Stability studies of periodic solutions Final report
Stability of periodic orbits of restricted three- body problem
THREE-BODY PROBLEM↗
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(abstract) The Impactor Flux in the Pluto-Charon System
The impactor flux on Pluto and Charon consists of long-period comets from the Oort cloud passing through the region, and intermediate-period comets evolving inward to (or outward from) short-period orbits. The source of the intermediate-period comets is likely an extended disk of remnant planetesimals beyond the orbit of Neptune, commonly referred to as the Kuiper belt, though the Oort cloud may be an additional source of some short-period comets. The Pluto-Charon system actually circulates within the Kuiper belt, and with an aphelion of 49.3 AU, moves through a region where remnant planetesimal orbits would likely be stable over the age of the solar system. The recent discovery of two objects at Kuiper belt distances, 1992 QB 1 and 1993 FW, and the fact that the orbit determined for 1992 QB 1 is likely of low eccentricity and low inclination, have provided strong observational evidence for the Kuiper belt. Weisman et al (1989) showed that, for the expected number of objects in the Kuiper belt necessary to provide the short-period comet flux, cometary cratering on Pluto and Charon is dominated by Kuiper belt comets. We will provide updated estimates of the numbers, based on an improved understanding of Oort cloud and Kuiper belt dynamics since 1989, and on improved estimates for the radii and masses for Pluto and Charon. Because Pluto and Charon actually penetrate the stable region of the Kuiper belt beyond 40 AU, expected cratering rates for the pair are substantially higher than for Triton, which is located at the inner edge of the Kuiper belt. However, the Pluto-Charon system is tidally evolved and this may have led to resurfacing events at various times in its history. Thus, detailed predictions of the integrated crater density or comparisons with Triton are not very meaningful without a knowledge of that history. Differences in the suspected compositions of Pluto and Charon may also lead to different surface rheologies and thus, different retention times for cratered surfaces.
Pluto↗
Rotating emission ring in binary systems.
Representation of rotating gaseous emission rings in eclipsing binary systems by periodic orbits around more massive component in restricted three-body problem
PERIODIC ORBIT↗
The Importance of Semi-Major Axis Knowledge in the Determination of Near-Circular Orbits
Modem orbit determination has mostly been accomplished using Cartesian coordinates. This usage has carried over in recent years to the use of GPS for satellite orbit determination. The unprecedented positioning accuracy of GPS has tended to focus attention more on the system's capability to locate the spacecraft's location at a particular epoch than on its accuracy in determination of the orbit, per se. As is well-known, the latter depends on a coordinated knowledge of position, velocity, and the correlation between their errors. Failure to determine a properly coordinated position/velocity state vector at a given epoch can lead to an epoch state that does not propagate well, and/or may not be usable for the execution of orbit adjustment maneuvers. For the quite common case of near-circular orbits, the degree to which position and velocity estimates are properly coordinated is largely captured by the error in semi-major axis (SMA) they jointly produce. Figure 1 depicts the relationships among radius error, speed error, and their correlation which exist for a typical low altitude Earth orbit. Two familiar consequences are the relationship Figure 1 shows are the following: (1) downrange position error grows at the per orbit rate of 3(pi) times the SMA error; (2) a velocity change imparted to the orbit will have an error of (pi) divided by the orbit period times the SMA error. A less familiar consequence occurs in the problem of initializing the covariance matrix for a sequential orbit determination filter. An initial covariance consistent with orbital dynamics should be used if the covariance is to propagate well. Properly accounting for the SMA error of the initial state in the construction of the initial covariance accomplishes half of this objective, by specifying the partition of the covariance corresponding to down-track position and radial velocity errors. The remainder of the in-plane covariance partition may be specified in terms of the flight path angle error of the initial state. Figure 2 illustrates the effect of properly and not properly initializing a covariance. This figure was produced by propagating the covariance shown on the plot, without process noise, in a circular low Earth orbit whose period is 5828.5 seconds. The upper subplot, in which the proper relationships among position, velocity, and their correlation has been used, shows overall error growth, in terms of the standard deviations of the inertial position coordinates, of about half of the lower subplot, whose initial covariance was based on other considerations.
