A computer program utilizes the classical theory of gravitation, implemented by means of the finite-element method, to calculate the near gravitational fields of bodies of arbitrary size, shape, and mass distribution. The program was developed for application to a spacecraft and to floating proof masses and associated equipment carried by the spacecraft for detecting gravitational waves. The program can calculate steady or time-dependent gravitational forces, moments, and gradients thereof. Bodies external to a proof mass can be moving around the proof mass and/or deformed under thermoelastic loads. An arbitrarily shaped proof mass is represented by a collection of parallelepiped elements. The gravitational force and moment acting on each parallelepiped element of a proof mass, including those attributable to the self-gravitational field of the proof mass, are computed exactly from the closed-form equation for the gravitational potential of a parallelepiped. The gravitational field of an arbitrary distribution of mass external to a proof mass can be calculated either by summing the fields of suitably many point masses or by higher-order Gauss-Legendre integration over all elements surrounding the proof mass that are part of a finite-element mesh. This computer program is compatible with more general finite-element codes, such as NASTRAN, because it is configured to read a generic input data file, containing the detailed description of the finite-element mesh.

This program was written by Marco Quadrelli of Caltech for NASA's Jet Propulsion Laboratory. For further information, access the Technical Support Package (TSP) free on-line at www.techbriefs.com/tsp under the Software category.

This software is available for commercial licensing. Please contact Karina Edmonds of the California Institute of Technology at (818) 393-2827.Refer to NPO-40651.

Topics:
Computer software and hardware Gravity Logistics Software Spacecraft Tools and equipment Vehicles
This Brief includes a Technical Support Package (TSP).
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Computing Gravitational Fields of Finite-Sized Bodies

(reference NPO-40651) is currently available for download from the TSP library.

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NASA Tech Briefs Magazine

This article first appeared in the September, 2005 issue of NASA Tech Briefs Magazine (Vol. 29 No. 9).

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Overview

The document is a Technical Support Package from NASA's Jet Propulsion Laboratory (JPL) focused on "Computing Gravitational Fields of Finite-Sized Bodies." It outlines the development of a self-gravity tool designed to predict and control the motion of proof masses in the Laser Interferometer Space Antenna (LISA), a space-borne gravitational wave detector. LISA consists of three spacecraft forming an equilateral triangle, with each spacecraft housing two proof masses that reflect laser light to detect gravitational waves with high sensitivity.

The paper discusses the challenges of modeling gravitational interactions among extended bodies, emphasizing the need for accurate computation of gravitational forces and moments. The self-gravity tool aims to address these challenges by employing a finite element-based approach to compute gravitational interactions, which is crucial for the spacecraft's gravitational balancing and overall performance.

Key functionalities of the self-gravity analysis tool include the ability to handle multiple moving bodies of arbitrary geometry, manage gravitational interactions in close proximity, and dynamically adjust the system's topology by adding or removing bodies. The tool's performance is linked to the spacecraft's Attitude Control System (ACS) and Disturbance Rejection System, highlighting the importance of gravitational modeling in various operational scenarios, such as gravity trimming during telescope articulation and mass depletion.

The document also outlines future work plans, which involve validating existing models with benchmark cases and implementing the finite element method using simplicial meshing. This method is favored for its compatibility with NASTRAN meshes, and the team aims to validate their computational codes through experimental verification.

The research is conducted under the auspices of NASA, with acknowledgments to the collaborative efforts at JPL and references to foundational literature in spacecraft dynamics and gravitational theory. The document serves as a resource for understanding the complexities of gravitational field computation and its applications in advanced aerospace technology, particularly in the context of gravitational wave detection and spacecraft formation dynamics.

Overall, this Technical Support Package provides a comprehensive overview of the methodologies and future directions in the field of gravitational modeling, emphasizing its significance in enhancing the capabilities of space exploration technologies.