The Utilization of Halo Orbit§ in Advanced Lunar Operation§

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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
Rendezvous Design in a Cislunar Near Rectilinear Halo Orbit Emmanuel Blazquez, Laurent Beauregard, Stéphanie Lizy-Destrez, Finn Ankersen, Francesco Capolupo

Rendezvous Design in a Cislunar Near Rectilinear Halo Orbit Emmanuel Blazquez, Laurent Beauregard, Stéphanie Lizy-Destrez, Finn Ankersen, Francesco Capolupo To cite this version: Emmanuel Blazquez, Laurent Beauregard, Stéphanie Lizy-Destrez, Finn Ankersen, Francesco Capolupo. Rendezvous Design in a Cislunar Near Rectilinear Halo Orbit. International Symposium on Space Flight Dynamics (ISSFD), Feb 2019, Melbourne, Australia. pp.1408-1413. hal-03200239 HAL Id: hal-03200239 https://hal.archives-ouvertes.fr/hal-03200239 Submitted on 16 Apr 2021 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. Open Archive Toulouse Archive Ouverte (OATAO) OATAO is an open access repository that collects the wor of some Toulouse researchers and ma es it freely available over the web where possible. This is an author's version published in: h ttps://oatao.univ-toulouse.fr/22865 To cite this version : Blazquez, Emmanuel and Beauregard, Laurent and Lizy-Destrez, Stéphanie and Ankersen, Finn and Capolupo, Francesco Rendezvous Design in a Cislunar Near Rectilinear Halo Orbit.
Rideshare and the Orbital Maneuvering Vehicle: the Key to Low-Cost Lagrange-Point Missions

SSC15-II-5 Rideshare and the Orbital Maneuvering Vehicle: the Key to Low-cost Lagrange-point Missions Chris Pearson, Marissa Stender, Christopher Loghry, Joe Maly, Valentin Ivanitski Moog Integrated Systems 1113 Washington Avenue, Suite 300, Golden, CO, 80401; 303 216 9777, extension 204 [email protected] Mina Cappuccio, Darin Foreman, Ken Galal, David Mauro NASA Ames Research Center PO Box 1000, M/S 213-4, Moffett Field, CA 94035-1000; 650 604 1313 [email protected] Keats Wilkie, Paul Speth, Trevor Jackson, Will Scott NASA Langley Research Center 4 West Taylor Street, Mail Stop 230, Hampton, VA, 23681; 757 864 420 [email protected] ABSTRACT Rideshare is a well proven approach, in both LEO and GEO, enabling low-cost space access through splitting of launch charges between multiple passengers. Demand exists from users to operate payloads at Lagrange points, but a lack of regular rides results in a deficiency in rideshare opportunities. As a result, such mission architectures currently rely on a costly dedicated launch. NASA and Moog have jointly studied the technical feasibility, risk and cost of using an Orbital Maneuvering Vehicle (OMV) to offer Lagrange point rideshare opportunities. This OMV would be launched as a secondary passenger on a commercial rocket into Geostationary Transfer Orbit (GTO) and utilize the Moog ESPA secondary launch adapter. The OMV is effectively a free flying spacecraft comprising a full suite of avionics and a propulsion system capable of performing GTO to Lagrange point transfer via a weak stability boundary orbit. In addition to traditional OMV ’tug’ functionality, scenarios using the OMV to host payloads for operation at the Lagrange points have also been analyzed.
Habitability of Planets on Eccentric Orbits: Limits of the Mean Flux Approximation