Carpenter, J. Russell↗
X-Ray Spectral Study of a Newly Ginga-Detected DQ Her
The goal of this proposal was to observe with ASCA, YY Dra, a DQ Her objected identified using archival Ginga data, in order to complete a high quality ASCA study of Ginga-detected DQ Her stars. There are relatively few DQ Her objects characterized by X-ray pulsations at the white dwarf spin period and optical pulsations at the orbital period and extremely complex X-ray spectra. The ASCA study included seven DQ Her objects. ASCA is able to resolve separate components of the Fe K emission and to set constraints on temperatures in the accretion column, and the mass of the white dwarf. The 40ksec observation, corresponding to roughly three orbital cycles, allowed the study of continuum changes with spin and orbital phase. The ASCA spectrum can be modelled as a bremsstrahlung with evidence for cold, helium-like and hydrogen-like iron emission, and helium-like argon emission. The lines yield a plasma temperature that is compatible with that from the continuum modelling (10-20 keV). The X-ray light-curve clearly shows sinusoidal variation from the spin pulse and shallow absorption dips at the orbital cycle. The derived parameters match well with the -accretion curtain, model for intermediate polars. The results will be presented together with the seven other DQ Her type sources observed with ASCA.
Vrtilek, S.↗
A spectroscopic study of the cataclysmic binary star SU Ursae Majoris
Spectroscopic observations of SU UMa, the prototype of a class of short-period cataclysmic binaries, are reported. The orbital period is found to be 0.076351 + or - 4.3 x 10 to the -5th days. The velocity amplitude of the emission line source is 58 + or - 4 km/s, leading to a mass function of about 0.0015 solar mass and implying a moderately low inclination. The line cores in H-alpha and H-beta lead the wings slightly in orbital phase, contrary to the predictions of simple hot spot models of the line core. The velocity widths of the Balmer series increase toward higher members of the series, suggesting that pressure broadening may contribute nonnegligibly to the emission line widths.
Thorstensen, John R.↗
Periodic landing zone analysis for earth- orbital missions
Periodic landing zone analysis for earth-orbital missions - graphs
Green, R. I.↗
The discovery of 50 minute periodic absorption events from 4U 1915-05
An analysis of X-ray observations shows that the steady flux from 4U 1915-05 undergoes periodic absorption dips with a period of 50 minutes. This period most probably represents the underlying orbital period of the system, and variations in the depth and duration of these events suggest that they are caused by a bulge on the edge of the accretion disk at the point where the gas stream impacts the disk. The mass-losing star in this system is probably a low-mass white dwarf, and the spectrum of the dips indicates that the metallicity of the absorbing material is at least a factor of 17 below solar values. The discovery of the 50-minute binary period supports earlier suggestions that X-ray burst sources are in binary systems.
White, N. E.↗
Amalthea
Voyager images have revealed Amalthea to be an irregular object 270 x 165 x 150 km in size. The spin period is probably synchronous with the orbital period of 11.9 hr, with the long axis pointing toward Jupiter. The satellite's surface is heavily scarred by impact craters, the largest of which has a diameter of 90 km (comparable to the mean radius of the satellite). Amalthea is very dark (reflectance about 5-6%) and very red, but isolated bright spots (reflectance up to 20%) occur. The spectrum of these bright spots is less red and may show an absorption feature near 0.6 micron. It is likely that the surface of Amalthea has been severely altered by its environment and by contamination from Io (especially by sulfur). It may, therefore, be very difficult to obtain definitive information on the composition of the intrinsic Amalthea material from remote sensing measurements.
Thomas, P.↗
Ultraviolet, optical, and infrared observations of the intermediate polar TV Columbae
Forty-three IUE spectra of the X-ray discovered, triply periodic cataclysmic variable, TV Col are examined. The results show that the UV flux varies with the four-day period discovered by Motch in 1981. By fitting continuum models to the UV and optical fluxes, it is inferred that this modulation corresponds to the periodic heating of a normally 9000 K source within the binary system due to reprocessing of beamed X-ray and (possibly) EUV radiation from the vicinity of the degenerate star. The observed flux from this heated source is consistent with its origin at either the disk hot spot or the secondary star. Phasing arguments, however, favor the identification of the latter as the primary reprocessing site in the system. The infrared observations are not consistent with the model proposed by Watts et al. in 1982 and imply that the four-day period does not correspond to the orbital period of the binary.
