..., and predictions of performance and orbital maneuvering capability. ii ACKNOWLEDGEMENTS The... SELECTION.............................................................................................................71 3.4.1 Spacecraft Orbital Lifetime Analysis .........................................................................................71 3.4.2 Spacecraft Orbital Lighting Analysis.........................................................................................74... Centered Fixed Reference Frame ....................................................................................85 4.2.3 Orbital Reference Frame ...............................................................................................................85 4.2.4 SatL and... ECI and Orbital Reference Frames..............................................91 iv 4.2.8 Transformation between Orbital and SatL... 5 ............................................................................................................................................................183 ORBITAL MANEUVERING ..................................................................................................................................183 5.1 GAUSS VARIATION OF PARAMETERS EQUATIONS OF ORBITAL MOTION .............................................183 5.2 SPECIFIC FORCES DURING ORBITAL MANEUVERING ...........................................................................186 5.3 ORBITAL MANEUVERING SIMULATION RESULTS ..................................................................................190 5.3.1 Comparison of Results with Edelbaum Orbital Transfer Analysis ..................................190 5.3.2 Orbital Maneuvers Neglecting Earth Oblateness .................................................................191 5.3.3 Orbital Maneuvers... lastly predictions of performance and orbital maneuvering capability. The most difficult.... (7) Analysis of propulsive capability for orbital maneuvers. 18 (8) Final mission design... satellite is initiated with precomputed orbital ephemeris and control weight matrices... deployment ω ω VI. Nominal operations VII. Orbital maneuvering VIII. Deorbiting ω Velocity Solar.... Lastly, v is the orbital velocity which, for a circular orbital with an altitude.... Deployment possible regardless of the orbital inclination, eccentricity, or altitude Initial.... Table 6. Transfer times for three orbital maneuvers. Scenario (1) (2) (3) 3.4 Δi Δalt [º] [km] 0.4 5 5 100... insertion altitude. 3.4.1 Spacecraft Orbital Lifetime Analysis Initial orbital lifetime analysis is performed... 1000 Table 7. Orbital Lifetime vs. altitude and configuration Altitude Orbital Lifetime [yrs... (edge-on) configuration. 73 3.4.2 Spacecraft Orbital Lighting Analysis The two candidate... Fixed Reference Frame 4.2.3 Orbital Reference Frame The Orbital reference frame, also referred... frame. 4.2.7 Transformation between ECI and Orbital Reference Frames The local vertical... = ( AORB ) = AECI −1 [76] 4.2.8 Transformation between Orbital and SatL and SatU reference... magnitude of orbital radius, i is the orbital inclination, and f is the orbital true... orbital reference frames between the Ravindran/Hughes and CubeSail frames. The orbital... the orbital plane, and the y-axis as normal to the orbital plane... Hughes Orbital Reference Frame.64 The transformation matrix between these two orbital... Orbital Radius [km] 6378.132 + 800 Orbital Speed (circular) [km/s] 7.4518 Orbital eccentricity Orbital Inclination [deg] Orbital Argument of Perigee [deg] Orbital Right Ascension of the Ascending Node [deg] Orbital True Anomaly... CHAPTER 5 ORBITAL MANEUVERING 5.1 Gauss Variation of Parameters Equations of Orbital Motion The variation in the orbital elements due...] with a 1 = a + b 1 + 1 − e2 [257] The classical orbital elements are easily recovered using... integrating the differential equations of orbital elements. Due to computational complexity... 5.3 [270] Orbital Maneuvering Simulation Results 5.3.1 Comparison of Results with Edelbaum Orbital Transfer Analysis The first orbital maneuvering simulation aims... and Earth oblateness are neglected. 5.3.2 Orbital Maneuvers Neglecting Earth Oblateness It... Earth oblateness effects are neglected. 5.3.3 Orbital Maneuvers Including Earth Oblateness The... perpendicular to the orbital plane (either due to orbital maneuvers or initial... energy usage, orbital maneuvering scenarios and power consumption, and orbital lifetime predictions... 20m2 CubeSail spacecraft. As a result, orbital maneuvers generally require a more involved.... 220 96 Prussing, J. and Conway, B., Orbital Mechanics, Oxford University Press, 1993.... 101 NASA Johnson Spaceflight Center Orbital Debris Program Office, http://orbitaldebris...

