Solar sail formation flying for deep-space remote sensing

In this paper we consider how 'near' term solar sails can be used in formation above the ecliptic plane to provide platforms for accurate and continuous remote sensing of the polar regions of the Earth. The dynamics of the solar sail elliptical restricted three-body problem (ERTBP) are exploited for formation flying by identifying a family of periodic orbits above the ecliptic plane. Moreover, we find a family of 1 year periodic orbits where each orbit corresponds to a unique solar sail orientation using a numerical continuation method. It is found through a number of example numerical simulations that this family of orbits can be used for solar sail formation flying. Furthermore, it is illustrated numerically that Solar Sails can provide stable formation keeping platforms that are robust to injection errors. In addition practical trajectories that pass close to the Earth and wind onto these periodic orbits above the ecliptic are identified

Some Exact Results on the Potts Model Partition Function in a Magnetic Field

We consider the Potts model in a magnetic field on an arbitrary graph $G$. Using a formula of F. Y. Wu for the partition function $Z$ of this model as a sum over spanning subgraphs of $G$, we prove some properties of $Z$ concerning factorization, monotonicity, and zeros. A generalization of the Tutte polynomial is presented that corresponds to this partition function. In this context we formulate and discuss two weighted graph-coloring problems. We also give a general structural result for $Z$ for cyclic strip graphs.Comment: 5 pages, late

A Search for Sub-Millisecond Pulsars

We have conducted a search of 19 southern Galactic globular clusters for sub-millisecond pulsars at 660 MHz with the Parkes 64-m radio telescope. To minimize dispersion smearing we used the CPSR baseband recorder, which samples the 20 MHz observing band at the Nyquist rate. By possessing a complete description of the signal we could synthesize an optimal filterbank in software, and in the case of globular clusters of known dispersion measure, much of the dispersion could be removed using coherent techniques. This allowed for very high time resolution (25.6 us in most cases), making our searches in general sensitive to sub-millisecond pulsars with flux densities greater than about 3 mJy at 50 cm. No new pulsars were discovered, placing important constraints on the proportion of pulsars with very short spin periods in these clusters.Comment: 8 pages, 3 figures, to appear in Ap

Pulsar Radio Emission Altitude from Curvature Radiation

We assume that the relativistic sources moving along the dipolar magnetic field lines emit curvature radiation. The beamed emission occurs in the direction of tangents to the field lines, and to receive it, the sight line must align with the tangent within the beaming angle 1/gamma, where gamma is the particle Lorentz factor. By solving the viewing geometry in an inclined and rotating dipole magnetic field, we show that, at any given pulse phase, observer tends to receive radiation only from the specific heights allowed by the geometry. We find outer conal components are emitted at higher altitudes compared to inner components including the core. At any pulse phase, low frequency emission comes from higher altitudes than high frequency emission. We have modeled the emission heights of pulse components of PSR B0329+54, and estimated field line curvature radii and particle Lorentz factors in the emission regions.Comment: 14 pages, 3 figures. Accepted for Astrophysical Journal, 200

A VLA Search for the Geminga Pulsar: A Bayesian Limit on a Scintillating Source

We derive an upper limit of 3 mJy (95% confidence) for the flux density at 317 MHz of the Geminga pulsar (J0633+1746). Our results are based on 7 hours of fast-sampled VLA data, which we averaged synchronously with the pulse period using a period model based on CGRO/EGRET gamma-ray data. Our limit accounts for the fact that this pulsar is most likely subject to interstellar scintillations on a timescale much shorter than our observing span. Our Bayesian method is quite general and can be applied to calculate the fluxes of other scintillated sources. We also present a Bayesian technique for calculating the flux in a pulsed signal of unknown width and phase. Comparing our upper limit of 3 mJy with the quoted flux density of Geminga at 102 MHz, we calculate a lower limit to its spectral index of 2.7. We discuss some possible reasons for Geminga's weakness at radio wavelengths, and the likelihood that many of the unidentified EGRET sources are also radio-quiet or radio-weak Geminga-like pulsars.Comment: 27 pages, including figures. Published in Ap

