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Orbital Resonances in the Solar Nebula: Strengths and Weaknesses

A planetesimal moving in the Solar Nebula experiences an aero- dynamic drag which causes its orbit to circularize and shrink. However, resonant perturbations from a protoplanet interior to the planetesimal's orbit ran counteract both the orbital decay and the damping of the eccentricity: the planetesimal can be captured into an orbital resonance and its eccentricity pumped up to a modestly high equilibrium value. Thus, orbital resonances constitute (partial) barriers to the delivery of planetesimals into the feeding zone of the protoplanet. We have established the characteristics of the phenomenon of resonance capture by gas drag in the circular restricted three-body approximation. We have determined the strengths of the equilibrium resonant orbits with respect to impulsive velocity perturbations. We conclude that planetesimals captured in orbital resonances are quite vulnerable to being dislocated from these orbits by mutual planetesimal interactions, but that the resonances are effective in slowing down the rate of orbital decay of planetesimals. Only very small bodies, less or approx. equal to 100 m, are able to reach a approx. 1 mass of the earth protoplanet without being slowed down by resonances.

Malhotra, Renu↗

Satellite Orbital Drag During Magnetic Storms

We investigate satellite orbital drag effects at lowEarth orbit associated with thermosphere heating during magnetic storms caused by coronal mass ejections. CHAllenge Minisatellite Payload (CHAMP) and Gravity Recovery And Climate Experiment (GRACE) neutral density data are used to compute orbital drag. Stormtoquiet density comparisons are performed with background densities obtained by the JacchiaBowman 2008 (JB2008) empirical model. Our storms are grouped in different categories regarding their intensities as indicated by minimum values of the SYMH index. We then perform superposed epoch analyses with storm main phase onset as zero epoch time. In general, we find that orbital drag effects are larger for CHAMP (lower altitudes) in comparison to GRACE (higher altitudes). Results show that storm time drag effects manifest first at high latitudes, but for extreme storms, particularly observed by GRACE, stronger orbital drag effects occur during early main phase at low/equatorial latitudes, probably due to heating propagation from high latitudes. We find that storm time orbital decay along the satellites' path generally increases with storm intensity, being stronger and faster for the most extreme events. For these events, orbital drag effects decrease faster probably due to elevated cooling effects caused by nitric oxide, which introduce modeled density uncertainties during storm recovery phase. Errors associated with total orbit decay introduced by JB2008 are generally the largest for the strongest storms and increase during storm times, particular during recovery phases. We discuss the implication of these uncertainties for the prediction of collision between space objects at lowEarth orbit during magnetic storms.

Oliveira, D. M.↗

Orbital period changes in Centaurus X-3

Two new times of mid-X-ray eclipse for Cen X-3 are presented on the basis of pulse arrival time analyses of pointed observations with SAS 3. When combined with all other published eclipse times based on Doppler delay measurements, the results show that the 2.1d binary period is decreasing at an average rate of 1.8 x 10 to the -6th/yr. The decrease, however, is seen as having significant fluctuations about a smooth, linear decrease. The changes observed in the orbital period can be accounted for by mass loss from the system through the L2 point, although the rates required are implausibly high. It is also shown that the long-term overall orbital decay can readily be interpreted as the result of torques exerted by the tidally distorted companion star (Krzeminski's star) on the orbiting neutron star. It is noted that the inferred asynchronism between the orbital frequency and the rotation frequency of the companion star may be maintained by mass and angular momentum loss in a stellar wind or by a tidal instability related to the Darwin effect. However, this would not provide a natural explanation for any short-term deviations from a constant rate of orbital decay.

Kelley, R. L.↗

Spacecraft Orbital Debris Reentry: Aerothermal Analysis

In the past 40 years, thousands of objects have been placed in Earth orbit and are being tracked. Space hardware reentry survivability must be evaluated to assess risks to human life and property on the ground. The objective of this paper is to present results of a study to determine altitude of demise (burn-up) or survivability of reentering objects. Two NASA/JSC computer codes - Object Reentry Survival Analysis Tool (ORSAT) and Miniature ORSAT (MORSAT) were used to determine trajectories, aerodynamic aerothermal environment, and thermal response of selected spacecraft components. The methodology of the two codes is presented, along with results of a parametric study of reentering objects modeled as spheres and cylinders. Parameters varied included mass, diameter, wall thickness, ballistic coefficient, length, type of material, and mode of tumbling/spinning. Two fragments of a spent Delta second stage undergoing orbital decay, stainless steel cylindrical propellant tank and titanium pressurization sphere, were evaluated with ORSAT and found to survive entry, as did the actual objects. Also, orbital decay reentry predictions of the Japanese Advanced Earth Observing Satellite (ADEOS) aluminum and nickel box-type components and the Russian COSMOS 954 satellite beryllium cylinders were made with MORSAT. These objects were also shown to survive reentry.

