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An independent variable different from the time for elliptic orbit integration is used. Such a time transformation provides an analytical step-size regulation along the orbit. An intermediate anomaly (an anomaly intermediate between the eccentric and the true anomaly) is suggested for optimum performances. A particular case of an intermediate anomaly (the elliptic anomaly) is defined, and its relation with the other anomalies is developed.
The two Dynamics Explorer spacecraft, DE-1 and DE-2, were launched on August 3, 1981, into polar coplanar orbits at different altitudes for the purpose of studying interactive processes within the atmosphere-ionosphere-magnetosphere system. The DE-1 spacecraft (high-altitude mission) used an elliptical orbit that was selected to allow: (1) measurements extending from the hot magnetospheric plasma through the plasmasphere to the cool ionosphere; (2) global auroral imaging, wave measurements in the heart of the magnetosphere, and crossing of auroral field lines at several earth radii; and (3) measurements for significant periods of time along a magnetic field flux tube. The orbit of Dynamics Explorer 1 offered an opportunity to obtain global images of Earth's dayglow and auroral luminosities and to acquire consecutive images of the entire auroral oval during the growth, onset, expansion, and recovery phases of substorms. The University of Iowa's Spin-scan Auroral Imaging (SAI) instrument, was on-board DE-1. SAI was activated in orbit and placed in routine operation on September 23, 1981, and has provided outstanding new contributions in the fields of auroral, magnetospheric and geocoronal physics, introduced a powerful tool for the study of global atmospheric ozone, and initiated the first search from space for marine bioluminescence on the surface of the global ocean. The SAI instrumentation consists of three imaging photometers, two for visible wavelengths and the third for vacuum-ultraviolet wavelengths equipped with primary catoptric optics with superpolished mirror surfaces. The primary focusing element is an off-axis section of a parabolic mirror that is used to provide an optical path completely free of support structures for the mirrors.
On 6 August, 2012, Russia launched two commercial satellites aboard a Proton rocket, and attempted to place them in geosynchronous orbit using a Briz-M upper stage (2012-044C, SSN 38746). Unfortunately, the upper stage failed early in its burn and was left stranded in an elliptical orbit with a perigee in low Earth orbit (LEO). Because the stage failed with much of its fuel on board, it was deemed a significant breakup risk. These fears were confirmed when it broke up 16 October, creating a large cloud of debris with perigees below that of the International Space Station. The debris cloud was tracked by the US Space Surveillance Network (SSN), which can reliably detect and track objects down to about 10 cm in size. Because of the unusual geometry of the breakup, there was an opportunity for NASA Orbital Debris Program Office to request radar assets to characterize the extent of the debris cloud in sizes smaller than the standard debris tracked by the SSN. This paper will describe the observation campaign to measure the small particle distributions of this cloud, and presents the results of the analysis of the data. We shall compare the data to the modelled size distribution, number, and shape of the cloud, and what implications this may have for future breakup debris models. We shall conclude the paper with a discussion how this measurement process can be improved for future breakups.
On 6 August, 2012, Russia launched two commercial satellites aboard a Proton rocket, and attempted to place them in geosynchronous orbit using a Briz-M upper stage (2012-044C, SSN 38746). Unfortunately, the upper stage failed early in its burn and was left stranded in an elliptical orbit with a perigee in low Earth orbit (LEO). Because the stage failed with much of its fuel on board, it was deemed a significant breakup risk. These fears were confirmed when it broke up 16 October, creating a large cloud of debris with perigees below that of the International Space Station. The debris cloud was tracked by the US Space Surveillance Network (SSN), which can reliably detect and track objects down to about 10 cm in size. Because of the unusual geometry of the breakup, there was an opportunity for NASA Orbital Debris Program Office to use specialized radar assets to characterize the extent of the debris cloud in sizes smaller than the standard debris tracked by the SSN. This paper will describe the observation campaign to measure the small particle distributions of this cloud, and presents the results of the analysis of the data. We shall compare the data to the modelled size distribution, number, and shape of the cloud, and what implications this may have for future breakup debris models. We shall conclude the paper with a discussion how this measurement process can be improved for future breakups.
