A satellite relative motion model including $$J_2$$ and $$J_3$$J3 via Vinti’s intermediary

Vinti’s potential is revisited for analytical propagation of the main satellite problem, this time in the context of relative motion. A particular version of Vinti’s spheroidal method is chosen that is valid for arbitrary elliptical orbits, encapsulating \(J_2\), \(J_3\), and generally a partial \(J_4\) in an orbit propagation theory without recourse to perturbation methods. As a child of Vinti’s solution, the proposed relative motion model inherits these properties. Furthermore, the problem is solved in oblate spheroidal elements, leading to large regions of validity for the linearization approximation. After offering several enhancements to Vinti’s solution, including boosts in accuracy and removal of some singularities, the proposed model is derived and subsequently reformulated so that Vinti’s solution is piecewise differentiable. While the model is valid for the critical inclination and nonsingular in the element space, singularities remain in the linear transformation from Earth-centered inertial coordinates to spheroidal elements when the eccentricity is zero or for nearly equatorial orbits. The new state transition matrix is evaluated against numerical solutions including the \(J_2\) through \(J_5\) terms for a wide range of chief orbits and separation distances. The solution is also compared with side-by-side simulations of the original Gim–Alfriend state transition matrix, which considers the \(J_2\) perturbation. Code for computing the resulting state transition matrix and associated reference frame and coordinate transformations is provided online as supplementary material.     

Bayesian modelling of the cool core galaxy group NGC 4325

We present an X-ray analysis of the radio-quiet cool-core galaxy group NGC 4325  ( z = 0.026)  based on Chandra and ROSAT observations. The Chandra data were analysed using xspec deprojection, 2D spectral mapping and forward-fitting with parametric models. Additionally, a Markov Chain Monte Carlo method was used to perform a joint Bayesian analysis of the Chandra and ROSAT data. The results of the various analysis methods are compared, particularly those obtained by forward-fitting and deprojection. The spectral mapping reveals the presence of cool gas displaced up to 10 kpc from the group centre. The Chandra X-ray surface brightness shows the group core to be highly disturbed, and indicates the presence of two small X-ray cavities within 15 kpc of the group core. The xspec deprojection analysis shows that the group has a particularly steep entropy profile, suggesting that an active galactic nucleus (AGN) outburst may be about to occur. With the evidence of prior AGN activity, but with no radio emission currently observed, we suggest that the group in a pre-outburst state, with the cavities and displaced gas providing evidence of a previous, weak AGN outburst.     

Field measurements of horizontal forward motion velocities of terrestrial dust devils: Towards a proxy for ambient winds on Mars and Earth

Dust devils – convective vortices made visible by the dust and debris they entrain – are common in arid environments and have been observed on Earth and Mars. Martian dust devils have been identified both in images taken at the surface and in remote sensing observations from orbiting spacecraft. Observations from landing craft and orbiting instruments have allowed the dust devil translational forward motion (ground velocity) to be calculated, but it is unclear how these velocities relate to the local ambient wind conditions, for (i) only model wind speeds are generally available for Mars, and (ii) on Earth only anecdotal evidence exists that compares dust devil ground velocity with ambient wind velocity. If dust devil ground velocity can be reliably correlated to the ambient wind regime, observations of dust devils could provide a proxy for wind speed and direction measurements on Mars. Hence, dust devil ground velocities could be used to probe the circulation of the martian boundary layer and help constrain climate models or assess the safety of future landing sites.We present results from a field study of terrestrial dust devils performed in the southwest USA in which we measured dust devil horizontal velocity as a function of ambient wind velocity. We acquired stereo images of more than a 100 active dust devils and recorded multiple size and position measurements for each dust devil. We used these data to calculate dust devil translational velocity. The dust devils were within a study area bounded by 10 m high meteorology towers such that dust devil speed and direction could be correlated with the local ambient wind speed and direction measurements.Daily (10:00–16:00 local time) and 2-h averaged dust devil ground speeds correlate well with ambient wind speeds averaged over the same period. Unsurprisingly, individual measurements of dust devil ground speed match instantaneous measurements of ambient wind speed more poorly; a 20-min smoothing window applied to the ambient wind speed data improves the correlation. In general, dust devils travel 10–20% faster than ambient wind speed measured at 10 m height, suggesting that their ground speeds are representative of the boundary layer winds a few tens of meters above ground level. Dust devil ground motion direction closely matches the measured ambient wind direction.The link between ambient winds and dust devil ground velocity demonstrated here suggests that a similar one should apply on Mars. Determining the details of the martian relationship between dust devil ground velocity and ambient wind velocity might require new in situ or modelling studies but, if completed successfully, would provide a quantitative means of measuring wind velocities on Mars that would otherwise be impossible to obtain.     