Rochelle, Wm. C.↗

Orbital Injection of the SEDSAT Satellite: Tethered Systems Dynamics and Flight Data Analysis

This report deals with the following topics which are all related to the orbital injection of the SEDSAT satellite: Dynamics and Stability of Tether Oscillations after the First Cut. The dynamics of the tether after the first cut (i.e., without the Shuttle attached to it) is investigated. The tether oscillations with the free end are analyzed in order to assess the stability of the rectilinear configuration in between the two tether cuts; analysis of Unstable Modes. The unstable modes that appear for high libration angles are further investigated in order to determine their occurrences and the possible transition from bound librations to rotations; Orbital Release Strategies for SEDSAT. A parametric analysis of the orbital decay rate of the SEDSAT satellite after the two tether cuts has been carried out as a function of the following free parameters: libration amplitude at the end of deployment, deviation angle from LV at the first cut, and orbital anomaly at the second cut. The values of these parameters that provide a minimum orbital decay rate of the satellite (after the two cuts) have been computed; and Dynamics and Control of SEDSAT. The deployment control law has been modified to cope with the new ejection velocity of the satellite from the Shuttle cargo bay. New reference profiles have been derived as well as new control parameters. Timing errors at the satellite release as a function of the variations of the initial conditions and the tension model parameters have been estimated for the modified control law.

Lorenzini, Enrico C.↗

Atmospheric drag as the cause of the secular decrease in the semimajor axis of LAGEOS's orbit

An unmodeled acceleration is causing the semimajor axis of LAGEOS to decrease at the rate of about 1.1 mm/day. Drag from charged particles or neutral helium or both is the most probable cause. The rate of orbital decay is conceivably explained by the theories of charged particle drag. Unfortunately, these theories are not yet developed to the point where a definitive statement as to the importance of charged particle drag can be made. Neutral helium may also be the cause of the orbital decay. While the abundance required to account for the secular decrease is high, it also helps solve the 'helium problem'. Neutral hydrogen probably accounts for no more than 12 percent of the observed decay.

Rubincam, D. P.↗

HyperPASS, a New Aeroassist Tool

A new software tool designed to perform aeroassist studies has been developed by Global Aerospace Corporation (GAC). The Hypersonic Planetary Aeroassist Simulation System (HyperPASS) [1] enables users to perform guided aerocapture, guided ballute aerocapture, aerobraking, orbit decay, or unguided entry simulations at any of six target bodies (Venus, Earth, Mars, Jupiter, Titan, or Neptune). HyperPASS is currently being used for trade studies to investigate (1) aerocapture performance with alternate aeroshell types, varying flight path angle and entry velocity, different gload and heating limits, and angle of attack and angle of bank variations; (2) variable, attached ballute geometry; (3) railgun launched projectile trajectories, and (4) preliminary orbit decay evolution. After completing a simulation, there are numerous visualization options in which data can be plotted, saved, or exported to various formats. Several analysis examples will be described.

Gates, Kristin↗

The source of Neptune's internal heat and the value of Neptune's tidal dissipation factor

The suggestion is made that Neptune's observed internal heating is the action of tidal torques between Triton and Neptune in despinning the planet and causing the orbital decay of Triton's orbit. These result from the frictional dissipation of tides within Neptune. It is shown that the considered process implies a value of the tidal dissipation factor of approximately 170. The results of the investigation do not change the conclusion which follows from the lack of internal heating for Uranus that the interiors of Uranus and Neptune differ significantly.

Trafton, L.↗

The Venus atmospheric response to solar cycle variations

Atmospheric drag measurements from the orbital decay of the Pioneer Venus Orbiter and Magellan spacecraft have recently been obtained of the Venus dayside and nightside atmosphere between 130 and 210 km during a period of low solar activity. These new measurements, combined with the earlier Pioneer Venus drag measurements (1978-80) obtained near the maximum of the 11-year solar cycle, have allowed the detection of the detailed response of temperature, atomic oxygen and carbon dioxide to solar variations. We have found a weak but detectable temperature response on the dayside which is in accord with the response predicted by Keating and Bougher when they assumed very strong CO2 radiative cooling resulting from atomic oxygen exciting CO2 into 15 micron emission. This same radiative process may cause strong cooling in the Earth's upper atmosphere with the doubling of CO2 in the future. With decreasing solar activity, the O/CO2 ratio in the lower thermosphere is found to decrease, apparently due to decreased photodissociation of CO2 and lower temperatures. The percent decrease in atomic oxygen with decreasing solar activity on the dayside is found to be approximately the same as the percent decreases of atomic oxygen transported to the nightside. A very weak response of nightside temperatures to solar activity variations has also been detected.