... propulsion up to, or near, orbital speed, and providing rapid and... thrust from takeoff to near orbital speeds; reusable thermal structures that...-toorbit rockets, hypersonic vehicles, and orbital transfer vehicies; and eEcierii aiiiilysis..., advanced space transportation systems, and orbital transfer vehicles; development of lightweight... supporting a wide range of aeromaneuvering orbital transfer vehicles. Also, in the... transportation vehicles, including the aerobraking orbital transfer vehicle, Shuttle 11, and... of autonomous space systems (e.g., rovers, orbital transfer vehicles, and life support... design of future cryogenically fueled orbital transfer vehicles (OTV) and for... the orbiter flight schedule. The orbital acceleration research experiment, which will... expand the data base for orbital drag predictions, has completed critical... the design of an aeroassisted orbital transfer vehicle (AOTV).The technology... the data handled from earth-orbital missions increase from a current peak... doors, vertical tail, and the orbital maneuvering system pods. The procurement.... Support is provided for Earth orbital, planetary and solar system exploration... and balloons. Included in Earth orbital support are the Space Shuttle... Network (STDN), which supports Earth orbital missions; the Deep Space Network... will provide all low Earth orbital mission support when it becomes.... The STDN will provide Earth orbital support until the TDRSS becomes... communications services to low Earth orbital spacecraft. The TDRSS itself, when... a six-fold increase in the orbital coverage provided by ground track... broad categories of missions: earth orbital spaceflight; planetary and solar system..., balloons and sounding rockets. Earth orbital support is provided primarily by... missions as well as earth orbital missions not supportable by TDRSS... well as limited orbital support. Also included is the orbital tracking facility a t the Wallops Flight Facility which provides orbital tracking... support as well as limited orbital support. The FY 1988 funding... earth orbiters and synchronous earth orbital miss:ons; and ($1 to provide... facilities support NASA aeronautics, sub-orbital and a limited number of low....-Development and operation of Earth orbital flight experiments and automated spacecraft... Advanced programs Tethered satellite system Orbital maneuvering vehicle 3 Space science A Physics... Satellite System, development of the Orbital Maneuvering Vehicle, development and operations... the develo ment of the Orbital Maneuvering Vehicle. S acelab is a major... tether. The development of the Orbital Maneuvering Vehicle (OMV), initiated in... crew systems, geostationary Earth orbital unmanned platforms, reusable orbital transfer vehicles (OTVs), new capability mission kits for orbital maneuvering... development efforts in 1984. Orbital Maneuvering Vehicle The Orbital Maneuvering Vehicle (OMV... reusable extension capability for conducting orbital operations with spacecraft and payloads... of multiple payloads to different orbital altitudes and inclinations in a single... space debris which could represent a n orbital hazard to all future space... progress being made in (1) the Orbital Maneuvering Vehicle program and its.../Spaceiab flights, reirievabk Spartans, and E& orbital opportunities. The latter include balloons.... - $25,000,000 from the orbital maneuvering vehicle (OMV). - $5,000,000... of the Committees on Appropriations. 1. Orbital Maneuvering Vehicle-$55,000,000... system, and development of the orbital maneuvering vehicle. The space science...: -$25,000,000 from the orbital maneuvering vehicle program. This reduces... data acquisition support for Earth-orbital spacecraft, planetary missions, sounding rockets.... +$25.000.000 from the orbital maneuverSupport areas. I t Is noted. for...

... − gain of parabole antenna hOrbit m orbital altitude HRW kgm2 angular momentum... cos(θ) SW m swath width tOrbit s orbital period tSatellite s satellite time tEclipse... βs ◦ incident sun angle on the orbital plane ◦ elevation angle η − antenna efficiency...-Geosynchronous Orbit P/L Payload POD Picosatellite Orbital Deployer Prop Propulsion SA Solar... are launched in standardized Picosatellite Orbital Deployers (PODs) as piggybacks of... consumed by the spacecraft, the orbital period or simply the volume... fixed) as well as the orbital parameters and a mission fitting to... remark that in practice the orbital altitude, an approximate satellite lifetime... the solar panels. Thus, the orbital period is supposed to interplay... mass, power, volume/length and orbital period, it was assumed that... consumption. The position of the orbital period tOrbit in the parameter... found in higher orbital altitudes, thus with higher orbital Page 54 Dimensional.... Supposing equal orbital periods for the investigated satellites, the orbital period tOrbit... the orbital period and the power requirement. Furthermore, as the same orbital..., however, the consideration of the orbital period tOrbit is assumed to... was again to eliminate the orbital period tOrbit and investigate Π∗3 . The... confirm the assumption that the orbital period is not a suitable time... LEO satellites when taking the orbital period into account, namely 146... of the contribution of the orbital period, but also when introducing... account of the orbital period tOrbit . When the orbital parameters are more... not satellites with complete different orbital parameters. This means that their... that the consideration of the orbital period with power 3 in the... where no information on the orbital parameters was available), on the... the orbital period tOrbit reduces the dispersion for satellites with similar orbital... that for satellites with similar orbital period Π∗3 instead of Π1 is Page... spacecraft’s volume VS/C and the orbital period tOrbit . Π∗6 = Π∗3 · V 2 3 = PS/C mS/C (3.30... of the influence of the orbital period tOrbit . Nevertheless, especially the...: mass, power, length/volume and orbital period. Three parameters of them... to the orbital period tOrbit but a complex function of the orbital altitude... on the inclination i of the orbital plane and the Right Ascension... analysis, dependencies between θ and the orbital parameters as well as