Mateo, M.↗
Optical and UV spectroscopy of the black hole binary candidate LMC X-1
Both further optical spectroscopy of the binary star identified with LMC X-1, obtained between 1983 and 1985, and a series of IUE UV spectra taken during a 5 day interval in 1984 are presented. The optical data are used to refine the orbital period to 4.2288 days, and improved orbital parameters are derived. The velocity of the optical emission lines is antiphased with the absorption lines and has twice the velocity amplitude. These new results support the estimates of the masses in the system given earlier. The most probable component masses are approximately 20 solar masses for the primary and near 6 solar masses (for the x-ray star), suggesting the the latter may be a black hole. The UV spectra show very weak, low-velocity stellar-wind lines. It is suggested that much of the surrounding medium is highly ionized by the X-ray flux. The 'nonwind' UV spectral lines and the UV continuum temperature are consistent with the optical data, indicating a late O type star of M(bol) = -8.5. There is a weak modulation of absorption-line strengths with orbital phase, suggestive of a lack of axisymmetry in the X-irradiation of the primary star and indicative of a fairly low orbital inclination.
Hutchings, J. B.↗
The photometric variability of the chromospherically active binary star HD 80715
Differential UBVRI photometry of the double-lined BY Dra system HD 80715 (K3 V + K3 V) obtained in December 1987 is presented. The star is found to be a variable with a full amplitude of 0.06 mag in V and a period similar or equal to the orbital period of 3.804 days. The mechanism of the variability is interpreted as rotational modulation due to dark starspots. In an attempt to detect chromospheric activity, high-resolution CCD spectra were obtained at Ca II H and K and at Fe I 6430 A and Ca I 6439 A, the photospheric lines normally used for Doppler imaging. HD 80715 shows double H and K emission features at a constant flux level for each component.
Strassmeier, Klaus G.↗
The Charon-Pluto mass ratio from MKO astrometry
Using the University of Hawaii (UH) 2.2-m telescope, we obtained charge coupled device (CCD) images of Pluto as it passed through a single field of 10 stars during 6 nights of Charon's 6.4-day orbital period. From these data, Charon's orbital semimajor axis is found to be 19,460 +/- 58 km, which is consistent with the recent measurement by Null et al. (1993), of 19,405 +/- 86 km. Our semimajor axis implies a system mass of (14.32 +/- 0.13) x 10(exp 24) g. From the motions of Pluto and Charon around their barycenter, we find that the ratio of Charon's mass to Pluto's is 0.1566 +/- 0.0035, indicating that the bodies both have densities near 2 g/cc. Our ratio is nearly twice that of Null et al., who find a ratio of 0.0837 +/- 0.0147. Possible reasons for the large discrepancy are discussed.
Young, L. A.↗
1ES 1113+432: Luminous, soft X-ray outburst from a nearby cataclysmic variable (AR Ursae Majoris)
A remarkable X-ray transient from the Einstein Slew Survey, 1 ES 1113+432, is identified with a nearby, short-period cataclysmic variable. Wenzel (1993) has confirmed that the optical counterpart is the variable star, AR UMa (cataloged as 'semiregular'), erroneously reported 5.7 min southeast of the true position. One of the Einstein slew observations recorded a flux of 43 IPC counts/s, which is an order of magnitude above the flux observed from the brightest cataclysmic variables in other X-ray surveys. The outburst spectrum is extremely 'soft,' with an implied blackbody temperature of approximately 22 eV. The optical counterpart (V = 16.5) exhibits a strong UV component, TiO bands from an M star, and broadened Balmer emission lines. Optical states as bright as V approx. 13 were found on photographs from the Harvard Plate Library, confirming outburst behavior in the optical counterpart. The historical photographic record suggests that 1ES 1113+432 remains in a low-accretion state most of the time. Both of the soft X-ray spectrum and the transitions between high and low-accretion states are suggestive of the AM Her (magnetic) subclass. Photometric observations in the I band show 0.18 mag modulations at a period of 0.966 hr. These are interpreted as ellipsiodal variations in the secondary star for a binary period of 1.932 hr, which is near the lower boundary of the 'period gap' in the histogram, of orbital periods of accreting white dwarfs. Thus 1ES 1113+432 provides the rare opportunity to study a secondary star in a cataclysmic binary that has evolved through the period gap. The optical spectral features from the secondary imply a spectral type of approximately M6 and a distance of approximately 88 pc. The peak luminosity in the soft X-ray component (unabsorbed) is then estimated to be 3 X 10(exp 33) ergs/s, assuming emission from a blackbody slab with a temperature of 22 eV. While this luminosity is higher than previous measures of the soft X-ray component, it does not exceed the amount of radiation that could be emitted from the accretion-heated surface of a white dwarf.
