Delta-V To Near-Earth Asteroids: An Examination Of The Shoemaker-Helin Equations
Creators: name: Murphy, Max
Publisher: name: Zenodo
Year: 2015
Subjects: Astronomy
Near-Earth objects
Space exploration

description: Near-Earth asteroids present promising opportunities for future human spaceflight missions. Many of these objects have orbits that come within close proximity to the Earth, allowing a significantly lower cost in comparison to missions to Mars or even the Moon. This cost is directly related to the change in velocity (Delta-V) necessary to move a vehicle from low-Earth orbit to the orbit of a near-Earth asteroid.

This paper will discuss the merits of asteroid rendezvous missions in the near future and assess the validity of Delta-V approximations for ~1200 known asteroids candidates. A 1979 paper by Shoemaker and Helin suggested a class-specific set of equations for approximating the Delta-V for these objects. Modern numerical calculations provide accurate measurements for these values and will serve as a test to the strength of the Shoemaker-Helin equations.
description: Astro 99
description: {"references": ["Bottke, W. F., Cellino, A., Paolicchi, P., &amp; Binzel, R. P. (2002). Asteroids III. Tuscon: University of Arizona Press.", "Bottke, W. F., Durda, D., Nesvorny\u0301, D., Jedicke, R., Morbidelli, A., Vokrouhlicky\u0301, D., et al. (2005). The fossilized size distribution of the main asteroid belt. Icarus , 175, 111-140.", "Bottke, W. F., Jedicke, R., Morbidelli, A., Petit, J. M., &amp; Gladman, B. (2000). Understanding the distribution of near-Earth asteroids. Science , 288, 2190\u20132194.", "Bottke, W. F., Jedicke, R., Morbidelli, A., Petit, J. M., Levison, H. F., Michael, P., et al. (2002). Debiased orbital and absolute magnitude distribution of the near-Earth objects. Icarus , 156, 399- 433.", "Bottke, W. F., Vokrouhlicky, D., Rubincam, D. P., &amp; Broz, M. (2002). The effect of Yarkovsky thermal forces on the dynamical evolution of asteroids and meteoroids. In Asteroids III (pp. 395- 408). Tuscon, AZ: University of Arizona Press.", "Bowell, E., Virtanen, J., Muinonen, K., &amp; Boattini, A. (2002). Asteroid Orbit Computation. In B. e. al., Asteroids III (pp. 27-43). Tuscon: University of Arizona Press.", "Brown, P., Spalding, R. E., Revelle, D. O., Tagliaferri, E., &amp; Worden, S. P. (2002). The flux of small near-Earth object colliding with the Earth. Nature , 420, 294-296.", "Carpino, M., Milani, A., &amp; Chesley, S. R. (2002). Error statistics of asteroid optical astrometric observations. Icarus .", "Chang, K., &amp; Schwartz, J. (2014, October 31). Virgin Galactic\u2019s SpaceShipTwo Crashes in New Setback for Commercial Spaceflight. Retrieved from The New York Times: http://www.nytimes.com/2014/11/01/science/virgin-galactics-spaceshiptwo-crashes-during-test- flight.html?_r=0", "Cheng, A. F. (1997). Near Earth Asteroid Rendezvous: Mission Overview. Space Science Reviews , 82, 3-29.", "Day, J. D., Walker, R. J., Qin, L., &amp; Rumble, D. (2012). Late accretion as a natural consequence of planetary growth. Nature Geoscience , 5, 614-617.", "DeMeo, F. E., &amp; Carry, B. (2014). Solar System evolution from compositional mapping of the asteroid belt. Nature , 505, 629-634.", "Emery, J. P., Rivkin, A. S., Campins, H., Howell, E. S., Licandro, J., Takir, D., et al. (2015). Astronomical Observations of Volatiles on Asteroids. In F. D. P. Michel (Ed.), Space Science Series Book: Asteroids IV. University of Arizona Press.", "Farinella, P., Foschini, L., Froeschle, C., Gonczi, R., Jopek, T. J., Longo, G., et al. (2001). Probable asteroidal origin of the Tunguska Cosmic Body. Astronomy &amp; Astrophysics , 377, 1081-1097.", "Forward, R. L. (1995). A TRANSPARENT DERIVATION OF THE RELATIVISTIC ROCKET EQUATION. The American Institute of Aeronautics and Astronautics, Joint Propulsion Conference and Exhibit, San Diego, CA.", "Gates, M., Stich, S., McDonald, M., Muirhead, B., Mazanek, D., Abell, P., et al. (2014). THE ASTEROID REDIRECT MISSION AND SUSTAINABLE HUMAN EXPLORATION. 65th International Astronautical Congress, Administrator of the National Aeronautics and Space Administration, and Jet Propulsion Laboratory \u2013 California Institute of Technology, Toronto, Canada.", "Hirata, C. (n.d.). Rockets and Space Transportation. Retrieved 2015, from web.archive.org: http://web.archive.org/web/20070701211813/http://www.pma.caltech.edu/~chirata/deltav.html", "Howell, E. (2015, February 11). Boeing CST-100: Next-Generation Spaceship. Retrieved from Space.com: http://www.space.com/19367-boeing-cst-100.html", "Khatri, M. K., Poudel, P. R., &amp; Gautam, A. K. (2010). Principles of Physics. Kathmandu , 170-171.", "Mainzer, A., Bauer, J., Cutri, R. M., Grav, T., Masiero, J., &amp; Beck, R. (2014). Initial Performance", "of the NEOWISE Reactivation Mission. The Astrophysical Journal , 792 (1).", "Morbidelli, A., Jedicke, R., Bottke, W. F., Michael, P., &amp; Tedesco, E. F. (2002). From magnitudes to diameters: the albedo distribution of near Earth objects and the Earth collision hazard. Icarus , 158, 329-342.", "Muinonen, K., &amp; Bowell, E. (1993). Asteroid orbit determination using Bayesian probabilities . Icarus , 104 (2), 255-279.", "Popova, O. P., Jenniskens, P., Emel\u2019yanenko, V., Kartashova, A., Biryukov, E., Khaibrakhmanov, S., et al. (2013). Chelyabinsk Airburst, Damage Assessment, Meteorite Recovery, and Characterization. Science , 342 (6162), 1069-1073.", "Ross, S. D. (2001). Near-Earth Asteroid Mining. CA: Department of Control and Dynamical Systems, Pasadena.", "Rubin, M., Altwegg, K., Balsiger, H., Bar-Nun, A., Bertheller, J. J., Bieler, A., et al. (2015, March). Molecular nitrogen in comet 67P/Churyumov-Gerasimenko indicates a low formation temperature. Science.", "Schmidt, O. J. (1944). A meteoric theory of the origin of Earth and planets. ibid. , 45, 229-33.", "Shoemaker, L. M., &amp; Helin, L. E. (1978). Earth-approaching asteroids as targets for exploration. California Institute of Technology, Division of Geological and Planetary Sciences , Pasadena, CA.", "SpaceX Capabilities and Services. (2014, September). Retrieved February 2015, from SpaceX: http://www.spacex.com/about/capabilities Vallado, D. A. (2001). Fundamentals of Astrodynamics and Applications, 2nd Edition. Springer.", "Vasile, M., &amp; De Pascale, P. (2006). On the Preliminary Design of Multiple Gravity-Assist Trajectories. J. Spacecraft Rockets , 43 (4), 5-22."]}