High Earth Orbit Research Articles

Optimization of Many-Burn Orbital Transfers

Optimization of medium and low-thrust orbital transfers is important for future upper stages. Previous research has generally either considered a fairly small number of burns with medium thrust or has assumed continuous thrusting for low-thrust transfers. The acceleration level considered in this paper is too high to use orbit averaging and too low (in most cases) to use only a few burns. The optimization scheme used is an optimal control solution for each burn, and a parameter optimization for the ensemble of burns. The solution for each burn is available in open-loop and closed-loop form, so that the method also provides a guidance scheme for flying the transfers. The optimization includes oblateness terms, complicating many-burn transfers with plane change. Results compare favorably to several published cases. This paper also includes additional transfer cases and parametric results. These results are easy to obtain in comparison with many-burn (non-averaged) multi-point boundary value problem solutions, which require the determination of a number of sensitive parameters. Cases examined include transfer to high-Earth orbit, transfer to geostationary orbit, transfer to the Global Positioning System (GPS) orbit, escape from orbit, and transfer to the lunar sphere of influence.

Tail lobe and open field line region entries at mid to high latitudes

New data from the POLAR and HEO (high earth orbit) 95-034 satellites are used in a preliminary study to estimate the position of the open/closed (OC) field line boundary using energetic particle and plasma observations. In this study, the OC boundary positions were compared in several different coordinate systems and the GSM and eccentric dipole coordinates were found to be equally effective in organizing the HEO 95-034 data. No coordinate system appeared to organize the POLAR data best. The HEO 95-034 and POLAR data were examined for interplanetary field and plasma dynamic pressure control of the dayside OC boundary. The HEO 95-034 data showed a clear response to solar wind dynamic pressure with the OC boundary being at lower latitude with increasing pressure. The HEO 95-034 data also showed some response to the IMF BZ, hinting that the OC boundary would move to lower latitude with increasingly negative BZ but be unchanged for positive BZ. The POLAR data showed no dependence on either the solar wind dynamic pressure or BZ in this initial study. The data were relatively sparse; about a month of observations for each satellite.

Issues arising from the NASA safety standard to control orbital debris

In 1992 NASA adopted a policy to limit the generation of orbital debris. This policy is stated in NASA Management Instruction (NMI) 1700.8, and provides a general statement of policy to take action to limit orbital debris generation if this action is cost effective and consistent with achieving mission objectives. The only specific requirement in the policy is to perform debris assessments during development of NASA programs. To implement this policy, the NASA Office of Safety and Mission Assurance, the sponsor of NMI 1700.8, tasked NASA Johnson Space Center (JSC) with developing guidelines to implement the policy. This tasking resulted in the development of NASA Safety Standard 1740.14: Guidelines and Assessment Procedures for Limiting Orbital Debris . The Safety Standard has been reviewed and approved by all NASA organizations and NASA programs are now required to perform two debris evaluations, one at Preliminary Design Review (PDR) and a second 45 days prior to Critical Design Review, once the final space system design has been approved. The purpose of the first report is to identify potential problems that a program may encounter in meeting the guidelines, and the second report is to document efforts by the program to resolve those problems. At this point in time, a primary concern by NASA managers has been the issue of postmission disposal of low Earth orbit systems and upper stages left in high eccentricity orbits. These systems in general wish to deorbit using atmospheric drag to limit the remaining orbit lifetime to 25 years, as stated by the guidelines. To address this issue, JSC has started a series of studies to investigate the most efficient options for reducing orbit lifetime. In this paper we will review issues raised by the NASA community and the responses that have been made to resolve concerns. Two studies that were designed to minimize costs for postmission disposal will also be discussed in this paper. The first investigates options for disposal maneuvers of upper stages that minimize the cost impact on upper stage development. The second investigates options for high altitude low Earth orbit satellites (e.g. Sun-synchronous spacecraft) that have no significant on-board propulsion.