The cloud of cataloged debris produced in low earth orbit by the fragmentation of the Fengyun-1C spacecraft was propagated for 15 years, taking into account all relevant perturbations. Unfortunately, the cloud resulted to be very stable, not suffering substantial debris decay during the time span considered. The only significant short term evolution was the differential spreading of the orbital planes of the fragments, leading to the formation of a debris shell around the earth approximately 7-8 months after the breakup, and the perigee precession of the elliptical orbits. Both effects will render the shell more "isotropic" in the coming years. The immediate consequence of the Chinese anti-satellite test, carried out in an orbital regime populated by many important operational satellites, was to increase significantly the probability of collision with man-made debris. For the two Italian spacecraft launched in the first half of 2007, the collision probability with cataloged objects increased by 12% for AGILE, in equatorial orbit, and by 38% for COSMO-SkyMed 1, in sun-synchronous orbit.
Computer program technique for determination of opportunities for recall of spacecraft to multiple landing sites from circular or elliptical orbits
Some simple guidelines based on the accuracy in determining a satellite formation s semi-major axis differences are useful in making preliminary assessments of the navigation accuracy needed to support such missions. These guidelines are valid for any elliptical orbit, regardless of eccentricity. Although maneuvers required for formation establishment, reconfiguration, and station-keeping require accurate prediction of the state estimate to the maneuver time, and hence are directly affected by errors in all the orbital elements, experience has shown that determination of orbit plane orientation and orbit shape to acceptable levels is less challenging than the determination of orbital period or semi-major axis. Furthermore, any differences among the member s semi-major axes are undesirable for a satellite formation, since it will lead to differential along-track drift due to period differences. Since inevitable navigation errors prevent these differences from ever being zero, one may use the guidelines this paper presents to determine how much drift will result from a given relative navigation accuracy, or conversely what navigation accuracy is required to limit drift to a given rate. Since the guidelines do not account for non-two-body perturbations, they may be viewed as useful preliminary design tools, rather than as the basis for mission navigation requirements, which should be based on detailed analysis of the mission configuration, including all relevant sources of uncertainty.
Some simple guidelines based on the accuracy in determining a satellite formation's semi-major axis differences are useful in making preliminary assessments of the navigation accuracy needed to support such missions. These guidelines are valid for any elliptical orbit, regardless of eccentricity. Although maneuvers required for formation establishment, reconfiguration, and station-keeping require accurate prediction of the state estimate to the maneuver time, and hence are directly affected by errors in all the orbital elements, experience has shown that determination of orbit plane orientation and orbit shape to acceptable levels is less challenging than the determination of orbital period or semi-major axis. Furthermore, any differences among the member's semi-major axis are undesirable for a satellite formation, since it will lead to differential along-track drift due to period differences. Since inevitable navigation errors prevent these differences from ever being zero, one may use the guidelines this paper presents to determine how much drift will result from a given relative navigation accuracy, or vice versa. Since the guidelines do not account for non-two-body perturbations, they may be viewed as useful preliminary design tools, rather than as the basis for mission navigation requirements, which should be based on detailed analysis of the mission configuration, including all relevant sources of uncertainty.
Some simple guidelines based on the accuracy in determining a satellite formation's semi-major axis differences are useful in making preliminary assessments of the navigation accuracy needed to support such missions. These guidelines are valid for any elliptical orbit, regardless of eccentricity. Although maneuvers required for formation establishment, reconfiguration, and station-keeping require accurate prediction of the state estimate to the maneuver we, and hence are directly affected by errors in all the orbital elements, experience has shown that determination of orbit plane orientation and orbit shape to acceptable levels is less challenging than the determination of orbital period or semi-major axis. Furthermore, any differences among the member s semi-major axes are undesirable for a satellite formation, since it will lead to differential along-track drift due to period differences. Since inevitable navigation errors prevent these differences from ever being zero, one may use the guidelines this paper presents to determine how much drift will result from a given relative navigation accuracy, or conversely what navigation accuracy is required to limit drift to a given rate. Since the guidelines do not account for non-two-body perturbations, they may be viewed as useful preliminary design tools, rather than as the basis for mission navigation requirements, which should be based on detailed analysis of the mission configuration, including all relevant sources of uncertainty.
The classical Poisson equations of rotational motion are used to study the attitude motions of an earth orbiting, rapidly spinning gyroscope perturbed by the effects of general relativity (Einstein theory). The center of mass of the gyroscope is assumed to move about a rotating oblate earth in an evolving elliptic orbit which includes all first-order oblateness effects produced by the earth. A method of averaging is used to obtain a transformation of variables, for the nonresonance case, which significantly simplifies the Poisson differential equations of motion of the gyroscope. Long-term solutions are obtained by an exact analytical integration of the simplified transformed equations. These solutions may be used to predict both the orientation of the gyroscope and the motion of its rotational angular momentum vector as viewed from its center of mass. The results are valid for all eccentricities and all inclinations not near the critical inclination.