Keating, Gerald M.↗

The Venus Atmospheric Response to Solar Cycle Variations

Atmospheric drag measurements from the orbital decay of the Pioneer Venus Orbiter and Magellan spacecraft have recently been obtained of the Venus dayside and nightside atmosphere between 130 and 210 km during a period of low solar activity. These new measurements, combined with the earlier Pioneer Venus drag measurements (1978-80) obtained near the maximum of the 11-year solar cycle, have allowed the detection of the detailed response of temperature, atomic oxygen and carbon dioxide to solar variations. We have found a weak but detectable temperature response on the dayside which is in accord with the response predicted by Keating and Bougher when they assumed very strong CO2 radiative cooling resulting from atomic oxygen exciting CO2 into 15 micron emission. This same radiative process may cause strong cooling in the Earth's upper atmosphere with the doubling of CO2 in the future. With decreasing solar activity, the O/CO2 ratio in the lower thermosphere is found to decrease, apparently due to decreased photodissociation of CO2 and lower temperatures. The percent decrease in atomic oxygen with decreasing solar activity on the dayside is found to be approximately the same as the percent decreases of atomic oxygen transported to the nightside. A very weak response of nightside temperatures to solar activity variations has also been detected.

Keating, Gerald M.↗

Long Term Missions at the Sun-Earth Libration Point L1: ACE, SOHO, and WIND

Three heliophysics missions -- the Advanced Composition Explorer (ACE), Solar Heliospheric Observatory (SOHO), and the Global Geoscience WIND -- have been orbiting the Sun-Earth interior libration point L1 continuously since 1997, 1996, and 2004, respectively. ACE and WIND (both NASA missions) and SOHO (an ESA-NASA joint mission) are all operated from the NASA Goddard Space Flight Center (GSFC). While ACE and SOHO have been dedicated libration point orbiters since their launches, WIND has had also a remarkable 10-year career flying a deep-space, multiple lunar-flyby trajectory prior to 2004. That era featured 36 targeted lunar flybys with excursions to both L1 and L2 before its final insertion in L1 orbit. A figure depicts the orbits of the three spacecraft, showing projections of the orbits onto the orthographic planes of a solar rotating ecliptic frame of reference. The SOHO orbit is a quasi-periodic halo orbit, where the frequencies of the in-plane and out-of-plane motions are practically equal. Such an orbit is seen to repeat itself with a period of approximately 178 days. For ACE and WIND, the frequencies of the in-plane and out-of-plane motions are unequal, giving rise to the characteristic Lissajous motion. ACE's orbit is of moderately small amplitude, whereas WIND's orbit is a large-amplitude Lissajous of dimensions close to those of the SOHO halo orbit. As motion about the collinear points is inherently unstable, stationkeeping maneuvers are necessary to prevent orbital decay and eventual escape from the L1 region. Though the three spacecraft are dissimilar (SOHO is a 3-axis stabilized Sun pointer, WIND is a spin-stabilized ecliptic pole pointer, and ACE is also spin-stabilized with its spin axis maintained between 4 and 20 degrees of the Sun), the stationkeeping technique for the three is fundamentally the same. The technique consists of correcting the energy of the orbit via a delta-V directed parallel or anti-parallel to the Spacecraft-to-Sun line. SOHO achieves this using thrusters oriented in line with the solar direction. WIND achieves the delta-V via pulsing radial thrusters when aligned with the Sun. ACE uses axial thrusters to apply delta-V with a component that is 94% or more aligned with the ACE-Sun line. Sunward thrust adds energy to the orbit preventing decay back toward Earth. Thrust directed anti-Sunward takes energy out of the L1 orbit, thereby preventing escape from the Earth-Moon system into independent heliocentric orbit. Libration point orbit stationkeeping delta-V costs grow exponentially with time elapsed from the last maneuver performed. The doubling time constant is approximately 16 days. For the sake of fuel conservation, and for limiting the absolute magnitude of propulsion performance errors, stationkeeping maneuvers should be performed before the delta-V grows too large; for our purposes 'too large' is considered to be greater than 0.5 m/sec. In practice, the typical interval between burns for this trio is about three months, and the typical delta-V is much smaller than 0.5 m/sec. Typical annual stationkeeping costs have been around 1.0 m/sec for ACE and WIND, and much less than that for SOHO. All three spacecraft have ample fuel remaining; barring contingencies all three could, in principle, be maintained at L1 for decades to come. This paper will review the L1 orbits and the mission history of ACE, WIND, and SOHO, and describe the stationkeeping techniques and orbit maneuver experience. The Lissajous phase control that was practiced for ACE during the period from 1999 to 2001 will also be briefly discussed. The final section will consider the future of these ongoing missions.

