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Analysis of Earth-Uranus Direct-Transfer Trajectory for Optimal Delta-V Using Lambert’s Problem

The Ice Giants may become a sought-after destination in the coming decades as researchers aim to have a better awareness of our Solar system- its origins and growth. The interplanetary trajectory optimization is an important aspect of the analysis of a mission to Uranus. This study investigates possible interplanetary paths to Uranus in the 2022-2030 timeframe. It provides a preliminary estimate of fuel consumption in units of ΔV for various mission durations. A variety of approaches can be used to travel from Earth to another planet. It is conceivable to use a direct transfer route with two engine burns, one at a parking orbit around the Earth and the other to capture around the target planet. This article emphasizes a direct transfer trajectory analysis towards Uranus using Lambert’s problem. Different lambert arcs were considered for the direct transfer. Variations of excess velocities at arrival and departure for various time-of-flight were obtained. The ceiling of the time-of-flight was fixed as 16.5 years by performing a Hohmann transfer. The minimum ΔV was obtained for various time-of-flight ranging from 8.5 years to 16.5 years. The ideal ΔV obtained during the fixed timeframe lies between 6.87 km/s and 7.98 km/s. The minimum value of ΔV was observed for the time-of-flight of 13.5 years.

Direct Transfer Trajectory, Lambert’s Problem, Patched-Conic Method, Earth-Uranus Mission, Optimal Delta-V, Interplanetary Mission

APA Style

Gisa Geoson Suseela, Yadu Krishnan Sukumarapillai, Hariprasad Thimmegowda, Pavan Kalyan Devaiah, Manjunath Nagendra, et al. (2022). Analysis of Earth-Uranus Direct-Transfer Trajectory for Optimal Delta-V Using Lambert’s Problem. International Journal of Astrophysics and Space Science, 10(1), 9-17.

ACS Style

Gisa Geoson Suseela; Yadu Krishnan Sukumarapillai; Hariprasad Thimmegowda; Pavan Kalyan Devaiah; Manjunath Nagendra, et al. Analysis of Earth-Uranus Direct-Transfer Trajectory for Optimal Delta-V Using Lambert’s Problem. Int. J. Astrophys. Space Sci. 2022, 10(1), 9-17. doi: 10.11648/j.ijass.20221001.12

AMA Style

Gisa Geoson Suseela, Yadu Krishnan Sukumarapillai, Hariprasad Thimmegowda, Pavan Kalyan Devaiah, Manjunath Nagendra, et al. Analysis of Earth-Uranus Direct-Transfer Trajectory for Optimal Delta-V Using Lambert’s Problem. Int J Astrophys Space Sci. 2022;10(1):9-17. doi: 10.11648/j.ijass.20221001.12

Copyright © 2022 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

1. J. Mansell, N. Kolencherry, K. Hughes, A. Arora, H. S. Chye, K. Coleman, J. Elliott, S. Fulton, N. Hobar, B. Libben, Y. Lu, J. Millane, A. Mudek, L. Podesta, J. Pouplin, E. Shibata, G. Smith, B. Tackett, T. Ukai, P. Witsberger, S. Saikia, Oceanus: A multi-spacecraft flagship mission concept to explore Saturn and Uranus, Advances in Space Research, Volume 59, Issue 9, 2017.
2. Sayanagi, K. M., Dillman, R. A., Atkinson, D. H., Li, J., Saikia, S., Simon, A. A., & Tran, L. D. (2020). Small next-generation atmospheric probe (SNAP) concept to enable future multi-probe missions: a case study for Uranus. Space Science Reviews, 216 (4), 1-47.
3. S. Jarmak, E. Leonard, A. Akins, E. Dahl, D. R. Cremons, S. Cofield, A. Curtis, C. Dong, E. T. Dunham, B. Journaux, D. Murakami, W. Ng, M. Piquette, A. Pradeepkumar Girija, K. Rink, L. Schurmeier, N. Stein, N. Tallarida, M. Telus, L. Lowes, C. Budney, K. L. Mitchell, QUEST: A New Frontiers Uranus orbiter mission concept study, Acta Astronautica, Volume 170, 2020.
4. Vasile, M., Martin, J. M. R., Masi, L., Minisci, E., Epenoy, R., Martinot, V., & Baig, J. F. (2015). Incremental planning of multi-gravity assists trajectories. Acta Astronautica, 115, 407-421.
5. Biesbroek, R. (2016). Lunar and Interplanetary Trajectories. Springer International Publishing.
6. Yam, C. H., Troy McConaghy, T., Joseph Chen, K., & Longuski, J. M. (2004). Design of low-thrust gravity-assist trajectories to the outer planets. In 55th International Astronautical Congress of the International Astronautical Federation, the International Academy of Astronautics, and the International Institute of Space Law (pp. A-6).
7. Hughes, K. M. (2016). Gravity-assist trajectories to Venus, Mars, and the ice giants: Mission design with human and robotic applications (Doctoral dissertation, Purdue University).
8. Longuski, J. M., & Williams, S. N. (1991). Automated design of gravity-assist trajectories to Mars and the outer planets. Celestial Mechanics and Dynamical Astronomy, 52 (3), 207-220.
9. Zuo, M., Dai, G., Peng, L., Wang, M., Liu, Z., & Chen, C. (2020). A case learning-based differential evolution algorithm for global optimization of interplanetary trajectory design. Applied Soft Computing, 94, 106451.
10. Fritz, S., & Turkoglu, K. (2016, March). Optimal trajectory determination and mission design for asteroid/deep space exploration via multi-body gravity assist maneuvers. In 2016 IEEE Aerospace Conference (pp. 1-9). IEEE.
11. Hughes, S. P., Qureshi, R. H., Cooley, S. D., & Parker, J. J. (2014). Verification and validation of the general mission analysis tool (GMAT). In AIAA/AAS astrodynamics specialist conference (p. 4151).
12. Paulino, T. (2008). Analytical representations of low-thrust trajectories.
13. Sena, Francesco & D'Ambrosio, Andrea & Curti, Fabio. (2021). “Study on Interplanetary Trajectories towards Uranus and Neptune.’ Conference: 31st AAS/AIAA Space Flight Mechanics Meeting, Virtual.
14. Sims, J., Finlayson, P., Rinderle, E., Vavrina, M., & Kowalkowski, T. (2006, August). Implementation of a low-thrust trajectory optimization algorithm for preliminary design. In AIAA/AAS Astrodynamics specialist conference and exhibit (p. 6746).
15. Evans, S., Taber, W., Drain, T., Smith, J., Wu, H. C., Guevara, M., & Evans, J. (2018). MONTE: The next generation of mission design and navigation software. CEAS Space Journal, 10 (1), 79-86.
16. Iorfida, E. (2016). On the characteristics of optimal transfers. University of Surrey (United Kingdom).
17. Woo, B., Coverstone, V. L., & Cupples, M. (2006). Low-thrust trajectory optimization procedure for gravity-assist, outer-planet missions. Journal of Spacecraft and Rockets, 43 (1), 121-129.
18. Torla, J., & Peet, M. (2019). Optimization of low fuel and time-critical interplanetary transfers using space elevator apex anchor release: Mars, Jupiter and Saturn. In Proceedings of the International Astronautical Congress, IAC (Vol. 2019, pp. IAC-19_D4_3_4_x51420). International Astronautical Federation, IAF.
19. Tang, S., & Conway, B. A. (1995). Optimization of low-thrust interplanetary trajectories using collocation and nonlinear programming. Journal of Guidance, Control, and Dynamics, 18 (3), 599604.
20. Darani, S. A., & Abdelkhalik, O. (2018). Space trajectory optimization using hidden genes genetic algorithms. Journal of Spacecraft and Rockets, 55 (3), 764-774.
21. Parvathi, S. P., & Ramanan, R. V. (2016). Iterative pseudostate method for transfer trajectory design of interplanetary orbiter missions. Journal of Guidance, Control, and Dynamics, 39 (12), 2799-2809.
22. Hargraves, C. R., & Paris, S. W. (1987). Direct trajectory optimization using nonlinear programming and collocation. Journal of guidance, control, and dynamics, 10 (4), 338-342.
23. Dachwald, B. (2004). Optimization of interplanetary solar sailcraft trajectories using evolutionary neurocentral. Journal of Guidance, Control, and Dynamics, 27 (1), 66-72.
24. Dachwald, B. (2004). Low-thrust trajectory optimization and interplanetary mission analysis using evolutionary neurocontrol. Doktorarbeit, Institut für Raumfahrttechnik, Universität der Bundeswehr, München.
25. Molenaar, S. (2009). Optimization of interplanetary trajectories with deep space maneuvers-model development and application to a Uranus orbiter mission.
26. Morante, D., Sanjurjo Rivo, M., & Soler, M. (2021). A survey on low-thrust trajectory optimization approaches. Aerospace, 8 (3), 88.
27. Parvathi, S. P., & Ramanan, R. V. (2017). Direct transfer trajectory design options for interplanetary orbiter missions using an iterative patched conic method. Advances in Space Research, 59 (7), 1763-1774.
28. Standish, E. M., & Williams, J. G. (1992). Orbital ephemerides of the Sun, Moon, and planets. Explanatory supplement to the astronomical almanac, 279-323.
29. Howard D. Curtis, Orbital Mechanics for Engineering Students (Third Edition), Butterworth-Heinemann, 2014.
30. Iwabuchi, M., Satoh, S., & Yamada, K. (2021). Smooth and continuous interplanetary trajectory design of spacecraft using iterative patched-conic method. Acta Astronautica, 185, 58-69.