A rapid mission to Mars requires a large change in vehicle velocity upon arrival to establish a stable orbit. This demand is even greater for a Neptune science, requiring many kilometers per second of V. It is clear from past mission studies that a manned Mars mission and deep space planetary orbiters require aerobraking and aerocapture which use aerodynamic drag forces to slow the spacecraft. Aerocapture would enable long term studies of the outer planets and moons that would not be possible with existing braking methodologies. While the ability to utilize these atmospheres to slow down and capture spacecraft would dramatically reduce the cost, launch mass, and travel time, currently planned approaches require significant additional spacecraft mass and risk as the spacecraft must descend deep into the planetary atmosphere in order to produce significant drag on a relatively small aeroshell. The plasma based Magnetoshell being developed in this program holds the potential to perform the desired braking with significantly increased drag and control while dramatically reducing mass. Most importantly, this technology significantly lowers the risk involved with aerocapture thereby making manned planetary missions possible. The fundamental physics of the Magnetoshell is based on demonstrated experimental results. Successful implementation will dramatically decrease radiation exposures, mission risk, launch cost, and launch mass. Implementation of aerobraking by employing a solid deflector or aeroshell as a method for orbit insertion and circularization has been successfully demonstrated in the past, resulting in launch mass savings greater than 50%. In order to reduce the effect of frictional heating and dynamic pressure on the typically fragile aeroshell, or worse solar panels, the braking must be distributed over many orbital passes at a high altitude in the less dense regions of the atmosphere. It can thus take several months for a meter-scale, 1000 kg, aeroshell to execute the many elliptic orbital passes through the atmosphere to achieve the required V. This rather slow method of braking not only reduces frictional heating and dynamic forces, but also avoids unpredictable dynamic behavior due to turbulence, as well as unknown and seasonally variable atmospheric composition and temperature which has led to dangerous, mission-critical events. For exploration class missions such as DRA 5.0 aerocapture and Thermal Protection Systems (TPS) are proposed for breaking at Mars for cargo missions. Traditional aerocapture is considered too risky for manned missions. Even with the enormous mass savings that aerocapture allows, it still requires 80 tons of aeroshell and significantly increased launch mass and propellant. As will be shown, by using Magnetoshells for aerobraking, the DRA 5.0 mission will save 224 metric tons (MT) and greater than $2 B in launch costs. Beyond the dramatic savings for existing mission architectures, a low-mass, risk-free aerocapture system would allow much more rapid missions to Mars and deep space orbiters by allowing direct, faster trajectories. As will be shown, the plasma Magnetoshell Aerobraking, Aerocapture, and Entry System (AAES) not only reduces mass and cost while enabling significant new mission architectures, but also significantly reduces radiation exposures by decreasing trip times.
The JPL (Jet Propulsion Laboratory) Orbit Determination Software System is a set of computer programs developed for the primary purpose of determining the flight path of deep-space mission spacecraft in NASA's Planetary Program and highly elliptical orbiting spacecraft in Earth orbit. The filtering processes available within the JPL Orbit Determination Software are discussed, and several examples are presented. In particular, solutions obtained by the Square Root Information Filter (SRIF) using Bierman's Estimation Subroutine Library (ESL) are discussed and compared with the solutions obtained by the singular value decomposition (SVD) technique. It is concluded that the SRIF filtering and smoothing algorithms are efficient and numerically stable for well-conditioned systems. The use of Bierman's ESL simplifies the task of maintaining the orbit determination software by providing efficient, tested filtering tools. For solving a large well-conditioned system (rank higher than 120), SRIF is approximately four times faster than SVD; however, for solving an ill-conditioned system, SVD is recommended.
