On the Dynamics of a Deformable Satellite in the Gravitational Field of a Spherical Rigid Body

In this paper, a model is developed for the dynamics of a system of two bodies whose material points are under the influence of a central gravitational force. One of the bodies is assumed to be rigid and spherically symmetric, while the other is assumed to be deformable. To develop a tractable model for the system, the deformable body is modeled using Cohen and Muncaster's theory of a pseudo-rigid body. The resulting model of the system has several of the features, such as angular momentum conservation, exhibited by more restrictive models. We also show how the self-gravitation of the deformable body can be accommodated using appropriate constitutive equations for a force tensor. This enables our model to subsume many existing models of ellipsoidal figures of equilibrium. After the model and its conservations have been discussed, attention is restricted to steady motions of the system. Several results, which generalize recent works on rigid satellites, are established for these motions. For a specific choice of constitutive equations for the pseudo-rigid body, we determine the steady motions with the aid of a numerical continuation method. These results can also be considered as generalizations of earlier works on Roche's ellipsoids of equilibrium.     

On target for Venus – set oriented computation of energy efficient low thrust trajectories

Recently new techniques for the design of energy efficient trajectories for space missions have been proposed that are based on the circular restricted three body problem as the underlying mathematical model. These techniques exploit the structure and geometry of certain invariant sets and associated invariant manifolds in phase space to systematically construct energy efficient flight paths. In this paper, we extend this model in order to account for a continuously applied control force on the spacecraft as realized by certain low thrust propulsion systems. We show how the techniques for the trajectory design can be suitably augmented and compute approximations to trajectories for a mission to Venus.     

High speed photon-counting imager using a position sensitive diode

A new use for a 2-dimensional position sensitive diode (PSD) is described. A duolateral PSD was used with a microchannel plate image intensifier as a proof-of-concept photon counting (event driven) imager for astronomical imaging and photometry. This produced an imager capable of counting 25–30 kcps over the astronomical bands B, V & R, with an overall efficiency of ∼19%.     

Variation in Lake Baikal's phytoplankton distribution and fluvial input assessed by SeaWiFS satellite data

The current behaviour of selected climate proxies in Lake Baikal was assessed by remote sensing analyses of ‘Sea viewing Wide Field of view Sensor’ (SeaWiFS) satellite data. Suitable proxies include optically visible water constituents such as phytoplankton, suspended terrigenous matter and yellow substance. These limnological parameters reflect the present-day climate bioproductivity and the river discharge in the catchment area.A biological and geochemical ground truth data set for Lake Baikal was established with the help of members of the paleoclimate project ‘high-resolution CONTINENTal paleoclimate record in Lake Baikal’ (CONTINENT). For processing the SeaWiFS satellite data, the atmospheric correction was adapted to the case of Lake Baikal. Chlorophyll as a proxy for phytoplankton was quantified using global NASA ocean colour algorithms OC2 and OC4. In cases of no optical interferences by terrigenous input, the calculated chlorophyll concentrations in clear pelagic waters were within ±30% accuracy with the CONTINENT cruise data during the summers of 2001 and 2002. Within this range of accuracy, the SeaWiFS time series will be able to show the seasonal variations of chlorophyll of specified bio-optical provinces of Lake Baikal and of CONTINENT sites. In this study, the suspended matter as a proxy for the terrigenous input was calculated according to an empirical algorithm using ground truth data in the time frame of flooding events in summer 2001. The approach chosen correlates the suspended matter concentration with the remotely sensed parameter of ‘attenuation coefficient’ to account for the organic-rich terrigenous input that originates from the swampy watersheds.Seasonal and spatial information that is provided by the analyses of the SeaWiFS satellite data will assist paleoclimate researchers to interpret the autochthonous and allochthonous influences at the CONTINENT coring sites.     

Reconstructing seawater δO from paired coral δO and Sr/Ca ratios: Methods, error analysis and problems, with examples from Tahiti (French Polynesia) and Timor (Indonesia)

We compare several statistical routines that may be used to calculate δ¹⁸O_sw and SSS from paired coral Sr/Ca and δ¹⁸O measurements. Typically, the δ¹⁸O_coral-SST relationship is estimated by linear regression of coral δ¹⁸O vs. SST. If this method is applied, evidence should be given that at a particular site SST and SSS do not co-vary. In the tropical oceans, SST and δ¹⁸O_sw (SSS) often co-vary, and this will bias the estimate of the regression slope of δ¹⁸O_coral-SST. Using a stochastic model, we show that covariance leads to a bias in the coefficients of the univariate regression equations. As the slope of the δ¹⁸O_coral-SST relationship has known, we propose to insert this value for γ₁ in the regression models. This requires that the constants of the regression equations are removed. To omit the constants, we propose to center the regression equations (i.e., to remove the mean values from the variables). The statistical error propagation is calculated to assess our ability to resolve past variations in δ¹⁸O_sw (SSS). At Tahiti, we find that the combined analytical uncertainties of coral δ¹⁸O and Sr/Ca equal the amplitude of the seasonal cycle of δ¹⁸O_sw (SSS). Therefore, we cannot resolve the seasonal cycle of SSS at Tahiti. At Timor, the error of reconstructed δ¹⁸O_sw (SSS) is lower than the magnitude of seasonal variations of δ¹⁸O_sw (SSS), and the seasonal cycle of δ¹⁸O_sw (SSS) can be resolved.     

Tracking and orbit determination performance of the GRAS instrument on MetOp-A

The global navigation satellite system receiver for atmospheric sounding (GRAS) on MetOp-A is the first European GPS receiver providing dual-frequency navigation and occultation measurements from a spaceborne platform on a routine basis. The receiver is based on ESA’s AGGA-2 correlator chip, which implements a high-quality tracking scheme for semi-codeless P(Y) code tracking on the L1 and L2 frequency. Data collected with the zenith antenna on MetOp-A have been used to perform an in-flight characterization of the GRAS instrument with focus on the tracking and navigation performance. Besides an assessment of the receiver noise and systematic measurement errors, the study addresses the precise orbit determination accuracy achievable with the GRAS receiver. A consistency on the 5 cm level is demonstrated for reduced dynamics orbit solutions computed independently by four different agencies and software packages. With purely kinematic solutions, 10 cm accuracy is obtained. As a part of the analysis, an empirical antenna offset correction and preliminary phase center correction map are derived, which notably reduce the carrier phase residuals and improve the consistency of kinematic orbit determination results.