Gravitational wave detectors in space

In the next few years, we expect to see the beginning of a new branch of astronomy-gravitational wave astronomy. Space detectors, especially, will soon have the sensitivity to see the tiny changes in distance between separated masses that are produced by gravitational waves in Einstein's theory of General Relativity. One such space detector, named OMEGA, has been proposed to NASA as a future medium sized Explorer mission. This detector would be formed from six small miniprobes that are launched into high circular Earth orbit, two miniprobes at each of the vertices of a million-kilometre equilateral triangle. The probes track each other with lasers. By subtracting the measurements of the armlengths, a fine Michelson interferometer can be formed that will detect changes in distance of less than one picometre at time scales around 1000 s. At this sensitivity, OMEGA will be able to detect gravitational waves from known galactic binary stars and from possible events involving the massive black holes that are expected to reside in the nuclei of many galaxies.

Multiresolution‐element imaging of extrasolar Earthlike planets

It has been suggested recently that imaging of extrasolar Earthlike planets should be considered as a possible future goal of the NASA space program. As an aid to discussing what would be required in order to undertake imaging, a partial design is described for a separated spacecraft interferometer which could achieve images in the visible with 10 resolution elements across the planet. Between 15 and 25 large collector telescopes or clusters of telescopes spread out over roughly a 200‐km baseline in solar orbit at 1 AU from the Sun or possibly in high Earth orbit are required. A very preliminary approach to the use of multispectral remote sensing techniques is discussed also. Finally, the generalization of this approach to larger numbers of resolution elements across the planet is considered. Clearly, imaging is possible only if the truly staggering problem of avoiding the 1010 times stronger scattered light from the nearby star can be overcome. However, even if this can be done, the amount and precision of the required hardware for even poor‐quality images appears to present an obstacle to such a program which would be extremely difficult to overcome.

SIRTF: Capabilities for planetary science

The Space Infrared Telescope Facility, to be put into high earth orbit toward the end of the 1990s, will open broad new vistas for the study of the objects in the Solar System and planetary systems around other stars at infrared wavelengths. This paper focuses on three topics to which SIRTF will make fundamental contributions; the search for Kuiper-belt comets, IR spectroscopy of comets, and the study of circumstellar planetary debris disks.

The background in a high earth orbit as measured by the soft γ-ray telescope SIGMA

High detector background level is the major obstacle encountered in astronomical observations in the hard X- and γ-ray waveband. Progresses have been made in understanding and modelling the background in the space environment, particularly at LEO helped by valuable data obtained by instruments operating in such orbits. Telescope operating in a HEO is facing a different radiation environment, hence it is expected that its background will differ from what is known in the LEO. The measurements by the SIGMA telescope provide us the first opportunity to assess all aspects of the background of a soft γ-ray detector operating in a HEO, these include: the overall background level, its composition and stability, the effects of trapped radiation and solar activities, and the prominent background lines. Comparing to the backgrounds of detectors operating in LEOs, it shows that the HEO is a very competitive orbit for γ-ray observations from the point of view of the expected background level, and with the advantage of long and uninterrupted observations time and better sky coverage.

Gamma guidance of trajectories for coplanar, aeroassisted orbital transfer

The optimization and guidance of trajectories for coplaner, aeroassisted orbital transfer (AOT) from high Earth orbit (HEO) to low Earth orbit (LEO) are examined. In particular, HEO can be a geosynchronous Earth orbit (GEO). It is assumed that the initial and final orbits are circular, that the gravitational field is central and is governed by the inverse square law, and that at most three impulses are employed: one at HEO exit, one at atmospheric exit, and one at LEO entry. It is also assumed that, during the atmospheric pass, the trajectory is controlled via the lift coefficient. The presence of upper and lower bounds on the lift coefficient is considered. First, optimal trajectories are computed by minimizing the total velocity impulse (hence, the propellant consumption) required for AOT transfer. The sequential gradient-restoration algorithm (SGRA) is used for optimal control problems. The optimal trajectory is shown to include two branches: a relatively short descending flight branch (branch 1) and a long ascending flight branch (branch 2). Next, attention is focused on guidance trajectories capable of approximating the optimal trajectories in real time, while retaining the essential characteristics of simplicity, ease of implementation, and reliability. For the atmospheric pass, a feedback control scheme is employed and the lift coefficient is adjusted according to a two-stage gamma guidance law. Further improvements are possible via a modified gamma guidance which is more stable with respect to dispersion effects arising from navigation errors, variations of the atmospheric density, and uncertainties in the aerodynamic coefficients than gamma guidance trajectory. A byproduct of the studies on dispersion effects is the following design concept. For coplaner aeroassisted orbital transfer, the lift-range-to-weight ratio appears to play a more important role than the lift-to-drag ratio. This is because the lift-range-to-weight ratio controls mainly the minimum altitude (hence, the peak heating rate) of the guidance trajectory; on the other hand, the lift-to-drag ratio controls mainly the duration of the atmospheric pass of the guidance trajectory.