the.../C , PP/L or tSatellite up to orbital quantities such as the eclipse..., are a possibility for restoring the orbital altitude. Reaction wheels are relatively... spacecraft IS/C [kgm2 ] • and the orbital altitude hOrbit [m] Page 70 Dimensional.../C can be represented by the orbital altitude hOrbit as v = µ . REarth +hOrbit... a function of the orbital altitude hOrbit , decreasing with increasing orbital altitude [Hedin, 1991]. Developing this further, the orbital period is also a function of the orbital altitude with... orbital altitude hOrbit , they can be presented as functions of the orbital..., increasing the orbital period assuming circular orbits means increasing the orbital altitude... to gravity decrease with increasing orbital altitude, less angular momentum has... 3.4.1. Here, however, the orbital period tOrbit represents the orbital altitude and thus... spacecraft. With increasing orbital period tOrbit the orbital altitude hOrbit also rises... SCom is a function of the orbital altitude hOrbit , the position of..., S is only a function of the orbital altitude hOrbit . Furthermore, no pointing... of the sensor D [m], and the orbital altitude hOrbit . Their interrelations can..., 1999, p.264]. Thus with increasing orbital altitude hOrbit which implies an... it is a function of the orbital altitude hOrbit , so SW = 2 · ECAmax... 3.4.4, ECA is a function of the orbital altitude hOrbit and the elevation... of the orbital altitude (or, also possible, a function of the orbital period... is also a function of the orbital period tOrbit as 2 · π · REarth (3.76... an orbital altitude hOrbit of 700 km. This is the same orbital... Agency (DARPA) in collaboration with Orbital Sciences Corporation, the program shall... Phase 2 before the collaboration between Orbital Sciences Corporation and MIT was...’s industrial partner for the project, Orbital Sciences Corporation, was in the... in tOrbit means that the orbital altitude of the spacecraft hOrbit... of equation (3.52). A change in orbital altitude hOrbit , in turn, also... (A.3) Thus an increase in the orbital altitude hOrbit leads to an... with increasing orbital altitude. The maximum eclipse time for different orbital altitude... eclipse time decreases with increasing orbital altitude only until about 1500... time tEclipse and not the orbital period tOrbit as influencing parameter... above the orbital plane, thus the angle between the orbital plane and... whole mission lifetime assuming a constant orbital altitude over the mission duration... well as an attitude and orbital determination system can also be.... [CalPoly, 2007] CalPoly. Poly Picosatellite Orbital Deployer Mk III ICD (P-POD...

... Advanced Investigator Grant - 227571: VISIONSPACE: Orbital Dynamics at Extremes of Spacecraft... 67 3.5 Mass budget analysis 69 3.6 Orbital perturbations 77 3.6.1 J2 and J2... 6.1.1 Locally optimal steering laws 163 6.1.2 Orbital averaging 164 6.2 Optimal control problem... orbit 174 6.3.3 Eclipse analysis 176 6.4 Orbital averaging accuracy analysis 178 6.5 Chapter...-elliptic shape-based approach 227 A.1 Orbital transfers 227 A.1.1 Earth to Mars... of discretisation nodes N Number of orbital revolutions Ni Number of impulses... parameters P Solar radiation pressure Po Orbital period pe Part of low... vector x oe State vector of orbital elements y Y coordinate y Decision vector z Z coordinate... dimensional representation. b) Projection on the orbital plane. ........................................................................................................................ 17 Fig. 2.3 Schematic of... (a) and yaw (b) angles over one orbital period in winter when accounting... Fig. A.1 Optimal Earth to Mars orbital transfers for expo-elliptic and... k for an Earth to Mars orbital transfer…………………. 229 Table A.2 Optimal objective... controlled satellites (for which the orbital position is known) on geostationary... locally optimal steering laws and orbital averaging, will be outlined and... mass will be presented. The orbital averaging technique will be critically... dimensional representation. b) Projection on the orbital plane. Circular restricted three-body... displaced orbits according to their orbital period and to consider their... the equatorial plane for one orbital revolution and for different numbers.... 3.5 can be extended from one orbital revolution to multiple revolutions to... Earth-spacecraft vector during one orbital revolution. Furthermore, due to the... a function of time over multiple orbital periods, the displaced GEO is... lightness number, β0, and displacement distances, h. 3.6 Orbital perturbations A spacecraft in a (displaced) GEO... (a) and yaw (b) angles over one orbital period in winter when accounting... hundreds or even thousands of orbital revolutions and transfer times in... orbit, depending on where the orbital velocity is smallest. This approach...-elliptic shape for a range of orbital transfers and rendezvous transfers is... Section 6.1.1 and the use of orbital averaging to reduce the computational... of change of the orbital elements. The orbital elements have previously been... decrease (negative) in the corresponding orbital element. Out-of-plane f 1 2 α pi... the launch spiral steering laws. 6.1.2 Orbital averaging To investigate the influence... a huge computational effort. Therefore, the orbital averaging technique is used, which... orbital elements during a single revolution and dividing this change by the orbital period. For the launch spiral, this change in the orbital... orbital elements after one revolution. Subsequently dividing by 2π (instead of the orbital... of orbital elements, x oe = [ a e i Ω ω ] . The integral represents the change in an orbital element during one revolution, assuming all other orbital elements... the overbar indicates the averaged orbital elements. Equation (6.8) still includes a few... state variables, x , are the averaged orbital elements in the inertial, Earth... However, the use of classical orbital elements is preferred here because... T Tout ] (6.17) Note that the orbital averaging technique of Section 6.1.2 already... required substantial changes to the orbital elements. A way to reduce the... the reference frame of Fig. 6.5. 