NASA's requirements for high reliability, high performance satellite laser instruments have driven the investigation of many critical components; specifically, 808 nm laser diode array (LDA) pump devices. The MESSENGER mission is flying the Mercury Laser Altimeter (MLA) which is a diode-pumped Nd:YAG laser instrument designed to map the topography of Mercury. The environment imposed on the instrument by the orbital dynamics places special requirements on the laser diode arrays. In order to limit the radiative heating of the satellite from the surface of Mercury, the satellite is designed to have a highly elliptical orbit. The satellite will heat near perigee and cool near apogee. The laser power is cycled during these orbits so that the laser is on for only 30 minutes (perigee) in a 12 hour orbit. The laser heats 10 C while powered up and cools while powered down. In order to simulate these operational conditions, we designed a test to measure the LDA performance while being temperature and power cycled. Though the mission requirements are specific to NASA and performance requirements are derived from unique operating conditions, the results are general and widely applicable. We present results on the performance of twelve LDAs operating for several hundred million pulses. The arrays are 100 watt, quasi-CW, conductively-cooled, 808 nm devices. Prior to testing, we fully characterize each device to establish a baseline for individual array performance and status. Details of this characterization can be found in reference. Arrays are divided into four groups and subjected to the temperature and power cycling matrix are shown.
The following paper reports on a design study of a novel space transportation concept known as a 'NIMF' (Nuclear rocket using Indigenous Martian Fuel). The NIMF is a ballistic vehicle which obtains its propellant out of the Martian air by compression and liquefaction of atmospheric CO2. This propellant is subsequently used to generate rocket thrust at a specific impulse of 264 s by being heated to high temperature (2800 K) gas in the NIMFs' nuclear thermal rocket engines. The vehicle is designed to provide surface to orbit and surface to surface transportation, as well as housing, for a crew of three astronauts. It is capable of refueling itself for a flight to its maximum orbit in less than 50 days. The ballistic NIMF has a mass of 44.7 tonnes and, with the assumed 2800 K propellant temperature, is capable of attaining highly energetic (250 km by 34,000 km elliptical) orbits. This allows it to rendezvous with interplanetary transfer vehicles which are only very loosely bound into orbit around Mars. If a propellant temperature of 2000 K is assumed, then low Mars orbit can be attained; while if 3100 K is assumed, then the ballistic NIMF is capable of injecting itself onto a minimum energy transfer orbit to Earth in a direct ascent from the Martian surface.
Potential requirements for planetary missions in the 1980s, capabilities of the Interim Upper Stage (IUS) candidates to perform those missions, and Shuttle/IUS mission profile options for performance enhancement are examined. The most demanding planetary missions are the Pioneer Saturn/Uranus/Titan Probe and the Mariner-class orbiters of Mercury, Jupiter, and Saturn. Options available to designers of these missions will depend on the specific IUS selected for development and the programmatic phasing of the IUS and the NASA Tug. Use of Shuttle elliptic orbits as initial conditions for IUS ignition offers significant performance improvements; specific values are mission dependent.
Flight maneuvers and strategies to transport a vehicle from the Martian surface to orbiter rendezvous are analyzed to determine the most fuel-efficient method. Both endo- and exo-atmospheric flight strategies are considered for orbiter rendezvous into parking orbits of arbitrary inclination. It is found that optimal mass efficiency is achieved where the orbiter inclination is equal to or exceeds the latitude of the launch site. It is shown that high aerodynamic lifting capability improves performance for low circular orbit (LCO) rendezvous. It is suggested that the synergetic ballistic-projecting technique is best for optimal LCO rendezvous and that the all-thrust technique with plane change at apoapsis is best for optimal high elliptical orbit rendezvous.
The effectiveness of accretional capture is studied with the aid of a simple model involving a small secondary body in a hyperbolic orbit which approaches a large primary body. When the separation is a minimum, the mass of the primary body increases. An investigation is conducted regarding the conditions under which this change in mass will result in an elliptic orbit with capture.
The use of solar wind measurements made by ISEE-3 in its halo orbit around the L1 libration point to predict the onsets of magnetospheric substorms and geomagnetic storms is discussed. Consideration is given to the limitations on the predictive ability of the satellite measurements set by the bulk solar wind velocity, the elliptical orbit of the satellite and the correlation lengths of the magnetic field and the solar wind plasma. The ISEE-3 real-time data system is presented, with attention given to the ground receiving stations, the NASCOM communications system, the Multisatellite Operations Control Center and Information Processing Division at the Goddard Space Flight Center, the link between Goddard and the NOAA Space Environmental Services Center, and the NOAA Space Environment Laboratory data acquisition and display data system, which includes displays allowing storm forecasts. It is noted that the entire system should be operational by March, 1980.