Sailing off the edge of the earth. . .again

The Columbus 500 Space Sail Race, which is intended to stimulate worldwide space exploration, education, and enterprise as well as commemorate the European discovery of the Americas, is described. Three solar sailing flagships-the Nina, Pinta, and Santa Maria -will be the official entries from three geographical regions: Europe, whence Columbus initiated his voyage; Asia, where he was headed; and the Americas, where he landed. Other vessels are also expected to compete. The vessel that takes the shortest time to travel from high Earth orbit to a point where it can place a commemorative plaque in high orbit around Mars will be judged the winner. The rules for the race are given, the science of solar sailing is explained, and some of the physical configurations for the sails and methods of deploying them are briefly described. Some of the experiments that are being considered to be conducted during flight are tested. Some of the technological difficulties anticipated are discussed. Plans to use the race to develop interest in science in grade schools and high schools around the world are described. >

Properties of the optimal trajectories for coplanar, aeroassisted orbital transfer

The optimization of trajectories for coplaner, aeroassisted orbital transfer (AOT) from a high Earth orbit (HEO) to a low Earth orbit (LEO) is examined. In particular, HEO can be a geosynchronous Earth orbit (GEO). It is assumed that the initial and final orbits are circular, that the gravitational field is central and is governed by the inverse square law, and that two impulses are employed, one at HEO exit and one at LEO entry. During the atmospheric pass, the trajectory is controlled via the lift coefficient in such a way that the total characteristic velocity is minimized. First, an ideal optimal trajectory is determined analytically for lift coefficient unbounded. This trajectory is called grazing trajectory, because the atmospheric pass is made by flying at constant altitude along the edge of the atmosphere until the excess velocity is depleted. For the grazing trajectory, the lift coefficient varies in such a way that the lift, the centrifugal force due to the Earth's curvature, the weight, and the Coriolis force due to the Earth's rotation are in static balance. Also, the grazing trajectory minimizes the total characteristic velocity and simultaneously nearly minimizes the peak values of the altitude drop, dynamic pressure, and heating rate. Next, starting from the grazing trajectory results, a real optimal trajectory is determined numerically for the lift coefficient bounded from both below and above. This trajectory is characterized by atmospheric penetration with the smallest possible entry angle, followed by flight at the lift coefficient lower bound. Consistently with the grazing trajectory behavior, the real optimal trajectory minimizes the total characteristic velocity and simultaneously nearly minimizes the peak values of the altitude drop, the dynamic pressure, and the heating rate.

Fuel-optimal trajectories of aeroassisted orbital transfer with plane change

The fuel-optimal control problem arising in noncoplanar orbital transfer employing aeroassist technology is addressed. The mission involves the transfer from high Earth orbit to low Earth orbit with plane change. The complete maneuver consists of a deorbit impulse to inject a vehicle from a circular orbit to an elliptic orbit for atmospheric entry, a boost impulse at the exit from the atmosphere for the vehicle to attain a desired orbital altitude, and a reorbit impulse to circularize the path of the vehicle. In order to minimize the total fuel consumption, a performance index is chosen as the sum of the deorbit, boost, and reorbit impulses. The application of optimization principles leads to a nonlinear, two-point, boundary value problem, which is solved by a multiple shooting method. >

空力加熱の制限を含むＡＯＴＶの最適帰還に関する研究

In this paper optimal returns of an AOTV (Aeroassisted Orbital Transfer Vehicle) from the high earth orbit within the limit of the aerodynamic heating are studied numerically, which minimize the characteristic velocities for decelerations and plane changes at the atmospheric flights and the impulses in space. As a result from computations optimal control methods are remarkably changed by the heat limit, but with them in these cases we can still keep the characteristic velocities small.