6.4 Orbital averaging accuracy analysis The results... obtained through the use of orbital averaging. For that, assumptions have... investigating the accuracy of the orbital averaging method for the low..., the assumptions made for the orbital averaging technique no longer hold... of motion, rather than the orbital averaging method, the boundary conditions... these effects. Finally, since the orbital averaging technique is valid under... acceleration, the accuracy of the orbital averaging technique breaks down at... by optimally changing the orbital elements. Furthermore, orbital averaging is used to... has an effect on the orbital averaging technique employed that reduces....1145/1731022.1731032 [113]. Boltz, F. W. "Orbital Motion Under Continuous Tangential Thrust...: 10.2514/3.56583 [114]. Boltz, F. W. "Orbital Motion Under Continuous Radial Thrust... [152]. Gao, Y., and Kluever, C. A. "Analytic Orbital Averaging Technique for Computing Tangential..., including both time-free problems (i.e. orbital transfers) in Section A.1 and time... problems (i.e. Lambert’s problem) in Section A.2). A.1 Orbital transfers For an initial assessment... Fig. A.1 Optimal Earth to Mars orbital transfers for expo-elliptic and... k for an Earth to Mars orbital transfer. w = 10 w = 100 w = 500 w = 1000... can establish for time-free orbital transfers. This section will investigate... A.4. While the results for the orbital transfers in Section A.1 showed a clear... and the initial and final orbital velocities are better matched, especially... the accelerations required for the orbital transfers and the Earth Mars...

... from high resolution DEM and ORBITAL data ...........................................................................................................................................................................240 An Adaptive and.... frequency linear fit, provided that orbital parameters are known with sufficient... ratio. We empirically correct for orbital errors by flattening the radar... a network approach to mitigate planar orbital and linear topographically correlated atmospheric... potential errors associated with incorrect orbital corrections induced by varying correlated... node, as well as additional orbital and atmospheric terms for the... error: (a) Atmospheric water vapour and (b) orbital uncertainties. Difference in radar signal... signals from atmospheric effects and orbital ramps in order to recover... data was used to remove orbital ramps on InSAR derived line... estimated from a joint inversion of orbital errors and phase-elevation ratio... days delay. The optimal ERS2 orbital control allowed getting very short... as ENVISAT IS2 until the orbital change in October 2010. For... spurious longwavelength signals (such as orbital errors) that usually affect InSAR... atmospheric influence appears minimal. Residual orbital gradients must also be considered... the potential to bias empirical orbital corrections. The PSI results show... calibration to compensate atmosphere and orbital phase contributions. In this work... with respect to atmospheric or orbital contributions in the phase * joint... order to reduce atmospheric and orbital systematic errors. But the proposed... order to cancel atmospheric and orbital contributions. Finally, we propose also... the selection of the appropriate orbital pass it is possible to... several kilometers with respect the orbital passes of the two satellites... such as TerraSAR-X with smaller orbital tubes, higher bandwidth and shorter... temporally uncorrelated ramps caused by orbital errors, this kind of trend... the tectonic plate to the orbital state vectors, provided that the... removing artifacts due to strong orbital errors, the resultant displacement field... a new operative phase with degraded orbital control and, SAR data were... after the acquisition without precise orbital records. - Acknowledgments - ENVISAT data are... water vapor as well as orbital, unwrapping errors, topography distortion. The... necessary. To remove any residual orbital errors and reduce tropospheric phase..., we perform a network atmospheric and orbital correction. To determine the interseismic... stratified atmospheric effect and residual orbital trends. The interferograms covering the... to investigate the characteristics of orbital and atmospheric errors and phase... deformation that is caused by orbital errors and atmospheric delay. We... ability to distinguish between satellite orbital errors, tectonic signal and the... induced by the atmosphere and orbital errors. The fact that we... sources of InSAR like atmosphere, orbital, phase unwrapping, deccorelation show the... reduces a part of atmospheric noise, orbital and unwrapping errors of the... results obtained by the first orbital interferometry study over Amazon region... from high resolution DEM and ORBITAL data Author(s) Fernanda Ledo G. Ramos... sub-optimal results as the orbital and topographic artefacts induce a misinterpretation... based on the use of orbital data and digital elevation model... from the study that linear orbital errors can be effectively removed... directions while for non-linear orbital errors, it is useful to... the deformation signal, tropospheric delay, orbital and DEM residual and noise... is also fitted to remove orbital errors. A careful visual inspection of... an external DEM and precise orbital data, geometrical wrap function can... to 1) correct InSAR data for orbital errors while preserving any deformation... this new orbital configuration of Envisat, and the new orbital repeat cycle... the time series generation the orbital and the atmospheric phase contributions... instruments operated in the same orbital configuration is ERS – ENVISAT cross... ), the adaptation of basic procedures (orbital model, algorithm for calculating the... of atmospheric artifacts and residual orbital removal, followed by the inversion... different incidence angle and residual orbital fringes in C-band. The angle... rate ratio. Due to residual orbital fringes, more work is needed... the presence of atmospheric and orbital artifacts in the signal by... signals such as atmospheric or orbital artifacts, removing the need for... due to atmospheric delay and orbital errors, is strongly correlated in... pervious step includes atmospheric delay, orbital errors, nonlinear deformation and 317...

