Mission Orbits Research Articles

Mesoscale Structure and Properties of the Terrestrial Magnetotail Plasma Sheet From the Magnetospheric Multiscale Mission

AbstractUsing Magnetospheric Multiscale mission (MMS) orbits in the Earth's magnetotail from 2017 to 2020, plasma conditions and the 3D spatial structure of inner‐magnetotail plasma environments (with a focus on the plasma sheet (PS)) are studied with different approaches. Threshold conditions for distinguishing the PS, PS boundary layers, and lobes are derived from the statistical properties of background plasma parameters. Our results support previous studies that employed similar methods using Cluster data. However, stronger currents are observed in both the lobes and PS, likely due to the smaller spacecraft separation (≲70 km) that can resolve thin electron‐scale currents. Threshold conditions are used together with magnetic field and electric field measurements to image the spatial structure of the PS. Results are in good agreement with a global neutral sheet model based on solar wind conditions and magnetospheric configurations. Furthermore, the Earth's dipole tilts toward the Sun around June solstice, which warps the magnetotail as much as ∼2–4 RE in Z geocentric solar magnetospheric. This warping effect is relaxed toward September equinox. Consequently, as MMS travels through the magnetotail from dawn to dusk during this period, there is an apparent dawn‐dusk asymmetry in plasma conditions between June and September. Kink‐like flapping waves and interplanetary magnetic field twisting are other mesoscale processes attributed with a few RE of flaring near the flanks. These findings reveal important insights into the mesoscale structure and dynamics of the magnetotail.

A Synthetic Data Set Inspired by Satellite Altimetry and Impacts of Sampling on Global Spaceborne Discharge Characterization

AbstractDespite being a critical component of Earth's water cycle, much remains unknown about freshwater fluxes in the world's rivers. Discharge can be estimated in situ by monitoring water surface elevation yet the declining worldwide coverage of gauges makes global discharge quantification challenging. Numerous studies have shown that satellite radar altimetry could provide global discharge estimates. In anticipation such groundbreaking datasets, one key question remains unanswered: how accurately could the various orbital configurations of altimetry missions capture global discharge distributions under optimal retrieval conditions? We here generate an idealized synthetic global discharge data set following mission orbits, and present the first evaluation of various spatiotemporal sampling strategies on global discharge distribution estimation. Our data are produced by superimposing six measurement footprints representing nine altimetry missions onto existing global discharge simulations. While this approach assumes accurate simulations and ignores uncertainties in spaceborne discharge estimation, it allows for an upper limit assessment of how satellite missions might capture global characteristics of hydrographs. We show that most orbits used could lead to accurate global mean flow distribution (<7%), which was expected but never demonstrated. We also find that accurate distributions of minimum flow (respectively, maximum flow and peak flow duration) require revisit times more frequent than 10 (respectively, 5 and 5) days, that is, finer than allowed by existing orbital strategies, and that global extreme discharge and peak flow distributions rely on temporal frequency rather than spatial coverage. Our analysis could inform future mission development and our data set be used to support potential global gap‐filling experiments.

Parameterizing large constellation post-mission disposal success to predict the impact to future space environment

Future large constellations are being proposed that may include hundreds to thousands of satellites, spread across multiple orbit altitudes in LEO, some of which are already highly populated. The long-term hazard to the safe operational space environment's utility posed by these new constellations is not fully understood. The magnitude of debris generated via explosions and collisions with other space objects will be significantly influenced by the constellation characteristics, and the post-mission disposal (PMD) policy followed by these satellite operators. This study models the future orbital environment for debris based on different levels and types of space activity and PMD success rates. The future constellation model (FCM) utilized in the study consists of numerous constellations representative of proposed systems. These constellations manifest a wide range of characteristics relevant to their impact on the future debris environment, including mission and disposal orbits, satellite counts, masses, and areas. The PMD success rate is varied across scenarios from 70% to 100%. Unsuccessfully disposed satellites are modeled to either remain in their operational orbit after end-of-life or along the ascent or disposal paths. Given the satellite count, size, mass, and replenishment cadence of each constellation, and varying PMD success rate, each scenario is parameterized to simple undisposed object metrics. By parameterizing in this way, the environment impact of scenarios with different satellite counts and physical characteristics are compared on a normalized plot.