Fuel-optimal trajectories for aeroassisted coplanar orbital transfer problem

The optimal control problem arising in coplanar, orbital transfer employing aeroassist technology is addressed. The maneuver involves the transfer from high Earth orbit to low Earth orbit by means of the atmosphere with the object of minimizing the total fuel consumption. Simulations are carried out to obtain the fuel-optimal trajectories for flying the spacecraft through the atmosphere. A highlight is the application of an efficient multiple-shooting method for treating the nonlinear, two-point boundary value problem resulting from the optimization procedure. The strategy for the atmospheric portion of the minimum-fuel transfer is to fly at the maximum lift-to-drag ratio L/D initially in order to recover from the downward plunge, and then to fly at a negative L/D to level off the flight so that the vehicle skips out of the atmosphere with a flight path angle near zero degrees.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The Space Infrared Telescope Facility (SIRTF)

AbstractThe Space Infrared Telescope Facility (SIRTF) is a one-meter class observatory for infrared astronomy that will be launched into high earth orbit by NASA in the late 1990’s. SIRTF’s three focal plane instruments will permit imaging and spectroscopy over most of the infrared spectrum with sensitivities of 100 to 10,000 times their predecessors. This paper briefly reviews SIRTF’s capabilities, science objectives, and current status.

Low Frequency Radio Astronomy from Earth Orbit

AbstractLow frequency radio astronomy for the purpose of this discussion is defined as frequencies ≲100 MHz. Since the technology is fairly simple at these frequencies and even Jansky’s original observations were made at 20.5 MHz, there have been many years of research at these wavelengths. However, though radio astronomers have been working at low frequencies since the first days of science, the observing limitations and the move of much of the effort to ever shorter wavelengths has meant that most areas still remain to be fully exploited with modern techniques and instruments. In particular, the possibilities for pursuing the very lowest frequencies by interferometry of ground to space, in Earth orbit, or from the Moon promises a rebirth of work in this wavelength range.We present concepts for space-ground VLBI and a fully space-based array in high Earth orbit to pursue the astrophysics which can only be probed at these frequencies. An Orbiting Low Frequency Radio Astronomy Satellite (OLFRAS) and a Low Frequency Space Array (LFSA) are two concepts which will open this last, poorly explored area of astronomy at relatively low cost and well within the limits of current technology.

Astronomy with EXOSAT

The European Space Agency's X-ray observatory EXOSAT was operational from May 1983 to April 1986 and in that time made 1780 observations of a wide variety of objects including active galactic nuclei, stellar coronae, cataclysmic variables, white dwarfs, X-ray binaries, clusters of galaxies and supernova remnants. The 90hr high earth orbit allowed for the first time long uninterupted observations. In addition the instrumentation had a broad band spectral response from 0.05–30.0 keV with good spectral resolution. This allowed the continuum to be studied over two or three decades in frequency and also revealed many new spectral absorption and emission line features. In this review an overview of the strengths of the EXOSAT observatory are illustrated using a selection of key results.

Demonstration of sub-meter GPS orbit determination and 1.5 parts in 108 three-dimensional baseline accuracy

Differential tracking of theGPS satellites in high-earth orbit provides a powerful relative positioning capability, even when a relatively small continental U.S. fiducial tracking network is used with less than one-third of the fullGPS constellation. To demonstrate this capability, we have determined baselines of up to2000 km in North America by estimating high-accuracyGPS orbits and ground receiver positions simultaneously. The2000 km baselines agree with very long baseline interferometry(VLBI) solutions at the level of1.5 parts in10 8 and showrms daily repeatability of0.3–2 parts in10 8. The orbits determined for the most thoroughly trackedGPS satellites are accurate to better than1 m. GPS orbit accuracy was assessed from orbit predictions, comparisons with independent data sets, and the accuracy of the continental baselines determined along with the orbits. The bestGPS orbit strategies included data arcs of at least one week, process noise models for tropospheric fluctuations, estimation ofGPS solar pressure coefficients, and combined processing ofGPS carrier phase and pseudorange data. For data arcs of two weeks, constrained process noise models forGPS dynamic parameters significantly improved the solutions.