..., Longitude, Radius ........................................... 13 2.1.4 Perifocal ............................................................................................ 14 2.2.1 Orbital................................................................................................ 15 2.2.2 Body Fixed ........................................................................................ 16 2.3 Attitude... 2.4: Perifocal reference frame ............................................................................... 14 Figure 2.5: Orbital reference frame .................................................................................. 15 Figure 2.6: Body... and developed the Poly Picosatellite Orbital Deployer (P-POD). The P-POD is... important to note that the orbital frame in particular varies between... fundamental plane (pq) is the orbital plane with the principal direction... w which is orthogonal to the orbital plane and aligned with the... (Curtis). Page 14 2.2.1 Orbital Figure 2.5: Orbital reference frame The Orbital frame is an... 𝑍𝑂 axis is aligned with the orbital angular momentum vector (cross-track... done so to match the orbital reference frame and the equations... of the orbital frame that is aligned with the orbital position vector... matrix for the body to orbital transformation 𝑄𝑏𝑜 . 5.1.1 Gravity Gradient Stability By... the Earth, and 𝑖 is the orbital inclination (Varma). 5.4 Solar Radiation Pressure... 400 km. Since the desired orbital regime for ExoCube is between... with knowledge of the spacecraft’s orbital position and the local magnetic... with knowledge of the spacecraft’s orbital position and the local sun... neglected. The error from onboard orbital position knowledge is negligible The... in the Orbital Frame - The magnetic field components in the orbital frame... when a magnetic lookup table and orbital position are combined - Peaks indicate... 8.4.1.1 Optimal Case -5 5 -5 a) Magnetic Field in Orbital Frame [T] x 10 6 -6 b) Magnetic Field in...-Optimal Case -5 5 -5 a) Magnetic Field in Orbital Frame [T] x 10 6 -6 b) Magnetic Field in...] 8.4.1.3 Local Instability -5 5 -5 a) Magnetic Field in Orbital Frame [T] x 10 8 -6 b) Magnetic Field in... Pulse Time -5 5 -5 a) Magnetic Field in Orbital Frame [T] x 10 8 -6 b) Magnetic Field in... Resolution Error -5 5 -5 a) Magnetic Field in Orbital Frame [T] x 10 8 0 -5 0 20 40 60... Resolution Error -5 5 -5 a) Magnetic Field in Orbital Frame [T] x 10 8 -5 b) Magnetic Field in... error quaternion as follows: 𝜃𝑒𝑟𝑟 = 2 acos(𝑞4,𝑒𝑟𝑟 ) e) Orbital Angular Rates - The components of... the body-orbital rates - The dotted lines represent the desired orbital rates... the control torques f) - Page 88 - Orbital Quaternions The components of the... the body-orbital quaternion The dotted lines represent the desired orbital quaternion... 350 400 450 -1 0 50 100 e) Orbital Angular Rates [deg/s] 60 150... 400 450 350 400 450 f) Orbital Quaternions 1 1 50 0.5 40 0.5 30 0 20... 700 800 900 0 100 200 e) Orbital Angular Rates [deg/s] 60 300... 800 900 700 800 900 f) Orbital Quaternions 0.4 1 0.3 50 0.2 40 0.5 0.1 30 0 0 -0.1 20... 700 800 900 -1 0 100 200 e) Orbital Angular Rates [deg/s] 60 300... 800 900 700 800 900 f) Orbital Quaternions 1 1 50 0.5 40 0.5 30 0 20...] 600 700 800 -1 0 100 200 e) Orbital Angular Rates [deg/s] 60 300... 700 800 600 700 800 f) Orbital Quaternions 1 1 50 0.5 40 0.5 30 0 20... 800 900 -1 0 100 200 300 e) Orbital Angular Rates [deg/s] 60 400... 800 900 700 800 900 f) Orbital Quaternions 1 1 50 0.5 40 0.5 30 0 20... 800 900 -1 0 100 200 300 e) Orbital Angular Rates [deg/s] 60 400... 800 900 700 800 900 f) Orbital Quaternions 1 1 50 0.5 40 0.5 30 0 20... 700 800 900 -1 0 100 200 e) Orbital Angular Rates [deg/s] 60 0.06... 800 900 700 800 900 f) Orbital Quaternions 1 0.5 0 -0.5 0 0 100 200 300 400... 700 800 900 -1 0 100 200 e) Orbital Angular Rates [deg/s] 60 300... 800 900 700 800 900 f) Orbital Quaternions 0.1 1 0.05 0.5 0 0 -0.05 -0.5 50 40...] 1000 1200 1400 0 200 400 e) Orbital Angular Rates [deg/s] 60 600... 1200 1400 1000 1200 1400 f) Orbital Quaternions 2 1 1.5 50 1 40 0.5 0.5 30 0 0 -0.5 20... ram-pointing orientation in the orbital frame. It was discovered that.... 19 February 2013. . Curtis, Howard D. Orbital Mechanics for Engineering Students. 2nd...

