On the Formulation of the Gravitational Potential in Terms of Equinoctial Variables

Analytical averaging techniques are used to expand the disturbing potential in the equinoctial coordinate frame by considering third body harmonics and zonal functions harmonics. General results are developed through applications of Legendre and associated Legendre polynomials and the Q sub nm functions for the gravitational potential

A semianalytical satellite theory for weak time-dependent perturbations

The modifications of the semianalytical satellite theory required to include these 'weak' time dependent perturbations are described. The new formulation results in additional terms in the short periodic variations but does not change the averaged equations of motion. Thus the m monthly terms are still included in the averaged equations of motion. This contrasts with the usual approach for the strongly time dependent perturbations in which the m monthly (or m daily, if tesseral harmonics are being considered) terms would be eliminated from the averaged equations of motion and included in the short periodics computation. Numerical test results for the GPS case obtained with a numerical averaging implementation of the new theory demonstrate the accuracy improvement

Sensitivity guidance for entry into an uncertain Martian atmosphere

Sensitivity guidance for entry into uncertain Mars atmosphere using onboard compute

The transition of GTDS to the Unix workstation environment

Future Flight Dynamics systems should take advantage of the possibilities provided by current and future generations of low-cost, high performance workstation computing environments with Graphical User Interface. The port of the existing mainframe Flight Dynamics systems to the workstation environment offers an economic approach for combining the tremendous engineering heritage that has been encapsulated in these systems with the advantages of the new computing environments. This paper will describe the successful transition of the Draper Laboratory R&D version of GTDS (Goddard Trajectory Determination System) from the IBM Mainframe to the Unix workstation environment. The approach will be a mix of historical timeline notes, descriptions of the technical problems overcome, and descriptions of associated SQA (software quality assurance) issues

Sensor-based irrigation reduces water consumption without compromising yield and postharvest quality of soilless green bean

Real-time monitoring of substrate parameters in the root-zone through dielectric sensors is considered a promising and feasible approach for precision irrigation and fertilization management of greenhouse soilless vegetable crops. This research investigates the effects of timer-based (TIMER) compared with dielectric sensor-based irrigation management with different irrigation set-points [SENSOR_0.35, SENSOR_0.30 and SENSOR_0.25, corresponding to substrate volumetric water contents (VWC) of 0.35, 0.30 and 0.25 m3 m−3, respectively] on water use, crop performance, plant growth and physiology, product quality and post-harvest parameters of soilless green bean (Phaseolus vulgaris L., cv Maestrale). In SENSOR treatments, an automatic system managed irrigation in order to maintain substrate moisture constantly close to the specific irrigation set-point. The highest water amount was used in TIMER treatment, with a water saving of roughly 36%, 41% and 47% in SENSOR_0.35, SENSOR_0.30 and SENSOR_0.25, respectively. In TIMER, the leaching rate was ≈31% of the total water consumption, while little leaching (<10%) was observed in SENSOR treatments. TIMER and SENSOR_0.35 resulted in similar plant growth and yield, while irrigation set-points corresponding to lower VWC values (SENSOR_0.30 and SENSOR_0.25) resulted in inad-equate water availability conditions and impaired the crop performance. The study confirms that rational sensor-based irrigation allows to save water without compromising anyhow the product quality. In SENSOR irrigation management, in fact, especially in the case of optimal water availability conditions, it was possible to obtain high quality pods, with fully satisfactory characteristics during storage at 7◦ C for 15 days

Atmospheric Density Uncertainty Quantification for Satellite Conjunction Assessment

Conjunction assessment requires knowledge of the uncertainty in the predicted orbit. Errors in the atmospheric density are a major source of error in the prediction of low Earth orbits. Therefore, accurate estimation of the density and quantification of the uncertainty in the density is required. Most atmospheric density models, however, do not provide an estimate of the uncertainty in the density. In this work, we present a new approach to quantify uncertainties in the density and to include these for calculating the probability of collision Pc. For this, we employ a recently developed dynamic reduced-order density model that enables efficient prediction of the thermospheric density. First, the model is used to obtain accurate estimates of the density and of the uncertainty in the estimates. Second, the density uncertainties are propagated forward simultaneously with orbit propagation to include the density uncertainties for Pc calculation. For this, we account for the effect of cross-correlation in position uncertainties due to density errors on the Pc. Finally, the effect of density uncertainties and cross-correlation on the Pc is assessed. The presented approach provides the distinctive capability to quantify the uncertainty in atmospheric density and to include this uncertainty for conjunction assessment while taking into account the dependence of the density errors on location and time. In addition, the results show that it is important to consider the effect of cross-correlation on the Pc, because ignoring this effect can result in severe underestimation of the collision probability.Comment: 15 pages, 6 figures, 5 table

Analysis of the suitability of analytical, semi-analytical, and numerical approaches for important orbit propagation tasks

Astrodynamies encompasses phenomena on diverse and disparate time scales. That solar electromagnetic atmospheric density proxies are developed every few hours demonstrates phenomena on that scale. In the most simple two body Newtonian formulation that includes only inverse square gravitation, there are equilibrium solutions that persist forever. Tidal effects are diurnal. Collisions last only milliseconds. Explosion debris migrates over weeks or months. The equations of astrodynamies initial value problem in the analytical, semi-analytical, and numerical formulation of astrodynamies exhibit stiffness. We emphasize the well-known mathematical fact that explicit numerical methods can create numerical stiffness where there was no physical stiffness and can produce reasonable but erroneous outcomes. Implicit methods should always be used even though more computational operations might be required