A&A 591, A106 (2016) Astronomy DOI: 10.1051/0004-6361/201628073 & c ESO 2016 Astrophysics Habitability of planets on eccentric orbits: Limits of the mean flux approximation Emeline Bolmont1, Anne-Sophie Libert1, Jeremy Leconte2; 3; 4, and Franck Selsis5; 6 1 NaXys, Department of Mathematics, University of Namur, 8 Rempart de la Vierge, 5000 Namur, Belgium e-mail: [email protected] 2 Canadian Institute for Theoretical Astrophysics, 60st St George Street, University of Toronto, Toronto, ON, M5S3H8, Canada 3 Banting Fellow 4 Center for Planetary Sciences, Department of Physical & Environmental Sciences, University of Toronto Scarborough, Toronto, ON, M1C 1A4, Canada 5 Univ. Bordeaux, LAB, UMR 5804, 33270 Floirac, France 6 CNRS, LAB, UMR 5804, 33270 Floirac, France Received 4 January 2016 / Accepted 28 April 2016 ABSTRACT Unlike the Earth, which has a small orbital eccentricity, some exoplanets discovered in the insolation habitable zone (HZ) have high orbital eccentricities (e.g., up to an eccentricity of ∼0.97 for HD 20782 b). This raises the question of whether these planets have surface conditions favorable to liquid water. In order to assess the habitability of an eccentric planet, the mean flux approximation is often used. It states that a planet on an eccentric orbit is called habitable if it receives on average a flux compatible with the presence of surface liquid water. However, because the planets experience important insolation variations over one orbit and even spend some time outside the HZ for high eccentricities, the question of their habitability might not be as straightforward. We performed a set of simulations using the global climate model LMDZ to explore the limits of the mean flux approximation when varying the luminosity of the host star and the eccentricity of the planet.
1961Apj. . .133. .6575 PHYSICAL and ORBITAL BEHAVIOR OF

.6575 PHYSICAL AND ORBITAL BEHAVIOR OF COMETS* .133. Roy E. Squires University of California, Davis, California, and the Aerojet-General Corporation, Sacramento, California 1961ApJ. AND DaVid B. Beard University of California, Davis, California Received August 11, I960; revised October 14, 1960 ABSTRACT As a comet approaches perihelion and the surface facing the sun is warmed, there is evaporation of the surface material in the solar direction The effect of this unidirectional rapid mass loss on the orbits of the parabolic comets has been investigated, and the resulting corrections to the observed aphelion distances, a, and eccentricities have been calculated. Comet surface temperature has been calculated as a function of solar distance, and estimates have been made of the masses and radii of cometary nuclei. It was found that parabolic comets with perihelia of 1 a u. may experience an apparent shift in 1/a of as much as +0.0005 au-1 and that the apparent shift in 1/a is positive for every comet, thereby increas- ing the apparent orbital eccentricity over the true eccentricity in all cases. For a comet with a perihelion of 1 a u , the correction to the observed eccentricity may be as much as —0.0005. The comet surface tem- perature at 1 a.u. is roughly 180° K, and representative values for the masses and radii of cometary nuclei are 6 X 10" gm and 300 meters. I. INTRODUCTION Since most comets are observed to move in nearly parabolic orbits, questions concern- ing their origin and whether or not they are permanent members of the solar system are not clearly resolved.
Analysis of Interplanetary Transfers Between the Earth and Mars Halo Orbits

Analysis of Interplanetary Transfers between the Earth and Mars Halo orbits M. Nakamiya (1), H. Yamakawa (2), D. J. Scheeres (3) and M. Yoshikawa (4) (1) Japan Aerospace Exploration Agency, 3-1-1 Sagamihara, Kanagawa 229-8510, Japan. nakamiya,[email protected] (2) University of Colorado, Boulder, Colorado 80309, USA. [email protected] (3) KyotoUniversity, Gokasho, Uji, Kyoto 611-0011, Japan. [email protected] (4) Japan Aerospace Exploration Agency, 3-1-1 Sagamihara, Kanagawa 229-8510, Japan. [email protected] Spacecraft interplanetary transportation systems using Earth and Mars Halo orbits are analyzed. This application is motivated by future proposals to place “deep space ports” at the Earth and Mars Halo orbits as space hub for planetary Mission. First, the feasibility of interplanetary trajectories between Earth Halo orbit and Mars Halo orbit was investigated, and such trajectories were designed with reasonable DV and flight time. Here, we utilize unstable and stable manifolds associated with the Halo orbit to approach the vicinity of the planet’s surface, and assume impulsive maneuver for escape and capture trajectories from/to Halo Orbits. Next, applying to Earth-Mars transportation system using spaceports on Halo orbits, we evaluated the system with respect to the mass of round-trip transfer. As a result, the transfer between the low Earth orbit and the low Mars orbit via the Earth Halo orbit and the Mars Halo orbit could be saved the fuel cost compared with a direct transfer between the low Earth orbit and the low Mars orbit 1. INTRODUCTION These days there has been great interest in the libration points of the circular restricted 3-body problem (CR3BP), where the gravity of the primary and secondary bodies and centrifugal force are balanced.
Orbital Stability Zones About Asteroids

