Abstract: The ability to observe small celestial bodies has grown drastically over the last decade. The increase in interest for these bodies has increased demand for higher fidelity trajectory simulations in order to assure mission success. Most methods that are available for simulating trajectories about asymmetric bodies assume they are of uniform density. Here we propose a modification to two well-known methods: the mascon model and the spherical harmonic series approximation, for use in simulating trajectories about variable density bodies. In particular, we will look at contact binaries which are bodies consisting of two different densities.
Abstract: A number of recent missions by space agencies to irregularly shaped asteroids have initiated an interest in accurately modeling the irregular gravitational field of these bodies. Two common methods for approximating these irregular gravity field are the polyhedral model and the mascon model. The polyhedral model employs Gauss's Divergence Theorem to calculate gravitational potential from a closed surface mesh. The mascon model uses a finite number of point-masses, distributed throughout the interior of the body, to approximate the gravitational field. In the present study, the accuracy and computational efficiency of the mascon model and polyhedral model are directly compared. The unit sphere is used as a test-case allowing the error of both methods to be calculated analytically. Both models are then applied to the real-world case of asteroid 25143 Itokawa. Results indicate that, for the same computational expenditure, the mascon model can provide the same level of accuracy as the polyhedral model at the surface of the body. Moreover, in general, away from the body the mascon model is more accurate and requires a shorter run-time.
Abstract: A number of recent and future missions to irregularly shaped asteroids have initiated an interest in accurately modeling the irregular gravitational potential field of these bodies. Close to highly irregular asteroids this is often accomplished using the polyhedral model. This method uses a small number of computational elements because only the surface is discretized; however, the number of computations required per element is large. As such, a simplification of the polyhedral potential model is proposed that approximates each face of the surface mesh as a surface-concentration. The simplified surface-concentration model and the full polyhedral model are compared using a sphere as test case so that the accuracy of both methods can be compared to an analytical solution. Both methods are then applied to surface meshes of Asteroid 24153 Itokawa to assess their abilities to model irregular bodies. For a given level of surface resolution, the surface-concentration model is found to be 30$\times$ faster than the polyhedral model with only a marginal reduction in accuracy. Moreover, for meshes requiring equivalent CPU-times the surface-concentration model is found to be over an order of magnitude more accurate.
Abstract: Micronozzles represent a unique flow regime defined by low Reynolds numbers (Re<1000) and supersonic Mach numbers. Currently, the classic method of calculating thrust is used by the micropropulsion community to determine nozzle performance from simulation data. This approach accounts for momentum flux and pressure imbalance at the nozzle exit, and it assumes that the viscous stress tensor’s contribution to thrust is negligible. This assumption, however, can break down at low Reynolds numbers, where viscous forces play a significant role in the flow dynamics. In this paper, an extended method of calculating thrust, which accounts for the force due to the viscous stress tensor, is derived from the Navier–Stokes equation. Computational fluid dynamic simulations are then used to assess and quantify the error produced by the classic method at low Reynolds numbers (80
Abstract: A number of recent missions by national space agencies (NASA, JAXA, and ESA) to irregularly shaped asteroids has initiated an interest in accurately modeling the irregular gravitational potential field of these bodies. In this study, we examine using non-uniform mascon distributions derived from unstructured volume meshes to model the gravitational potential fields of irregular bodies. The type and topology of the unstructured mesh and its effect on the accuracy of the mascon model is examined. Meshes consisting of either tetrahedral cells or higher-order polyhedral cells with varying degrees of cell-size grading are considered. A unit sphere is used as a test case to compare numerical calculated mascon-based potentials with analytical results. Mascon models are then applied to asteroid 25143 Itokawa. The grid-dependence of the potential field and a spacecraft trajectory are examined as well as the effects of a variable density distribution. Results suggests that with the right mesh type and topology a greater than 90% reduction in the require number of mascons can be achieved in comparison to uniform distributions without sacrificing accuracy.
Abstract: A parametric, two-dimensional, computational study examining steady-state plug micronozzle performance has been conducted. As part of the study, a new method for plug contour construction is proposed. The performance of several different nozzle geometries is compared to that of a traditional plug nozzle geometry designed using the Method of Characteristics (MOC). New nozzle designs are derived from the MOC based design and geometric transformations are used to produce plug nozzles of reduced length. Spike lengths corresponding to 60, 50, 40, and 27% of the MOC nozzle’s length are examined. The throat Reynolds number is varied from 80–820. Thrust is used a metric to assess nozzle performance. The geometry which maximizes performance is found to vary with Reynolds number. It is observed that reducing the plug length improves thrust production for the range of Reynolds number examined.