Numerical simulation of sky localization for LISA-TAIJI joint observation

LISA is considered to be launched alongside the Athena to probe the energetic astrophysical processes. LISA can determine the direction of sources for Athena's follow-up observation. As another space gravitational wave mission, TAIJI is expected to be launched in the 2030s. The LISA-TAIJI network would provide abundant merits for sources understanding. In this work, we simulate the joint LISA-TAIJI observations for gravitational waves from coalescing supermassive black hole binaries and monochromatic sources. By using the numerical mission orbits, we evaluate the performances of sky localization for various time-delay interferometry channels. For 30 days observation until coalescence, the LISA-TAIJI network in optimal operation can localize all simulated binary sources, $({10}^{7},3.3\ifmmode\times\else\texttimes\fi{}{10}^{6}){M}_{\ensuremath{\bigodot}}$, $({10}^{6},3.3\ifmmode\times\else\texttimes\fi{}{10}^{5}){M}_{\ensuremath{\bigodot}}$, and $({10}^{5},3.3\ifmmode\times\else\texttimes\fi{}{10}^{4}){M}_{\ensuremath{\bigodot}}$ at redshift $z=2$, in $0.4\text{ }\text{ }{\mathrm{deg}}^{2}$ (field of view of Wide Field Imager on Athena). The angular resolution can be improved by more than ten times comparing to LISA or TAIJI single detector at a given percentage of population. The improvements for monochromatic sources at 3 and 10 mHz are relatively moderate in one year observation. The precision of sky localization could be improved by a factor of 2 to 4 comparing to single LISA at a given percentage of sources. For a simulated 90 days observation for monochromatic waves, the LISA-TAIJI network still represents a considerable localization advantage which could be more than ten times better.

NewSpace and its implications for space debris models

Until two decades ago, the dominance of the space industry by national governments shaped the key characteristics of the spacecraft population and hence the space debris models used to anticipate future orbital populations. The rise of `NewSpace’ with the growth of private sector involvement has brought innovations, disrupting the status quo and changing to the physical characteristics and mission orbits of commercial spacecraft. Analysis of shifts in mass and launch traffic for spacecraft launched between 1980 and 2019 (source: ESA's DISCOS database) suggests significant impacts for debris modelling. Results emphasised the ongoing change towards a more commercially focused space sector. 742 spacecraft were launched in the 1980s, of which 34 were labelled as commercial. By contrast, there were 1292 commercial missions out of 2325 launched in the 2010s - an increase from 4.6% to 55.6%. These increases correlate with a rise in the number of different organisations operating spacecraft and a clear trend can be seen towards smaller, lower mass spacecraft. This is likely to alter the distributions of fragments generated in collisions compared with the distributions obtained from empirical methods, such as the NASA Standard Breakup model, derived from the fragmentation of larger spacecraft in the 600-1,000 kg range. A study of observed breakup events indicates that the NASA Standard Breakup Model over-estimates the number of large debris released during fragmentations due to collisions or explosion of satellites while also under-estimating the number of small debris. It is believed that this will have a significant impact on the outcomes of simulations of the future debris environment where these fragmentation modes are expected to dominate the generation of new debris over the propulsion based explosions which have been historically prevalent.