Orbital dynamics of „smart dust‟ devices ...-lived orbits. Spacecraft mass, kg. Orbital angular velocity of the Earth... Earth, km. Orbit radius, km. Orbital period, s or days. Velocity relative... concepts requires an understanding of orbital dynamics at extremes of spacecraft... spacecraft, requires new insights into orbital dynamics since perturbations such as... the synchronous and semi-synchronous orbital regime [15, 16]. Furthermore, the... observed since 1960 in the orbital behavior of satellites such as... investigate the evolution of the orbital elements [23]. Due to the... active control. Given the initial orbital elements of the spacecraft, the... change of the in-plane orbital elements over a single orbit revolution... analysis of the change in orbital elements due to solar radiation... then performed. A search for initial orbital conditions for long-lived orbits... of the secular variation of orbital elements is used to characterize.... The secular variation of the orbital elements is obtained by averaging.... As a first approach to explore orbital dynamics at small length-scales... and transversal directions in the orbital plane, and the characteristic acceleration..., a, e and are the in-plane orbital elements, r is the orbit radius... orbital elements, i.e. Eqs. (3) are integrated in true anomaly, considering the other orbital..., the total variation of the orbital elements can be evaluated over... . Since we are assuming the orbital elements and aSRP to be..., the total variation of the orbital elements can be written as... a closed-form function of the orbital elements: fecl, enter a, e, Sun , fecl... of the Earth, and r the orbital radius. The expressions for fecl... provide the actual variation of orbital elements considering the Earth‟s shadow... orbital elements can be obtained by dividing Eqs. (6) by the Keplerian orbital... the secular perturbation on the orbital elements due to atmospheric drag... change of the in-plane orbital elements over a single revolution is... the orbital elements by dividing Eqs. (14) by the Keplerian orbital period... total secular variation of the orbital elements can then be expressed... the Keplerian elements over a single orbital revolution can be computed by... Earth inertial system) over one orbital period of the spacecraft, such... Sun, 2 nEarth-Sun T a , T being the orbital period, given by Eq. (10... around the Sun over one orbital period of the Journal of... Dynamics 15 a) b) Fig. 5 Variation of orbital elements over a single orbit revolution... for determining the change in orbital elements over a single orbit and..., in the representation of the orbital element phase-space. A. Spacecraft and... long-lived SpaceChip orbits on orbital parameters and area-tomass ratio... the looping trajectory in the orbital element space. The long-term... spacecraft describes a spiral in the orbital element phase-space. The orbit... increasing eccentricity. These sets of orbital elements are indicated in Fig... extended useful region of the orbital element space was identified to.... Conclusions This paper analyzed the orbital dynamics of future „smart dust... the useful region of the orbital element space for increasing science...-C1.8.2. Shapiro, I. I., Jones, H. M. and Perkins, C. W., “Orbital Properties of the West Ford...-629. Oyama, T., Yamakawa, H. and Omura, Y., “Orbital Dynamics of Solar Sails for..., London, 1964. Blitzer, L., “Handbook of Orbital Perturbations,” University of Arizona, 1970..., 1965, Ch. 9. Colombo, C. and McInnes, C., “Orbital Dynamics of Earth-Orbiting 'Smart...