Low-cost launch system and orbital fuel depot

A new system is proposed for the low-cost launching of large quantities of rocket fuel into Earth orbit and the storage and transfer of the fuel to the NASA Space Station. The system consists of an electromagnetic launcher that fires heat-shielded fuel tanks into high Earth orbit, where they are captured by a long, rotating tether. The tether is in an elliptical orbit that ranges from high Earth orbit down to low Earth orbit, where it drops the fuel tanks into an orbit near the Space Station. The payloads are used for upper stage rockets, for stationkeeping propulsion, and for high- g-tolerant supplies for the Space Station. The system has the potential for launching more than 100,000 kg into Earth bit each year at a launch cost of <$10/kg.

Aeroassisted orbital maneuvering using Lyapunov optimal feedback control

A Liapunov optimal feedback controller incorporating a preferred direction of motion at each state of the system which is opposite to the gradient of a specified descent function is developed for aeroassisted orbital transfer from high-earth orbit to LEO. The performances of the Liapunov controller and a calculus-of-variations open-loop minimum-fuel controller, both of which are based on the 1962 U.S. Standard Atmosphere, are simulated using both the 1962 U.S. Standard Atmosphere and an atmosphere corresponding to the STS-6 Space Shuttle flight. In the STS-6 atmosphere, the calculus-of-variations open-loop controller fails to exit the atmosphere, while the Liapunov controller achieves the optimal minimum-fuel conditions, despite the + or - 40 percent fluctuations in the STS-6 atmosphere.

Optimal trajectories for aeroassisted, noncoplanar orbital transfer

This paper considers both classical and minimax problems of optimal control which arise in the study of noncoplanar, aeroassisted orbital transfer. The maneuver considered involves the transfer from a high planetary orbit to a low planetary orbit with a prescribed atmospheric plane change. An example is the HEO-to-LEO transfer of a spacecraft with a prescribed plane change, where HEO denotes high Earth orbit and LEO denotes low Earth orbit. In particular, HEO can be GEO, a geosynchronous Earth orbit. The basic idea is to employ the hybrid combination of propulsive maneuvers in space and aerodynamic maneuvers in the sensible atmosphere. Hence, this type of flight is also called synergetic space flight. With reference to the atmospheric part of the maneuver, trajectory control is achieved by modulating the lift coefficient (hence, the angle of attack) and the angle of bank. The presence of upper and lower bounds on the lift coefficient is considered. Within the framework of classical optimal control, the following problems are studied: (P1) minimize the energy required for orbital transfer; (P2) minimize the time integral of the heating rate; (P3) minimize the time of flight during the atmospheric portion of the trajectory; (P4) maximize the time of flight during the atmospheric portion of the trajectory; (P5) minimize the time integral of the square of the path inclination; and (P6) minimize the sum of the squares of the entry and exit path inclinations. Problems (P1)–(P6) are Bolza problems of optimal control. Within the framework of minimax optimal control, the following problems are studied: (Q1) minimize the peak heating rate; (Q2) minimize the peak dynamic pressure; and (Q3) minimize the peak altitude drop. Problems (Q1)–(Q3) are Chebyshev problems of optimal control, which can be converted into Bolza problems by suitable transformations. Numerical solutions for Problems (P1)–(P6) and Problems (Q1)–(Q3) are obtained by means of the sequential gradient-restoration algorithm for optimal control problems. The engineering implications of these solutions are discussed, and it appears that the energy solution (P1) and the nearly-grazing solution (P5) are superior to the remaining solutions. While the nearly-grazing solution (P5) requires more energy than the energy solution (P1), at the same time it involves less integrated heating rate, less peak heating rate, less peak dynamic pressure, and less peak total acceleration. Therefore, it is felt that both solutions (P1) and (P5) should be considered as candidates for flight operations, and hence candidates for spacecraft design.