Orbit propagation in irregular and uncertain gravity field using differential algebra

Uncertainty propagation has been addressed extensively in space missions around the Earth, but much less for missions around small solar system bodies. Small bodies usually have irregular and weak gravity and our knowledge of their gravity, rotation speed and surrounding space environment is largely uncertain. These characteristics make the orbit propagation around these small bodies a challenging task.Focusing on the uncertainty of the small body's gravity, this paper applies the differential algebra (DA) technique to study the orbit propagation problem, and addresses its efficiency for a given the required accuracy. Different from traditional studies that focus on the uncertainty of the initial state, this study assumes an exact initial state and studies the influences that gravity model uncertainties have on the orbit. Taking the asteroid Steins as an example, the accuracy and the efficiency of the DA approach are firstly validated by comparison with the traditional Monte Carlo method. Then, the effects of gravity uncertainties on different types of orbits (prograde, retrograde and polar) are studied. The retrograde motion is found to be more robust to the gravity uncertainty than the prograde ones. For near polar orbits, the impact of gravity uncertainty on orbital motion depends significantly on the initial position, and it reaches the maximum if the initial position is near the polar regions. Moreover, short-term effects are found to play an important role in orbit deviation as a result of the gravity uncertainty. These discoveries can help mission designers assess the posed risk and design appropriate mission orbits.

Overview of China’s 2020 Mars mission design and navigation

Scheduled for an Earth-to-Mars launch opportunity in 2020, the China’s Mars probe will arrive on Mars in 2021 with the primary objective of injecting an orbiter and placing a lander and a rover on the surface of the Red Planet. For China’s 2020 Mars exploration mission to achieve success, many key technologies must be realized. In this paper, China’s 2020 Mars mission and the spacecraft architecture are first introduced. Then, the preliminary launch opportunity, Earth–Mars transfer, Mars capture, and mission orbits are described. Finally, the main navigation schemes are summarized.

Spin axis offset calibration on THEMIS using mirror modes

Abstract. A newly developed method for determining spin axis offsets of magnetic field instruments on spacecraft is applied to THEMIS. The formerly used determination method, relying on solar wind Alfvénic fluctuations, was rarely applicable due to the orbital restrictions of the mission. With the new procedure, based on magnetic field observation of mirror modes in the magnetosheath, updated spin axis offsets can be estimated approximately once per year. Retrospective calibration of all THEMIS magnetic field measurements is thereby made possible. Since, up to this point, spin axis offsets could hardly ever be calculated due to the mission's orbits, this update represents a substantial improvement to the data. The approximate offset stability is estimated to be < 0.75 nT year−1 for the complete course of the mission.

Orbit optimization and time delay interferometry for inclined ASTROD-GW formation with half-year precession-period

ASTROD-GW (ASTROD [astrodynamical space test of relativity using optical devices] optimized for gravitational wave detection) is a gravitational-wave mission with the aim of detecting gravitational waves from massive black holes, extreme mass ratio inspirals (EMRIs) and galactic compact binaries together with testing relativistic gravity and probing dark energy and cosmology. Mission orbits of the 3 spacecrafts forming a nearly equilateral triangular array are chosen to be near the Sun–Earth Lagrange points L3, L4, and L5. The 3 spacecrafts range interferometrically with one another with arm length about 260 million kilometers. For 260 times longer arm length, the detection sensitivity of ASTROD-GW is 260 fold better than that of eLISA/NGO in the lower frequency region by assuming the same acceleration noise. Therefore, ASTROD-GW will be a better cosmological probe. In previous papers, we have worked out the time delay interferometry (TDI) for the ecliptic formation. To resolve the reflection ambiguity about the ecliptic plane in source position determination, we have changed the basic formation into slightly inclined formation with half-year precession-period. In this paper, we optimize a set of 10-year inclined ASTROD-GW mission orbits numerically using ephemeris framework starting at June 21, 2035, including cases of inclination angle with 0° (no inclination), 0.5°, 1.0°, 1.5°, 2.0°, 2.5°, and 3.0°. We simulate the time delays of the first and second generation TDI configurations for the different inclinations, and compare/analyse the numerical results to attain the requisite sensitivity of ASTROD-GW by suppressing laser frequency noise below the secondary noises. To explicate our calculation process for different inclination cases, we take the 1.0° as an example to show the orbit optimization and TDI simulation.