...2010 Beijing Orbital Debris Mitigation Workshop Beihang University (... of Participants 15 2010 Beijing Orbital Debris Mitigation Workshop Oct.18... Kyushu University Hiroshi 1 2010 Beijing Orbital Debris Mitigation Workshop Oct.18... Stanford University Jan 2 2010 Beijing Orbital Debris Mitigation Workshop Oct.18... (CAEP) 38 39 3 2010 Beijing Orbital Debris Mitigation Workshop Oct.18...:00 Hypervelocity Impacts Effect of Orbital Debris on Spacecraft Pressurized Structures...:00-15:30 Overview of Orbital Debris Removal Brian WEEDEN, Secure... TRUSHLYAKOV, Omsk University 4 2010 Beijing Orbital Debris Mitigation Workshop Oct.18... BOMBARDELLI, Technical University of Madrid Orbital Debris Characteristic Analyze and a Small... – Dr. Jan STUPL, Stanford University Orbital Debris Removal by the Active...-14:00 Lunch 5 2010 Beijing Orbital Debris Mitigation Workshop Oct.18...:00 Workshop Dinner 6 2010 Beijing Orbital Debris Mitigation Workshop Oct.18... users and designers. 7 2010 Beijing Orbital Debris Mitigation Workshop Oct.18... addressed. Keyword: Micro meteoroids and orbital debris (M/OD), Hypervelocity impact, protection... flyer (LDF) system Effect of Orbital Debris on Spacecraft Pressurized Structures...-walled pressurized structure subjected to orbital debris impact. Experimental studies have... the experimental results. 8 2010 Beijing Orbital Debris Mitigation Workshop Oct.18... to impact location. Overview of Orbital Debris Removal Brian WEEDEN Secure... overview of the topic of orbital debris removal, including a summary of..., traffic management, orbital crowding, and collisions. 9 2010 Beijing Orbital Debris Mitigation Workshop... debris throughout their orbital lifetime. 10 2010 Beijing Orbital Debris Mitigation Workshop... tether maneuverability are also discussed. Orbital Debris Characteristic Analyze and a Small... a collision due to their high orbital speed. In this presentation, background... this concept. 11 2010 Beijing Orbital Debris Mitigation Workshop Oct.18...-satellite weapons. 12 2010 Beijing Orbital Debris Mitigation Workshop Oct.18... effects coupled with a high-precision orbital propagator to model the results... a debris-debris collision avoidance scheme. Orbital Debris Removal by the Active... upper stages is steadily increasing, orbital debris will become a serious problem... on an orbital debris removal system for the mitigation of orbital debris... other geosynchronous 13 2010 Beijing Orbital Debris Mitigation Workshop Oct.18... micro-satellite. 14 2010 Beijing Orbital Debris Mitigation Workshop Oct.18... Congressional committees. 15 2010 Beijing Orbital Debris Mitigation Workshop Oct.18....isunet.edu 16 2010 Beijing Orbital Debris Mitigation Workshop Oct.18....edu.cn 17 2010 Beijing Orbital Debris Mitigation Workshop Oct.18... Environment Engineering. 18 2010 Beijing Orbital Debris Mitigation Workshop Oct.18... impact phenomena, spacecraft vulnerability/survivability, orbital debris protection, low- and high...@gmail.com 19 2010 Beijing Orbital Debris Mitigation Workshop Oct.18... (JSpOC), Captain Weeden directed the orbital analyst training program and developed...-u.ac.jp 20 2010 Beijing Orbital Debris Mitigation Workshop Oct.18... are inert and electrodynamic tethers, orbital dynamics and mission analysis. claudio...@upm.es 21 2010 Beijing Orbital Debris Mitigation Workshop Oct.18...@163.com 22 2010 Beijing Orbital Debris Mitigation Workshop Oct.18...@stanford.edu 23 2010 Beijing Orbital Debris Mitigation Workshop Oct.18... objects. He 24 2010 Beijing Orbital Debris Mitigation Workshop Oct.18...@ucsusa.org 25 2010 Beijing Orbital Debris Mitigation Workshop Oct.18... National Security 26 2010 Beijing Orbital Debris Mitigation Workshop Oct.18...@olemiss.edu 27 2010 Beijing Orbital Debris Mitigation Workshop Oct.18...

... is subject to the variable orbital geometry of Earth, Mars and.... Preliminary communication link budget and orbital analysis of a two-constellation MIR...’s orbit ( group, 292 nodes). Potential orbital tracks are presented for network... figure = Occupied bandwidth = Orbital offset of Mars orbit = Orbital track separation at closest approach of Earth and Mars orbital track = Orbital track separation at farthest approach of Earth and Mars orbital... far proven extremely elusive: convenient orbital locations providing persistent line of... use regardless of the respective orbital positions of Earth, Mars and...-risk, mission events such as orbital maneuvers, entry/descent/landing maneuvers... relay satellites and their coordinated orbital track across a fair amount of... orbital platform, all placed in a single sun-synchronous dusk-dawn orbital plane... additional delta-vee resources for orbital maneuvers from Earth to the... satellites are usable due to orbital mechanics and limitations of the... the planet, or through an orbital gateway to communicate across the... satellite relay constellation connecting the orbital paths of Earth and Mars... of sight back to Earth’s orbital position at critical phases. B. Investigation... is not dependent upon any orbital geometry. The principal factors are... and Mars orbital tracks as well as Earth and Venus orbital tracks... to the fact that the orbital tracks of Mars and Earth... by utilizing the Earth Mean Orbital Elements (J2000) provided by NASA... the orbital eccentricity of Mars, , is greater than that of the orbital... is necessary to calculate an orbital offset to shift the major... between foci of Mars orbit = Orbital Offset ( ∗ (26) ) of Mars and... the at closest approach, the Orbital Track Separation, is approximately 0.38... and at farthest approach, the Orbital Track Separation, is approximately 0.67... calculated the required separation between orbital tracks. Number of spacecraft in... and ellipses. Therefore the 35th orbital track, 35was adjusted in an... as > > , and an extra 36th orbital track, 36 included inside of... Influence. The equations for T35 orbital track ellipse are provided below... for orbital track T36 is actually based upon the original orbital track... to proceed independent of the orbital geometry of the Sun, Mars... of required spacecraft, and the orbital tracks in heliocentric space will... topologies: . There will be an orbital fleet of MIR/G spacecraft in... orbit. There will be an orbital fleet of MIR/G spacecraft in... communicate directly with the stationary orbital platform MIR/G and request a local... is only valid in certain orbital configurations of the Earth/Mars... are varied somewhat in their orbital arrangement, they will not be... the group toward the Earth orbital track will be able to... supplementary MIR/R satellites in the orbital arc of Mars and this... Earth and space between the orbital track of Mars and Earth... chain. The orbits of Mars orbital tracks the N1 group will... MIR/R spacecraft (N2) in a single orbital track within Earth’s own orbit... for use regardless of the orbital positions of Earth, Mars and... for a Mars communications and navigation orbital infrastructure. AAS/AIAA Astrodynamics Specialist...