MERLIN/VLA imaging of the gravitational lens system B0218+357

Gravitational lenses offer the possibility of accurately determining the Hubble parameter (H_0) over cosmological distances, and B0218+357 is one of the most promising systems for an application of this technique. In particular this system has an accurately measured time delay (10.5+/-0.4 d; Biggs et al. 1999) and preliminary mass modelling has given a value for H_0 of 69 +13/-19 km/s/Mpc. The error on this estimate is now dominated by the uncertainty in the mass modelling. As this system contains an Einstein ring it should be possible to constrain the model better by imaging the ring at high resolution. To achieve this we have combined data from MERLIN and the VLA at a frequency of 5 GHz. In particular MERLIN has been used in multi-frequency mode in order to improve substantially the aperture coverage of the combined data set. The resulting map is the best that has been made of the ring and contains many new and interesting features. Efforts are currently underway to exploit the new data for lensing constraints using the LensClean algorithm (Kochanek & Narayan 1992).Comment: Accepted for publication in MNRAS. 6 pages, 4 included PostScript figure

Apollo experience report guidance and control systems: Primary guidance, navigation, and control system development

The primary guidance, navigation, and control systems for both the lunar module and the command module are described. Development of the Apollo primary guidance systems is traced from adaptation of the Polaris Mark II system through evolution from Block I to Block II configurations; the discussion includes design concepts used, test and qualification programs performed, and major problems encountered. The major subsystems (inertial, computer, and optical) are covered. Separate sections on the inertial components (gyroscopes and accelerometers) are presented because these components represent a major contribution to the success of the primary guidance, navigation, and control system

Modeling the Images of Relativistic Jets Lensed by Galaxies with Different Mass Surface Density Distributions

The images of relativistic jets from extragalactic sources produced by gravitational lensing by galaxies with different mass surface density distributions are modeled. In particular, the following models of the gravitational lens mass distribution are considered: a singular isothermal ellipsoid, an isothermal ellipsoid with a core, two- and three-component models with a galactic disk, halo, and bulge. The modeled images are compared both between themselves and with available observations. Different sets of parameters are shown to exist for the gravitationally lensed system B0218+357 in multicomponent models. These sets allow the observed geometry of the system and the intensity ratio of the compact core images to be obtained, but they lead to a significant variety in the Hubble constant determined from the modeling results.Comment: 26 pages, 9 figures, will be published in the Astronomy Letters, 2011, v.37, N4, pp. 233-24

CLASS B2108+213: A new wide separation gravitational lens system

We present observations of CLASS B2108+213, the widest separation gravitational lens system discovered by the Cosmic Lens All-Sky Survey. Radio imaging using the VLA at 8.46 GHz and MERLIN at 5 GHz shows two compact components separated by 4.56 arcsec with a faint third component in between which we believe is emission from a lensing galaxy. 5-GHz VLBA observations reveal milliarcsecond-scale structure in the two lensed images that is consistent with gravitational lensing. Optical emission from the two lensed images and two lensing galaxies within the Einstein radius is detected in Hubble Space Telescope imaging. Furthermore, an optical gravitational arc, associated with the strongest lensed component, has been detected. Surrounding the system are a number of faint galaxies which may help explain the wide image separation. A plausible mass distribution model for CLASS B2108+213 is also presented.Comment: 9 pages, 8 figures, accepted for publication in MNRA

Representing addition and subtraction : learning the formal conventions

The study was designed to test the effects of a structured intervention in teaching children to represent addition and subtraction. In a post-test only control group design, 90 five-year-olds experienced the intervention entitled Bi-directional Translation whilst 90 control subjects experienced typical teaching. Post-intervention testing showed some significant differences between the two groups both in terms of being able to effect the addition and subtraction operations and in being able to determine which operation was appropriate. The results suggest that, contrary to historical practices, children's exploration of real world situations should precede practice in arithmetical symbol manipulation