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A fast method of estimating the gravitational acceleration of asteroids with irregular shapes

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Abstract

In this paper, we propose a computational method for rapidly estimating the gravitational acceleration of irregular asteroids: the pseudocenter theory, triangular mesh, kriging interpolation (PTK) method. The method first uses a triangular mesh to discretize the asteroid's surface. Then, the fitting coefficients of all grid point directions are obtained using pseudocenter theory. Finally, kriging interpolation is used to quickly estimate the gravitational acceleration value at any location. Numerical simulation shows that the PTK method can ensure a high calculation speed, wide application range, and high accuracy with an extremely low storage cost. Overall, the PTK method is more balanced, faster, and more feasible than current methods for calculating gravitational acceleration for on-orbit use.

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References

  • Bartczak, P., Breiter, S.: Double material segment as the model of irregular bodies. Celest. Mech. Dyn. Astron. 86(2), 131–141 (2003)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Cheng, A.F., Santo, A.G., Heeres, K.J., Landshof, J.A., Farquhar, R.W., Gold, R.E., et al.: Near-earth asteroid rendezvous: Mission overview. Journal of Geophysical Research: Planets 102(E10), 23695–23708 (1997)

    Article  Google Scholar 

  • Chermnykh, S.V., Stability of libration points in a gravitational field. Leningradskii Universitet Vestnik Matematika Mekhanika Astronomiia, 73–77 (1987)

  • Colombi, A., Hirani, A.N., Villac, B.F.: Adaptive gravitational force representation for fast trajectory propagation near small bodies. J. Guid. Control. Dyn. 31(4), 1041–1051 (2008)

    Article  ADS  Google Scholar 

  • Duboshin, G.N.: On one particular case of the problem of the translational-rotational motion of two bodies. Sov. Astron. 3, 154 (1959)

    ADS  Google Scholar 

  • Fujiwara, A., Kawaguchi, J., Yeomans, D.K., Abe, M., Mukai, T., Okada, T., et al.: The rubble-pile asteroid Itokawa as observed by Hayabusa. Science 312(5778), 1330–1334 (2006)

    Article  ADS  Google Scholar 

  • Garmier, R., Barriot, J.P., Konopliv, A.S., Yeomans, D.K.: Modeling of the eros gravitational field as an ellipsoidal harmonic expansion from the NEAR doppler tracking data. Geophys. Res. Lett. 29(8), 72–81 (2002)

    Article  Google Scholar 

  • Gaskell, R. W. (2008). Gaskell eros shape model V1. 0. NASA Planet. Data Syst. NEAR-A

  • Geissler, P., Petit, J.M., Durda, D.D., Greenberg, R., Bottke, W., Nolan, M., et al.: Erosion and ejecta reaccretion on 243 Ida and its moon. Icarus 120(1), 140–157 (1996)

    Article  ADS  Google Scholar 

  • Hobson, E.W.: The Theory of Spherical and Ellipsoidal Harmonics. CUP Archive, Cambridge (1931)

    MATH  Google Scholar 

  • Hu, S.C., Ji, J.H.: Using Chebyshev polynomial interpolation to improve the computational efficiency of gravitational models near an irregularly-shaped asteroid. Res. Astron. Astrophys. 17(12), 120 (2017)

    Article  ADS  Google Scholar 

  • Hujsak, R.S.: Gravitational acceleration approximation functions. Spacefl. Mech. 1996, 335–349 (1996)

    Google Scholar 

  • Lauretta, D.S., Balram-Knutson, S.S., Beshore, E., Boynton, W.V., Drouet d’Aubigny, C., DellaGiustina, D.N., et al.: OSIRIS-REx: Sample return from asteroid (101955) Bennu. Space Sci. Rev. 212(1), 925–984 (2017)

    Article  ADS  Google Scholar 

  • Lauretta, D.S., DellaGiustina, D.N., Bennett, C.A., Golish, D.R., Becker, K.J., Balram-Knutson, S.S., et al.: The unexpected surface of asteroid (101955) Bennu. Nature 568(7750), 55–60 (2019)

    Article  ADS  Google Scholar 

  • Oliver, M.A., Webster, R.: Kriging: A method of interpolation for geographical information systems. Int. J. Geogr. Inf. Syst. 4(3), 313–332 (1990)

    Article  Google Scholar 

  • Rayman, M.D., Fraschetti, T.C., Raymond, C.A., Russell, C.T.: Dawn: A mission in development for exploration of main belt asteroids Vesta and Ceres. Acta Astronaut. 58(11), 605–616 (2006)

    Article  ADS  Google Scholar 

  • Romain, G., Jean-Pierre, B.: Ellipsoidal harmonic expansions of the gravitational potential: Theory and application. Celest. Mech. Dyn. Astron. 79(4), 235–275 (2001)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  • Scheeres, D.J., Marzari, F., Tomasella, L., Vanzani, V.: ROSETTA mission: Satellite orbits around a cometary nucleus. Planet. Space Sci. 46(6–7), 649–671 (1998)

    Article  ADS  Google Scholar 

  • