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Design of Mars Missions

  • Conference paper
Advanced Design Problems in Aerospace Engineering

Part of the book series: Mathematical Concepts in Science and Engineering ((MCSENG,volume 48))

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Abstract

This paper deals with the optimal design of round-trip Mars missions, starting from LEO (low Earth orbit), arriving to LMO (low Mars orbit), and then returning to LEO after a waiting time in LMO.

The assumed physical model is the restricted four-body model, including Sun, Earth, Mars, and spacecraft. The optimization problem is formulated as a mathematical programming problem: the total characteristic velocity (the sum of the velocity impulses at LEO and LMO) is minimized, subject to the system equations and boundary conditions of the restricted four-body model. The mathematical programming problem is solved via the sequential gradient-restoration algorithm employed in conjunction with a variable-stepsize integration technique to overcome the numerical difficulties due to large changes in the gravity field near Earth and near Mars.

The results lead to a baseline optimal trajectory computed under the assumption that the Earth and Mars orbits around Sun are circular and coplanar. The baseline optimal trajectory resembles a Hohmann transfer trajectory, but is not a Hohmann transfer trajectory, owing to the disturbing influence exerted by Earth/Mars on the terminal branches of the trajectory. For the baseline optimal trajectory, the total characteristic velocity of a round-trip Mars mission is 11.30 km/s (5.65 km/s each way) and the total mission time is 970 days (258 days each way plus 454 days waiting in LMO).

An important property of the baseline optimal trajectory is the asymptotic parallelism property: For optimal transfer, the spacecraft inertial velocity must be parallel to the inertial velocity of the closest planet (Earth or Mars) at the entrance to and exit from deep interplanetary space. For both the outgoing and return trips, asymptotic parallelism occurs at the end of the first day and at the beginning of the last day. Another property of the baseline optimal trajectory is the near-mirror property. The return trajectory can be obtained from the outgoing trajectory via a sequential procedure of rotation, reflection, and inversion.

Departure window trajectories are next-to-best trajectories. They are suboptimal trajectories obtained by changing the departure date, hence changing the Mars/Earth inertial phase angle difference at departure. For the departure window trajectories, the asymptotic parallelism property no longer holds in the departure branch, but still holds in the arrival branch. On the other hand, the near-mirror property no longer holds.

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References

  1. Lindorfer, W., and Moyer, H. G., Application of a Low Thrust Trajectory Optimization Scheme to Planar Earth-Mars Transfer, ARS Journal, Vol. 32, pp. 260–262, 1962.

    Google Scholar 

  2. Lecompte, M., New Approaches to Space Exploration, The Case for Mars, Edited by P. J. Boston, Univelt, San Diego, California, pp. 35–37, 1984.

    Google Scholar 

  3. Niehoff, J. C., Pathways to Mars: New Trajectory Opportunities, NASA Mars Conference, Edited by D. B. Reiber, Univelt, San Diego, California, pp. 381–401, 1988.

    Google Scholar 

  4. Roy, A. E., Orbital Motion, Adam Hilger, Bristol, England, 1988.

    MATH  Google Scholar 

  5. Striepe, S. A., Braun, R. D., Powell, R. W., and Fowler, W. T., Influence of Interplanetary Trajectory Selection on Mars Atmospheric Entry Velocity, Journal of Spacecraft and Rockets, Vol. 30, No. 4, pp. 426–430, 1993.

    Google Scholar 

  6. Tauber, M., Henline, W., Chargin, M., Papadopoulos, P., Chen, Y., Yang, L., and Hamm, K., Mars Environmental Survey Probe, Aerobrake Preliminary Design Study, Journal of Spacecraft and Rockets, Vol. 30, No.4, pp. 431–437, 1993.

    Google Scholar 

  7. Braun, R. D., Powell, R. W., Engelund, W. C., Gnoffo, P. A., Weilmuenster, K. J., and Mitcheltree, R. A., Mars Pathfinder Six-Degree-of-Freedom Entry Analysis, Journal of Spacecraft and Rockets, Vol. 32, No.6, pp. 993–1000, 1995.

    Article  Google Scholar 

  8. Gurzadyan, G. A., Theory of Interplanetary Flights, Gordon and Breach Publishers, Amsterdam, Netherlands, 1996.

    Google Scholar 

  9. Lee, W., and Sidney, W., Mission Plan for Mars Global Surveyor, Spaceflight Mechanics 1996, Edited by G. E. Powell, R. H. Bishop, J. B. Lundberg, and R. H. Smith, Univelt, San Diego, California, pp. 839–858, 1996.

    Google Scholar 

  10. Spencer, D. A., and Braun, R. D., Mars Pathfinder Atmospheric Entry: Trajectory Design and Dispersion Analysis, Journal of Spacecraft and Rockets, Vol. 33, No. 5, pp. 670–676, 1996.

    Google Scholar 

  11. Striepe, S. A., and Desai, P. N., Piloted Mars Missions Using Cryogenic and Storable Propellants, Journal of the Astronautical Sciences, Vol. 44, No. 2, pp.207–222, 1996.

    Google Scholar 

  12. Wagner, L. A., Jr., and Munk, M. M., MISR Interplanetary Trajectory Design, Spaceflight Mechanics 1996, Edited by G. E. Powell, R. H. Bishop, J. B. Lundberg, and R. H. Smith, Univelt, San Diego, California, pp. 859–876, 1996.

    Google Scholar 

  13. Wercinski, P. F., Mars Sample Return: A Direct and Minimum-Risk Design, Journal of Spacecraft and Rockets, Vol. 33, No.3, pp. 381–385, 1996.

    Google Scholar 

  14. Lohar, F. A., Misra, A. K., and Mateescu, J. D., Mars-Jupiter Aerogravity Assist Trajectories for High-Energy Missions, Journal of Spacecraft and Rockets, Vol. 34, No. 1, pp. 16–21, 1997.

    Google Scholar 

  15. Miele, A., and Wang, T., Optimal Trajectories for Earth-Mars Flight, Journal of Optimization Theory and Applications, Vol. 95, No. 3, pp. 467–499, 1997.

    Article  MathSciNet  MATH  Google Scholar 

  16. Miele, A., and Wang, T., Optimal Transfers from an Earth Orbit to a Mars Orbit, Acta Astronautica, Vol. 45, No. 3, pp.119–133, 1999.

    Article  MathSciNet  Google Scholar 

  17. Miele, A., and Wang, T., Optimal Trajectories and Asymptotic Parallelism Property for Round-Trip Mars Missions, Proceedings of the 2nd International Conference on Nonlinear Problems in Aviation and Aerospace, Edited by S. Sivasundaram, European Conference Publications, Cambridge, England, Vol. 2, pp. 507–539, 1999.

    Google Scholar 

  18. Miele, A., and Wang, T., Optimal Trajectories and Mirror Properties for Round-Trip Mars Missions, Acta Astronautica, Vol. 45, No. 11, pp. 655–668, 1999.

    Article  Google Scholar 

  19. Miele, A., Huang, H.Y., and Heideman, J. C., Sequential Gradient-Restoration Algorithm for the Minimization of Constrained Functions: Ordinary and Conjugate Gradient Versions, Journal of Optimization Theory and Applications, Vol. 4, No. 4, pp. 213–243, 1969.

    Article  MathSciNet  MATH  Google Scholar 

  20. Miele, A., Tietze, J. L., and Levy, A. V., Comparison of Several Gradient Algorithms for Mathematical Programming Problems, Omaggio a Carlo Ferrari, Edited by G. Jarre, Libreria Editrice Universitaria Levrotto e Bella, Torino, Italy, pp. 521–536, 1974.

    Google Scholar 

  21. Miele, A., Pritchard, R. E., and Damoulakis, J. N., Sequential Gradient-Restoration Algorithm for Optimal Control Problems, Journal of Optimization Theory and Applications, Vol. 5, No.4, pp. 235–282, 1970.

    Article  MathSciNet  MATH  Google Scholar 

  22. Miele, A., Tietze, J. L, and Levy, A. V., Summary and Comparison of Gradient-Restoration Algorithms for Optimal Control Problems, Journal of Optimization Theory and Applications, Vol. 10, No. 6, pp. 381–403, 1972.