Parameterization of Micro Satellite Launch Vehicle

The new trends in micro satellites mission for wide range of applications has motivated worldwide research in design and development of micro satellite launch vehicles (MSLVs) as a vital options in the deployment of such satellites into their respective mission orbits. Presently, most micro satellites are launched through rideshares with rockets or rocket-like systems, which were developed essentially in the seventieth and eightieth of the last century. The MSLV as a proportional micro satellite launch vehicle, up till now has only the status of technology and system study work and is well known that the research and development of MSLV are diversified in different fields. However, the realization of MSLVs is rigorous since such vehicles compound the inherent difficulties of traditional launch experiment with intrinsic problems of uneven mass distribution, slenderness, high frequency and amplitude of vibration etc. MSLV are also more likely to be affected by wind gusts and other disturbances than their conventional counterpart, and the physical parameters such as mass distribution and moments of inertia can be easily altered by changing the payload location and unpredictable propellant burning. All these factors compromise the additional velocities to overcome the aerodynamic drag, to account for steering of the vehicle and other losses. Consequently, We prototype a three stage micro-satellite launch equipment as a similitude of the European Space Agency’s VEGA launcher using a scale down derivation model and parameterized using existing VEGA launch vehicle (LV) technical data. VEGA launch data, total orbital velocity requirement including the losses and stage payload ratio are inferred and applied to the model of parameterization of launch vehicles through coupledparameters simulations. This approach can be helpful in viability and performance insights in terms of payload mass, stage mass distribution and material properties precision and effectiveness. It can also serve as a background for the development of time optimal waypoint trajectory of micro satellite launchers.

Orbit optimization for ASTROD-GW and its time delay interferometry with two arms using CGC ephemeris

Astrodynamical space test of relativity using optical devices optimized for gravitation wave detection (ASTROD-GW) is an optimization of ASTROD to focus on the goal of detection of gravitation waves. The detection sensitivity is shifted 52 times toward larger wavelength compared with that of laser interferometer space antenna (LISA). The mission orbits of the three spacecrafts forming a nearly equilateral triangular array are chosen to be near the Sun—Earth Lagrange points L3, L4, and L5. The three spacecrafts range interferometrically with one another with an arm length of about 260 million kilometers. In order to attain the required sensitivity for ASTROD-GW, laser frequency noise must be suppressed to below the secondary noises such as the optical path noise, acceleration noise, etc. For suppressing laser frequency noise, we need to use time delay interferometry (TDI) to match the two different optical paths (times of travel). Since planets and other solar-system bodies perturb the orbits of ASTROD-GW spacecraft and affect the TDI, we simulate the time delay numerically using CGC 2.7 (here, CGC stands for center for gravitation and cosmology) ephemeris framework. To conform to the ASTROD-GW planning, we work out a set of 20-year optimized mission orbits of ASTROD-GW spacecraft starting at June 21, 2028, and calculate the differences in optical path in the first and second generation TDIs separately for one-detector case. In our optimized mission orbits of 20 years, changes of arm lengths are less than 0.0003 AU; the relative Doppler velocities are all less than 3 m/s. All the second generation TDI for one-detector case satisfies the ASTROD-GW requirement.