ICARUS 92, 118-131 (1991) Orbital Stability Zones about Asteroids DOUGLAS P. HAMILTON AND JOSEPH A. BURNS Cornell University, Ithaca, New York, 14853-6801 Received October 5, 1990; revised March 1, 1991 exploration program should be remedied when the Galileo We have numerically investigated a three-body problem con- spacecraft, launched in October 1989, encounters the as- sisting of the Sun, an asteroid, and an infinitesimal particle initially teroid 951 Gaspra on October 29, 1991. It is expected placed about the asteroid. We assume that the asteroid has the that the asteroid's surroundings will be almost devoid of following properties: a circular heliocentric orbit at R -- 2.55 AU, material and therefore benign since, in the analogous case an asteroid/Sun mass ratio of/~ -- 5 x 10-12, and a spherical of the satellites of the giant planets, significant debris has shape with radius R A -- 100 km; these values are close to those of never been detected. The analogy is imperfect, however, the minor planet 29 Amphitrite. In order to describe the zone in and so the possibility that interplanetary debris may be which circum-asteroidal debris could be stably trapped, we pay particular attention to the orbits of particles that are on the verge enhanced in the gravitational well of the asteroid must be of escape. We consider particles to be stable or trapped if they considered. If this is the case, the danger of collision with remain in the asteroid's vicinity for at least 5 asteroid orbits about orbiting debris may increase as the asteroid is approached.
Orbital Inclination and Eccentricity Oscillations in Our Solar

Long term orbital inclination and eccentricity oscillations of the planets in our solar system Abstract The orbits of the planets in our solar system are not in the same plane, therefore natural torques stemming from Newton’s gravitational forces exist to pull them all back to the same plane. This causes the inclinations of the planet orbits to oscillate with potentially long periods and very small damping, because the friction in space is very small. Orbital inclination changes are known for some planets in terms of current rates of change, but the oscillation periods are not well published. They can however be predicted with proper dynamic simulations of the solar system. A three-dimensional dynamic simulation was developed for our solar system capable of handling 12 objects, where all objects affect all other objects. Each object was considered to be a point mass which proved to be an adequate approximation for this study. Initial orbital radii, eccentricities and speeds were set according to known values. The validity of the simulation was demonstrated in terms of short term characteristics such as sidereal periods of planets as well as long term characteristics such as the orbital inclination and eccentricity oscillation periods of Jupiter and Saturn. A significantly more accurate result, than given on approximate analytical grounds in a well-known solar system dynamics textbook, was found for the latter period. Empirical formulas were developed from the simulation results for both these periods for three-object solar type systems. They are very accurate for the Sun, Jupiter and Saturn as well as for some other comparable systems.
Station-Keeping and Momentum-Management on Halo Orbits Around L2: Linear-Quadratic Feedback and Model Predictive Control Approaches

MITSUBISHI ELECTRIC RESEARCH LABORATORIES http://www.merl.com Station-keeping and momentum-management on halo orbits around L2: Linear-quadratic feedback and model predictive control approaches Kalabi´c,U.; Weiss, A.; Di Cairano, S.; Kolmanovsky, I.V. TR2015-002 January 11, 2015 Abstract The control of station-keeping and momentum-management is considered while tracking a halo orbit centered at the second Earth-Moon Lagrangian point. Multiple schemes based on linear-quadratic feedback control and model predictive control (MPC) are considered and it is shown that the method based on periodic MPC performs best for position tracking. The scheme is then extended to incorporate attitude control requirements and numerical simulations are presented demonstrating that the scheme is able to achieve simultaneous tracking of a halo orbit and dumping of momentum while enforcing tight constraints on pointing error. AAS/AIAA Space Flight Mechanics Meeting This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonproﬁt educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of
Utilizing the Deep Space Gateway As a Platform for Deploying Cubesats Into Lunar Orbit