... Orbit Control . . . . . . . . . . . . 138 6.3.1 Close Proximity Orbital Dynamics . . . . . . . . . . . . . . . . . . . . . . 138 6.3.2 Fuel-Efﬁcient... [23]. . . . 10 . . . . . . . 10 1.8 A summary of orbital dispersion simulation study results for... [59, 60]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 5.2 Optimal intercept orbital geometry [59, 60]. . . . . . . . . . . . . . . . . . . . . . 114 5.3 ΔV contour... List of Tables 2.1 Physical and orbital properties of a reference target (asteroid... mission event time . . . . . . . . . . . . . . . . . . . . 112 5.2 Target orbital elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 5.3 Optimal intercept parameters... produce an actual orbital change much 2 larger than predicted orbital perturbation uncertainties... be to effectively change the orbital trajectories of asteroids of different... (i.e., destroying or fragmenting with substantial orbital dispersion), or by altering its... be presented in Chapter 4. The orbital dispersion problem of a fragmented asteroid... code was also used for orbital dispersion simulation and analysis in... [23]. 10 Figure 1.8: A summary of orbital dispersion simulation study results for... subsurface explo sions [23, 24]. • Orbital elements are evaluated for each... intercept to impact time. • The orbital elements of each fragment are... certain conditions, disruption (with large orbital dispersion) is the only feasible... are presented in Table 2.1. The orbital elements of 2006 CL9 listed... table are heliocentric ecliptic J2000 orbital elements at epoch JD 2456400... of the NEO along its orbital path, and the location of... 9 (very 22 Table 2.1: Physical and orbital properties of a reference target (asteroid... this initial trajectory design. A reference orbital trajectory of a PDFV mission to... D-type E-type 380 800 6 19 Orbital period (yrs) e i (deg) ΔV (km/s) Orbit... of the NEO along its orbital path, and the location of... also presented in [28]. A complex orbital trajectory optimization algorithm, developed in... to compensate for errors in orbital navigation toward the target asteroid... impact with a larger (5 km) comet. Orbital navigation during a terminal phase of... a predictive guidance scheme based on orbital perturbation theory has also been... from collisions with micrometeoroids and orbital debris with impact speed range... protect spacecraft from collisions with orbital debris and micrometeoroids for impact... lead time to achieve large orbital dispersion of NEO fragments, full...] consists of the following assumptions: • Orbital elements of the target NEO... a single impulse; • Restricted two-body orbital dynamics are assumed. For more... in terms of the geocentric orbital elements at the time of... typical for Earth-impacting NEOs. Orbital Trajectory Models The interceptor missile... t1 t2 Figure 5.2: Optimal intercept orbital geometry [59, 60]. Accounting for... point in time. From the orbital elements of the NEO at... 11 hours before impact. The orbital elements of the target NEO... window [59, 60]. Table 5.2: Target orbital elements Orbital elements Values a −4, 067 km... be strong enough to destabilize orbital motion of spacecraft about irregular... for maintaining stable, close proximity orbital motion with little propellant expen... Orbit Con trol 6.3.1 Close Proximity Orbital Dynamics Several illustrative orbits around... consider feedback con trol of orbital motion of a spacecraft around an...-shaped asteroid assuming that the orbital position and velocity of the... estimation or measurement of spacecraft’s orbital position and velocity relative to... tested in [72–74] for orbital motion simulation of a spacecraft around... a 3D Flash LIDAR. 6.4 Summary The orbital motions around small bodies are...-Efﬁcient Feedback Control of Orbital Motion Around an Irregular-Shaped...-Efﬁcient Feedback Control of Orbital Motion around Irregular-Shaped Asteroids..., May 2013. 154 [75] Scheeres, D. J., “Orbital Mechanics About Small Bodies,” Acta... Determination of Stability Regions for Orbital Mo tion in Uniformly Rotating...] Scheeres, D. J., Miller, J. K., and Yeomans, D. K., “The Orbital Dynamics Environment of 433 Eros...