Numerical simulation of time delay interferometry for eLISA/NGO

eLISA/NGO is a new gravitational wave detection proposal with arm length of 106 km and one interferometer down-scaled from LISA. Just like LISA and ASTROD-GW, in order to attain the requisite sensitivity for eLISA/NGO, laser frequency noise must be suppressed to below the secondary noises such as the optical path noise, acceleration noise, etc. In previous papers, we have performed the numerical simulation of the time delay interferometry (TDI) for LISA and ASTROD-GW with one arm dysfunctional by using the CGC 2.7 ephemeris. The results are well below their respective limits in which the laser frequency noise is required to be suppressed. In this paper, we follow the same procedure to simulate the time delay interferometry numerically. To do this, we work out a set of 1000-day optimized mission orbits of the eLISA/NGO spacecraft starting on 1 January 2021 using the CGC 2.7 ephemeris framework. We then use the numerical method to calculate the residual optical path differences in the second-generation TDI solutions as in our previous papers. The maximum path length difference, for all configurations calculated, is below 13 mm (43 ps). It is well below the limit in which the laser frequency noise is required to be suppressed for eLISA/NGO. We compare and discuss the resulting differences due to the different arm lengths for various mission proposals—eLISA/NGO, an NGO-LISA-type mission with a nominal arm length of 2 × 106 km, LISA and ASTROD-GW.

DEPLOYMENT AND SIMULATION OF THE ASTROD-GW FORMATION

Constellation or formation flying is a common concept in space Gravitational Wave (GW) mission proposals for the required interferometry implementation. The spacecraft of most of these mission proposals go to deep space and many have Earthlike orbits around the Sun. Astrodynamical Space Test of Relativity using Optical Devices optimized for Gravitation Wave detection (ASTROD-GW), Big Bang Observer (BBO) and DECIGO have spacecraft distributed in Earthlike orbits in formation. The deployment of orbit formation is an important issue for these missions. ASTROD-GW is to focus on the goal of detection of GWs. The mission orbits of the three spacecraft forming a nearly equilateral triangular array are chosen to be near the Sun–Earth Lagrange points L3, L4 and L5. The three spacecraft range interferometrically with one another with arm length about 260 million kilometers with the scientific goals including detection of GWs from Massive Black Holes (MBH) and Extreme-Mass-Ratio Black Hole Inspirals (EMRI), and using these observations to find the evolution of the equation of state of dark energy and to explore the co-evolution of MBH with galaxies. In this paper, we review the formation flying for fundamental physics missions, design the preliminary transfer orbits of the ASTROD-GW spacecraft from the separations of the launch vehicles to the mission orbits, and simulate the arm lengths of the triangular formation. From our study, the optimal delta-Vs and propellant ratios of the transfer orbits could be within about 2.5 km/s and 0.55, respectively. From the simulation of the formation for 10 years, the arm lengths of the formation vary in the range 1.73210 ± 0.00015 AU with the arm length differences varying in the range ±0.00025 AU for formation with 1° inclination to the ecliptic plane. This meets the measurement requirements. Further studies on the optimizations of deployment and orbit configurations for a period of 20 years and with inclinations between 1° to 3° are currently ongoing.

Dark energy, co-evolution of massive black holes with galaxies, and ASTROD-GW

The detection of low frequency band (100nHz–100mHz) and very low frequency band (300pHz–100nHz) gravitational waves (GWs) is important for exploration of the equation of state of dark energy and the co-evolution of massive black holes (MBHs) with galaxies. Most galaxies are believed to have a massive black hole in the galactic core. In the formation of these black holes, merging and accretion are the two main processes. Merging of massive black holes generate GWs which could be detected by space GW detectors and Pulsar Timing Arrays (PTAs) to cosmological distances. LISA (Laser-Interferometric Space Antenna) is most sensitive to the frequency band 1mHz–100mHz, ASTROD-GW (ASTROD [Astrodynamical Space Test of Relativity using Optical Devices] optimized for Gravitational Wave detection) is most sensitive to the frequency band 100nHz–1mHz and PTAs are most sensitive to the frequency band 300pHz–100nHz. In this paper, we discuss the sensitivities and outlooks of detection of GWs from binary massive black holes in these frequency bands with an emphasis on ASTROD-GW. The GWs generated by the inspirals, merging and subsequent ringdowns of binary black holes are standard sirens to the cosmological distance. Using GW observations, we discuss the methods for determining the equation of state of dark energy and for testing the co-evolution models of massive black holes. ASTROD-GW is an optimization of ASTROD to focus on the goal of detection of GWs. The mission orbits of the 3 spacecraft forming a nearly equilateral triangular array are chosen to be near the Sun-Earth Lagrange points L3, L4 and L5. The 3 spacecraft range interferometrically with one another with arm length about 260million kilometers. With 52 times longer in arm length compared to that of LISA, the strain detection sensitivity is 52 times better toward larger wavelength. The scientific aim is focused for gravitational wave detection at low frequency. The science goals include detection of GWs from MBHs, and Extreme-Mass-Ratio Black Hole Inspirals (EMRI), and using these observations to find the evolution of the equation of state of dark energy and to explore the co-evolution of massive black holes with galaxies.