Natural and artificial connections between atoll islets in the pacific,their process and environmental impact

Three types of natural connection between atoll islets are described. Causeway, as an artificial way of connecting islets, makes a connection to be completed in a few months. In this case shore adjustment becomes more vigorous than that in natural conditions, resulting in lagoon shore erosion. A causeway without short bridges or culverts should be built close to the lagoon shore to reduce lagoon shore erosion. A causeway-crossing channel assemblage is the worst type among all of the connection engineering constructions because the crossing channel traps sediment and further transports it out of the channel, resulting in long period coastal erosion. Reforming Nippon Causeway in Tarawa Atoll, Kiribati by simple means will stop sand loss, reduce shore erosion and greatly upgrade its stability.     

Temporal Evolution of the Solar-Wind Electron Core Density at Solar Minimum by Correlating SWEA Measurements from STEREO A and B

The twin STEREO spacecraft provide a unique tool to study the temporal evolution of the solar-wind properties in the ecliptic since their longitudinal separation increases with time. We derive the characteristic temporal variations at ～?1 AU between two different plasma parcels ejected from the same solar source by excluding the spatial variations from our datasets. As part of the onboard IMPACT instrument suite, the SWEA electron experiment provides the solar-wind electron core density at two different heliospheric vantage points. We analyze these density datasets between March and August 2007 and find typical solar minimum conditions. After adjusting for the theoretical time lag between the two spacecraft, we compare the two density datasets. We find that their correlation decreases as the time difference increases between two ejections. The correlation coefficient is about 0.80 for a time lag of a half day and 0.65 for two days. These correlation coefficients from the electron core density are somewhat lower than the ones from the proton bulk velocity obtained in an earlier study, though they are still high enough to consider the solar wind as persistent after two days. These quantitative results reflect the variability of the solar-wind properties in space and time, and they might serve as input for solar-wind models.     

The 2dF Galaxy Redshift Survey: luminosity dependence of galaxy clustering

We investigate the dependence of the strength of galaxy clustering on intrinsic luminosity using the Anglo-Australian two degree field galaxy redshift survey (2dFGRS). The 2dFGRS is over an order of magnitude larger than previous redshift surveys used to address this issue. We measure the projected two-point correlation function of galaxies in a series of volume-limited samples. The projected correlation function is free from any distortion of the clustering pattern induced by peculiar motions and is well described by a power law in pair separation over the range     . The clustering of     galaxies in real space is well-fitted by a correlation length     and power-law slope     . The clustering amplitude increases slowly with absolute magnitude for galaxies fainter than M *, but rises more strongly at higher luminosities. At low luminosities, our results agree with measurements from the Southern Sky Redshift Survey 2 by Benoist et al. However, we find a weaker dependence of clustering strength on luminosity at the highest luminosities. The correlation function amplitude increases by a factor of 4.0 between     and −22.5, and the most luminous galaxies are 3.0 times more strongly clustered than L * galaxies. The power-law slope of the correlation function shows remarkably little variation for samples spanning a factor of 20 in luminosity. Our measurements are in very good agreement with the predictions of the hierarchical galaxy formation models of Benson et al.