    Article  MathSciNet  MATH  Google Scholar 

  23. Miele, A., and Damoulakis, J. N., Modifications and Extensions of the Sequential Gradient-Restoration Algorithm for Optimal Control Theory, Journal of the Franklin Institute, Vol. 294, No. 1, pp. 23–42, 1972.

    Article  MathSciNet  MATH  Google Scholar 

  24. Miele, A., and Wang, T, Primal-Dual Properties of Sequential Gradient-Restoration Algorithms for Optimal Control Problems, Part 1: Basic Problem, Integral Methods in Science and Engineering, Edited by F. R. Payne et al, Hemisphere Publishing Corporation, Washington, DC, pp. 577–607, 1986.

    Google Scholar 

  25. Miele, A., and Wang, T., Primal-Dual Properties of Sequential Gradient-Restoration Algorithms for Optimal Control Problems, Part 2: General Problem, Journal of Mathematical Analysis and Applications, Vol. 119, Nos. 1–2, pp. 21–54, 1986.

    MathSciNet  MATH  Google Scholar 

  26. Miele, A., Wang, T., and Basapur, V. K., Primal and Dual Formulations of Sequential Gradient-Restoration Algorithms for Trajectory Optimization Problems, Acta Astronautica, Vol. 13, No. 8, pp. 491–505, 1986.

    Article  MATH  Google Scholar 

  27. Rishikof, B. H., McCormick, B. R, Pritchard, R. E., and Sponaugle, S. J., SEGRAM: A Practical and Versatile Tool for Spacecraft Trajectory Optimization, Acta Astronautica, Vol. 26, Nos. 8–10, pp. 599–609, 1992.

    Google Scholar 

  28. Miele, A., Theorem of Image Trajectories in the Earth-Moon Space, Astronautica Acta, Vol.4, No. 5, pp. 225–232, 1960.

    Google Scholar 

  29. Miele, A., and Wang, T., Nominal Trajectories for the Aeroassisted Flight Experiment, Journal of the Astronautical Sciences, Vol. 41, No.2, pp. 139–163, 1993.

    Google Scholar 

  30. Miele, A., Recent Advances in the Optimization and Guidance of Aeroassisted Orbital Transfers, The 1st John V. Breakwell Memorial Lecture, Acta Astronautica, Vol. 38, No. 10, pp. 747–768, 1996.

    Article  Google Scholar 

  31. Miele, A., and Wang, T., Robust Predictor-Corrector Guidance for Aeroassisted Orbital Transfer, Journal of Guidance, Control, and Dynamics, Vol. 19, No. 5, pp. 1134–1141, 1996.

    Article  MATH  Google Scholar 

  32. Miele, A., and Wang, T., Near-Optimal Highly Robust Guidance for Aeroassisted Orbital Transfer, Journal of Guidance, Control, and Dynamics, Vol. 19, No.3, pp. 549–556, 1996.

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Aerospace Sciences, and Mathematical Sciences, Aero-Astronautics Group, Rice University, Houston, Texas, 77005-1892, USA

    A. Miele (Research Professor and Foyt Professor Emeritus of Engineering) & T. Wang (Senior Research Scientist)

Authors
  1. A. Miele
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  2. T. Wang
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Editor information

Editors and Affiliations

  1. Rice University, Houston, Texas

    Angelo Miele

  2. University of Pisa, Pisa, Italy

    Aldo Frediani

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© 2004 Kluwer Academic Publishers

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Miele, A., Wang, T. (2004). Design of Mars Missions. In: Miele, A., Frediani, A. (eds) Advanced Design Problems in Aerospace Engineering. Mathematical Concepts in Science and Engineering, vol 48. Springer, Boston, MA. https://doi.org/10.1007/0-306-48637-7_3

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  • DOI: https://doi.org/10.1007/0-306-48637-7_3

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-306-48463-6

  • Online ISBN: 978-0-306-48637-1

  • eBook Packages: Springer Book Archive

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