Numerical simulation of time delay interferometry for a LISA-like mission with the simplification of having only one interferometer

In order to attain the requisite sensitivity for LISA, laser frequency noise must be suppressed below the secondary noises such as the optical path noise, acceleration noise etc. In a previous paper (Dhurandhar, S.V., Nayak, K.R., Vinet, J.-Y. Time delay interferometry for LISA with one arm dysfunctional. Class. Quantum Grav. 27, 135013, 2010), we have found a large family of second-generation analytic solutions of time delay interferometry with one arm dysfunctional, and we also estimated the laser noise due to residual time-delay semi-analytically from orbit perturbations due to Earth. Since other planets and solar-system bodies also perturb the orbits of LISA spacecraft and affect the time delay interferometry (TDI), we simulate the time delay numerically in this paper for all solutions with the generation number n⩽3. We have worked out a set of 3-year optimized mission orbits of LISA spacecraft starting at January 1, 2021 using the CGC2.7 ephemeris framework. We then use this numerical solution to calculate the residual optical path differences in the second-generation solutions of our previous paper, and compare with the semi-analytic error estimate. The accuracy of this calculation is better than 1cm (or 30ps). The maximum path length difference, for all configuration calculated, is below 1m (3ns). This is well below the limit under which the laser frequency noise is required to be suppressed. The numerical simulation in this paper can be applied to other space-borne interferometers for gravitational wave detection with the simplification of having only one interferometer.

Time-delay Interferometry for ASTROD-GW

ASTROD-GW(ASTROD[Astrodynamical Space Test of Relativity using Optical Devices] optimized for Gravitational Wave detection) is an optimization of ASTROD to focus on the detection of gravitational waves. Three spacecraft in the mission are positioned respectively in the vicinity of the Sun- Earth Lagrange points L3, L4 and L5. They form a nearly equilateral interferometerarray with the arm lengths of about 260 million kilometers. A set of optimized 20-yr mission orbits of the ASTROD-GW spacecraft are worked out by us. And with this, we have performed the numerical simulation of time-delay interferometry under the CGC2.7 (CGC: Center for Gravitation and Cosmology) ephemeris framework.

아리랑위성 2호, 5호의 우주파편 충돌회피기동 주기 분석

본 논문에서는 현재 운용 중인 아리랑위성 2호와 발사예정인 아리랑위성 5호의 우주파편 충돌 회피기동 주기를 분석하였다. 이때, 각 위성들의 임무궤도 특성, 충돌 회피 여유시간, 허용 충돌확률, 위치 불확실성 등의 인자들의 변화에 따라 분석을 수행하였다. 또한, 결과의 타당성을 검증하기 위해 실제 1년 동안 생성된 NORAD TLE 카탈로그(catalog) 상의 우주 물체들과 아리랑위성 2호와의 충돌 회피기동 주기를 계산하였다. 분석 결과, 두 위성 모두 연중 약 1회 충돌 회피기동이 요구됨을 확인할 수 있었으며, 계산 인자들의 변화에 따른 결과 분석을 통해 추후 발사 예정인 저궤도 위성들의 충돌 회피기동 주기 예측 정밀도를 향상시키기 위한 방안들을 제시하였다. In this paper, a collision avoidance maneuver frequency for the KOMPSAT-2 and the KOMPSAT-5 is analyzed. For the statistical prediction of the avoidance maneuver frequency, mission orbits, responsive time, accepted collision probabilities, and positional uncertainties of primary and secondary objects are considered. In addition, the collision avoidance maneuver frequency of the KOMPSAT-2 is compared to the case that NORAD catalog during one year is used to calculate that of the KOMPSAT-2. As a result, the collision avoidance maneuver frequency is one per year on average and effective factors on the statistical prediction of the avoidance maneuver frequency are investigated. Efforts to improve its prediction accuracy are also discussed.

