to maximize the return mass of asteroid capture-and-return (ACR) missions are investigated in detail. An analytical model is presented for the mission time and mass balance of an ACR mission based on the propellant requirements of each mission phase. Edelbaum’s approximation is used for the Earth-escape phase. The asteroid rendezvous and return phases of the mission are modeled as a low-thrust optimal control problem with a lunar assist. The numerical solution to this problem is used to derive scaling laws for the propellant requirements based on the maneuver time, asteroid orbit, and propulsion system parameters. Constraining the rendezvous and return phases by the synodic period of the target asteroid, a semi- empirical equation is obtained for the optimum specific impulse and power supply. It was found analytically that the optimum power supply is one such that the mass of the propulsion system and power supply are approximately equal to the total mass of propellant used during the entire mission. Finally, it is shown that ACR missions, in general, are optimized using propulsion systems capable of processing 100 kW – 1 MW of power with specific impulses in the range 5,000 – 10,000 s, and have the potential to return asteroids on the order of 103 104 tons. − Nomenclature -
AFSPC-CO TERMINOLOGY Revised: 12 Jan 2019
AFSPC-CO TERMINOLOGY Revised: 12 Jan 2019 Term Description AEHF Advanced Extremely High Frequency AFB / AFS Air Force Base / Air Force Station AOC Air Operations Center AOI Area of Interest The point in the orbit of a heavenly body, specifically the moon, or of a man-made satellite Apogee at which it is farthest from the earth. Even CAP rockets experience apogee. Either of two points in an eccentric orbit, one (higher apsis) farthest from the center of Apsis attraction, the other (lower apsis) nearest to the center of attraction Argument of Perigee the angle in a satellites' orbit plane that is measured from the Ascending Node to the (ω) perigee along the satellite direction of travel CGO Company Grade Officer CLV Calculated Load Value, Crew Launch Vehicle COP Common Operating Picture DCO Defensive Cyber Operations DHS Department of Homeland Security DoD Department of Defense DOP Dilution of Precision Defense Satellite Communications Systems - wideband communications spacecraft for DSCS the USAF DSP Defense Satellite Program or Defense Support Program - "Eyes in the Sky" EHF Extremely High Frequency (30-300 GHz; 1mm-1cm) ELF Extremely Low Frequency (3-30 Hz; 100,000km-10,000km) EMS Electromagnetic Spectrum Equitorial Plane the plane passing through the equator EWR Early Warning Radar and Electromagnetic Wave Resistivity GBR Ground-Based Radar and Global Broadband Roaming GBS Global Broadcast Service GEO Geosynchronous Earth Orbit or Geostationary Orbit ( ~22,300 miles above Earth) GEODSS Ground-Based Electro-Optical Deep Space Surveillance -
Handbook of Satellite Orbits from Kepler to GPS Michel Capderou
Handbook of Satellite Orbits From Kepler to GPS Michel Capderou Handbook of Satellite Orbits From Kepler to GPS Translated by Stephen Lyle Foreword by Charles Elachi, Director, NASA Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, USA 123 Michel Capderou Universite´ Pierre et Marie Curie Paris, France ISBN 978-3-319-03415-7 ISBN 978-3-319-03416-4 (eBook) DOI 10.1007/978-3-319-03416-4 Springer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2014930341 © Springer International Publishing Switzerland 2014 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. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this pub- lication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permis- sions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. -
The Speed of a Geosynchronous Satellite Is ___
Physics 106 Lecture 9 Newton’s Law of Gravitation SJ 7th Ed.: Chap 13.1 to 2, 13.4 to 5 • Historical overview • N’Newton’s inverse-square law of graviiitation Force Gravitational acceleration “g” • Superposition • Gravitation near the Earth’s surface • Gravitation inside the Earth (concentric shells) • Gravitational potential energy Related to the force by integration A conservative force means it is path independent Escape velocity Example A geosynchronous satellite circles the earth once every 24 hours. If the mass of the earth is 5.98x10^24 kg; and the radius of the earth is 6.37x10^6 m., how far above the surface of the earth does a geosynchronous satellite orbit the earth? G=6.67x10-11 Nm2/kg2 The speed of a geosynchronous satellite is ______. 1 Goal Gravitational potential energy for universal gravitational force Gravitational Potential Energy WUgravity= −Δ gravity Near surface of Earth: Gravitational force of magnitude of mg, pointing down (constant force) Æ U = mgh Generally, gravit. potential energy for a system of m1 & m2 G Gmm12 mm F = Attractive force Ur()=− G12 12 r 2 g 12 12 r12 Zero potential energy is chosen for infinite distance between m1 and m2. Urg ()012 = ∞= Æ Gravitational potential energy is always negative. 2 mm12 Urg ()12 =− G r12 r r Ug=0 1 U(r1) Gmm U =− 12 g r Mechanical energy 11 mM EKUrmvMVG=+ ( ) =22 + − mech 22 r m V r v M E_mech is conserved, if gravity is the only force that is doing work. 1 2 MV is almost unchanged. If M >>> m, 2 1 2 mM ÆWe can define EKUrmvG=+ ( ) = − mech 2 r 3 Example: A stone is thrown vertically up at certain speed from the surface of the Moon by Superman.