Deep Space Gateway Science Workshop 2018 (LPI Contrib. No. 2063) 3138.pdf UTILIZING THE DEEP SPACE GATEWAY AS A PLATFORM FOR DEPLOYING CUBESATS INTO LUNAR ORBIT. Fisher, Kenton R.1; NASA Johnson Space Center 2101 E NASA Pkwy, Houston TX 77508. [email protected] Introduction: The capability to deploy CubeSats from the Deep Space Gateway (DSG) may significantly increase access to the Moon for lower- cost science missions. CubeSats are beginning to demonstrate high science return for reduced cost. The DSG could utilize an existing ISS deployment method, assuming certain capabilities that are present at the ISS are also available at the DSG. Science and Technology Applications: There are many interesting potential applications for lunar CubeSat missions. A constellation of CubeSats Figure 1: Nanoracks CubeSat Deployer (NRCSD) being could provide a lunar GPS system for support of positioned by the Japanese Remote Manipulator System surface exploration missions. CubeSats could be used (JRMS) for deployment on ISS [4]. to provide communications relays for missions to the Present Lunar CubeSat Architecture: lunar far side. Potential science applications include While there are many opportunities for deploying using a CubeSat to produce mapping of the magnetic CubeSats into Earth orbits, the current options for fields of lunar swirls or to further map lunar surface deployment to lunar orbits are limited. Propulsive volatiles. requirements for trans-lunar injection (TLI) from International Space Station CubeSats: The Earth-orbit and lunar orbital insertion (LOI) International Space Station (ISS) has been a major significantly increase the cost, mass, and complexity platform for deploying CubeSats in recent years.
Exoplanet Orbital Eccentricity: Multiplicity Relation and the Solar System

Exoplanet orbital eccentricity: Multiplicity relation and the Solar System Mary Anne Limbacha,b and Edwin L. Turnera,c,1 Departments of aAstrophysical Sciences and bMechanical and Aerospace Engineering, Princeton University, Princeton, NJ 08544; and cThe Kavli Institute for the Physics and Mathematics of the Universe, The University of Tokyo, Kashiwa 227-8568, Japan Edited by Neta A. Bahcall, Princeton University, Princeton, NJ, and approved November 11, 2014 (received for review April 10, 2014) The known population of exoplanets exhibits a much wider range of The dataset is discussed in the next section. We then show the orbital eccentricities than Solar System planets and has a much higher trend in eccentricity with multiplicity and comment on possible average eccentricity. These facts have been widely interpreted to sources of error and bias. Next we measure the mean, median, indicate that the Solar System is an atypical member of the overall and probability density distribution of eccentricities for various population of planetary systems. We report here on a strong anti- multiplicities and fit them to a simple power-law model for correlation of orbital eccentricity with multiplicity (number of planets multiplicities greater than two. This fit is used to make a rough in the system) among cataloged radial velocity (RV) systems. The estimate of the number of higher-multiplicity systems likely to be mean, median, and rough distribution of eccentricities of Solar System contaminating the one- and two-planet system samples due to as planets fits an extrapolation of this anticorrelation to the eight-planet yet undiscovered members under plausible, but far from certain, case rather precisely despite the fact that no more than two Solar assumptions.
Aas 19-266 Designing Low-Thrust Enabled Trajectories for A

AAS 19-266 DESIGNING LOW-THRUST ENABLED TRAJECTORIES FOR A HELIOPHYSICS SMALLSAT MISSION TO SUN-EARTH L5 Ian Elliott,∗ Christoper Sullivan Jr.,∗ Natasha Bosanac,y Jeffrey R. Stuart,z and Farah Alibayx A small satellite deployed to Sun-Earth L5 could serve as a low-cost platform to observe solar phenomena such as coronal mass ejections. However, the small satellite platform introduces signiﬁcant challenges into the trajectory design pro- cess via limited thrusting capabilities, power and operational constraints, and ﬁxed deployment conditions. To address these challenges, a strategy employing dynam- ical systems theory is used to design a low-thrust-enabled trajectory for a small satellite to reach the Sun-Earth L5 region. This procedure is demonstrated for a small satellite that launches as a secondary payload with a larger spacecraft des- tined for a Sun-Earth L2 halo orbit. INTRODUCTION Low-thrust spacecraft trajectory design has the potential to enable targeted science missions for small satellites to explore solar processes. In fact, the Sun-Earth (SE) L5 equilibrium point, located at the vertex of an equilateral triangle formed with the Sun and the Earth, is a candidate for locating a SmallSat for a heliophysics mission. At SE L5, a spacecraft would have a currently unavailable perspective of the three-dimensional structure of the coronal mass ejections off the Sun-Earth line.1 Additionally, due to the rotation of the Sun, early warning of solar storms is possible from SE L5.2 This equilibrium point has previously been visited by the Solar TErrestrial RElations Observatory B (STEREO-B) spacecraft which drifted through the SE L5 region, but did not maintain long- term bounded motion.3;4 With the increasing availability of rideshare opportunities and the recent demonstration of CubeSats operations in deep space during the Mars Cube One (MarCO) mission,5 small satellites may soon have the potential to be deployed to SE L5 to perform heliophysics-based science objectives.