Constellation Deployment for the FORMOSAT-3/COSMIC Mission

The FORMOSA Satellite Series No. 3/Constellation Observing System for Meteorology, Ionosphere and Climate (FORMOSAT-3/COSMIC) spacecraft constellation consisting of six low-earth-orbiting satellites is the world's first operational Global Positioning System (GPS) radio occultation mission. The mission has been jointly developed by the National Space Organization of Taiwan and the University Corporation for Atmospheric Research of the U.S. in collaboration with the Jet Propulsion Laboratory, NASA, and the Naval Research Laboratory for three onboard payloads, including a GPS Occultation Receiver, a triband beacon, and a tiny ionospheric photometer. The FORMOSAT-3/COSMIC mission was successfully launched from Vandenberg into the same orbit plane of the designated 516-km circular parking orbit altitude on April 15, 2006. After the six satellites completed the in-orbit checkout activities, the mission was started immediately at the parking orbit for in-orbit checkout, calibration, and experiment of three onboard payloads. Individual spacecraft thrust burns for orbit raising were performed to begin the constellation deployment of the satellites into six separate orbit planes. All six FORMOSAT-3/COSMIC satellites are maintained in a good state of health except spacecraft flight model no. 2, which has had power shortages. Five out of the six satellites had reached their final mission orbits of 800 km as of November 2007. This paper provides an overview of the constellation spacecraft design, constellation mission operations, constellation deployment timeline evolution, associated spacecraft mass property and moment of inertia results, orbit-raising challenges, and lessons learned during the orbit-raising operations.

Optimal, Low-Thrust Earth-Orbit Transfers Using Higher-Order Collocation Methods

A trajectory optimization technique based upon higher-order collocation is used to solve optimal, low-thrust, Earth-orbit transfer problems. The optimal control problem solved is defined, and the solution method for solving this problem is described. For several example cases analyzed, a spacecraft is transferred from low Earth orbit to a variety of final mission orbits. A range of thrust accelerations from approximately 1 to 10 - 3 g was used. A comparison is made between the optimal transfers found in this work and the transfers found by using analytical blended control methods. Finally, conclusions drawn from this work are discussed.

電離層におけるロケット排出物の拡散と電子減少

In coming new space age, we will have frequent trips between the ground and mission orbits by large rockets to realize the large projects such as space stations and solar power satellite systems. In such cases a great deal of rocket effluents should be released in the atomosphere. But, its effects on our environment is still unknown, and therefore various studies on these problems are expected. About such environmental problems, some studies were performed which motivated by so called “ionospheric hole” observed when Skylab-I was launched, May 14, 1973. It was certified by later scientific studies that the phenomenon was caused by the chemical reaction between rocket effluents and ionized particles in the ionosphere, by which the electron density of the ionosphere suddenly decreased to about a half values of that in its normal state in the range of about 1, 000km in radius centering about rocket trajectory and it took about 4 hours to recover. In this study, the results of these fundamental studies are applied to the engineering problem, that is, the numerical simulation of the change in electron density in the ionosphere is carried out in consideration of the diffusion of rocket effluents released along arbitrary trajectory in upper atomosphere and their chemical reactions with the ionospheric constituents.