Discipline: Technology and Engineering
Subcategory: Electrical Engineering
Christopher Blake - Kapiolani Community College
The landing accuracy in previous landing missions to Mars—which include the NASA Viking 1 & 2 (1976), Pathfinder (1997), Opportunity and Spirit (2004), Phoenix (2008), and Curiosity (2012)— increased from 174 x 62 miles to 12 x 4 miles. However, the technologies and architectures used by the Mars Science Laboratory for the landing mission on Mars in 2012 are almost identical to the methods used in the 1976 Viking mission. The engineering problem of a 12 x 4 miles landing site is that it is still large enough to complicate landings for future missions and to endanger the progress of prior missions. Precision landing is based on exact spacecraft trajectories, which depend on several key factors such as fuel consumption, flight time, and mass loss. This research focuses on solving for accurate initial and final conditions to create a viable, fuel efficient, and precise landing solution. To begin to solve the problem of precise planetary landing, the equations of motion for a spacecraft with thrust were converted from second order differential equations to first order differential equations. The equations were then coded into MATLAB software, which uses a high-performance language for technical computations. Using MATLAB, backwards and forwards integration were performed in multiple coordinate systems. The coordinate systems used were polar, 2D Cartesian, and 3D Cartesian, as well as the spherical coordinate system. Several different elements of the equations were varied individually, such as specific thrust impulse, mass flow rate, and the directions of the thrust unit vectors. The initial conditions were also varied to create an envelope of landing areas and entry points into the atmosphere. This was done to isolate how each element affects fuel consumption, flight time, mass, and the trajectory of the spacecraft. The results created an envelope of landing locations based on the initial conditions presented and the variation of specific thrust impulse, mass flow rate, and thrust direction. Entering through the calculated envelope allows for a more precise landing location; missing the envelope greatly increases the chance of missing the exact destination. Through backwards integration, scientists are able to choose landing sites of possible interest and calculate an envelope of where the spacecraft must enter the Martian atmosphere. Future research will incorporate a simultaneous change in each of these elements to design a viable trajectory and testing different types of thrust maneuvers for landing. References: Vallado, D. A., & McClain, W. D. (2001). Fundamentals of astrodynamics and applications. Dordrecht: Kluwer Academic Azimov, D. (2017). Analytical Solutions for Extremal Space Trajectories. Boston, MA: Butterworth-Heinemann.
Funder Acknowledgement(s): This research was funded in part by NASA Minority University Research and Education Program (MUREP).
Faculty Advisor: Aaron Hanai, email@example.com
Role: I was the sole author of this work.