Remillard, R. A.↗
Identification of the Periodic Hard X-Ray Transient GRO J1849-03 with the X-Ray Pulsar GS 1843-02 = X1845-024: A New Be/X-Ray Binary
We identify the periodic transient hard X-ray source GRO J1849-03 with the transient x-ray pulsar GS 1843-02 = X1845-024 based on the detection of x-ray outbursts from X1845-024 coincident with hard x-ray outbursts of GRO J1849-03. Based on its spin period of 94.8 s and its orbital period of 241 days, we classify the system as a Be/X-ray binary.
Soffitta, P.↗
"X-Ray Transients in Star-Forming Regions" and "Hard X-Ray Emission from X-Ray Bursters"
This grant funded work on the analysis of data obtained with the Burst and Transient Experiment (BATSE) on the Compton Gamma-Ray Observatory. The goal of the work was to search for hard x-ray transients in star forming regions using the all-sky hard x-ray monitoring capability of BATSE. Our initial work lead to the discovery of a hard x-ray transient, GRO J1849-03. Follow-up observations of this source made with the Wide Field Camera on BeppoSAX showed that the source should be identified with the previously known x-ray pulsar GS 1843-02 which itself is identified with the x-ray source X1845-024 originally discovered with the SAS-3 satellite. Our identification of the source and measurement of the outburst recurrence time, lead to the identification of the source as a Be/X-ray binary with a spin period of 94.8 s and an orbital period of 241 days. The funding was used primarily for partial salary and travel support for John Tomsick, then a graduate student at Columbia University. John Tomsick, now Dr. Tomsick, received his Ph.D. from Columbia University in July 1999, based partially on results obtained under this investigation. He is now a postdoctoral research scientist at the University of California, San Diego.
Halpern, Jules P.↗
Thermal Analysis and Correlation of the Mars Odyssey Spacecraft's Solar Array During Aerobraking Operations
The Mars Odyssey spacecraft made use of multipass aerobraking to gradually reduce its orbit period from a highly elliptical insertion orbit to its final science orbit. Aerobraking operations provided an opportunity to apply advanced thermal analysis techniques to predict the temperature of the spacecraft's solar array for each drag pass. Odyssey telemetry data was used to correlate the thermal model. The thermal analysis was tightly coupled to the flight mechanics, aerodynamics, and atmospheric modeling efforts being performed during operations. Specifically, the thermal analysis predictions required a calculation of the spacecraft's velocity relative to the atmosphere, a prediction of the atmospheric density, and a prediction of the heat transfer coefficients due to aerodynamic heating. Temperature correlations were performed by comparing predicted temperatures of the thermocouples to the actual thermocouple readings from the spacecraft. Time histories of the spacecraft relative velocity, atmospheric density, and heat transfer coefficients, calculated using flight accelerometer and quaternion data, were used to calculate the aerodynamic heating. During aerobraking operations, the correlations were used to continually update the thermal model, thus increasing confidence in the predictions. This paper describes the thermal analysis that was performed and presents the correlations to the flight data.
Dec, John A.↗
A Thermal Analysis Approach for the Mars Odyssey Spacecraft's Solar Array
There are numerous challenges associated with placing a spacecraft in orbit around Mars. Often. trades must be made such as the mass of the payload and the amount of fuel that can be carried. One technique employed to more efficiently place a spacecraft in orbit while maximizing payload mass (minimizing fuel use) is aerobraking. The Mars Odyssey Spacecraft made use of aerobraking to gradually reduce its orbit period from a highly elliptical insertion orbit to its final science orbit. Aerobraking introduces its own unique challenges, in particular, predicting the thermal response of the spacecraft and its components during each aerobraking drag pass. This paper describes the methods used to perform aerobraking thermal analysis using finite element thermal models of the Mars Odyssey Spacecraft's solar array. To accurately model the complex behavior during aerobraking, the thermal analysis must be tightly coupled to the spatially varying, time dependent aerodynamic heating analysis. Also, to properly represent the temperatures prior to the start of the drag pass. the model must include the orbital solar and planetary heat fluxes. It is critical that the thermal behavior be predicted accurately to maintain the solar array below its structural flight allowable temperature limit. The goal of this paper is to describe a thermal modeling method that was developed for this purpose.
Dec, John A.↗