Roberts, Craig E.↗

Grazing impacts on Mars - A record of lost satellites

Over 170 grazing impact craters, representing more than 5% of the total crater population of the ridged plains of Mars, can be identified on the basis of the elongate shape of the crater and the resulting pattern of ejecta deposits. These craters appear to occur along great circles, of which the more recent are in an east-west direction while the older ones are in more northerly directions. The large number and common impact directions of craters are interpreted as due to satellites whose orbits decayed with time. The locations of the projected orbital axes on the Martian surface indicate that the geographic poles of Mars were originally located at lower latitudes. The estimated combined mass of grazing impactors would form a satellite at least 225 km in diameter. These results may provide new clues as to the origin of Phobos and Deimos.

Schultz, P. H.↗

Trends and Options in the Disposal of Launch Vehicle Orbital Stages

An increasing number of agencies and organizations around the world provide guidelines for the disposal of launch vehicle stages placed in Earth orbit. The limitation of orbital lifetime following the satellite delivery mission, particularly in low Earth orbit, is viewed as one of the most important space debris mitigation measures. For higher altitude missions, orbital stages may be maneuvered into more rapidly decaying orbits or may be left in longer-term disposal orbits. This paper summarizes the recent disposal practices of all launch vehicle types and evaluates their compliance with existing national standards. Although the owners and operators of some satellite systems, e.g., Iridium and Globalstar, have levied orbital stage disposal requirements on launch service providers, in general, insufficient attention and communication is given to this topic. Sunsynchronous and geosynchronous missions may pose some of the most difficult challenges for the responsible disposal of orbital stages. A variety of disposal options are normally available, some of which may even influence the design of the spacecraft to be deployed. Also at issue is whether normal launch vehicle propellant reserves can be relied upon for post-mission disposal of orbital stages.

Johnson, Nicholas L.↗

Investigation of thermospheric winds relative to space station orbital altitudes

An investigation of thermospheric winds, relative to the space station orbital altitudes, was made in order to provide information that is useful in an environmental disturbance assessment. Current plans are for this low Earth orbiting facility to orbit at an inclination of 28.5 deg. The orbital altitudes were not yet defined due to the evolutionary configuration of the Space Station. The upper and lower bounds of the orbital altitudes will be based on constraints set by the drag and expected orbital decay and delivery altitude capability of the Shuttle. The orbital altitude will be estimated on the order of 500 km. Neutral winds in the region from about 80 to 600 km which were derived from satellite drag data, Fabry-Perot interferometers, sounding rockets, ground-based optical Doppler techniques, incoherent scatter radar measurements from Millstone Hill combined with the mass spectrometer and lithium trail neutral wind measurements are examined. The equations of motion of the low Earth orbiting facility are also discussed.

Susko, M.↗

Instability of the Present LEO Satellite Populations

Several studies conducted during 1991-2001 demonstrated, with some assumed launch rates, the future unintended growth potential of the Earth satellite population, resulting from random, accidental collisions among resident space objects. In some low Earth orbit (LEO) altitude regimes where the number density of satellites is above a critical spatial density, the production rate of new breakup debris due to collisions would exceed the loss of objects due to orbital decay. A new study has been conducted in the Orbital Debris Program Office at the NASA Lyndon B. Johnson Space Center, using higher fidelity models to evaluate the current debris environment. The study assumed no satellites were launched after December 2005. A total of 150 Monte Carlo runs were carried out and analyzed. Each Monte Carlo run simulated the current debris environment and projected it 200 years into the future. The results indicate that the LEO debris environment has reached a point such that even if no further space launches were conducted, the Earth satellite population would remain relatively constant for only the next 50 years or so. Beyond that, the debris population would begin to increase noticeably, due to the production of collisional debris. Detailed analysis shows that this growth is primarily driven by high collision activities around 900 to 1000 km altitude - the region which has a very high concentration of debris at present. In reality, the satellite population growth in LEO will undoubtedly be worse than this study indicates, since spacecraft and their orbital stages will continue to be launched into space. Postmission disposal of vehicles (e.g., limiting postmission orbital lifetimes to less than 25 years) will help, but will be insufficient to constrain the Earth satellite population. To preserve better the near-Earth environment for future space activities, it might be necessary to remove existing large and massive objects from regions where high collision activities are expected.

Liou, Jer-Chyi↗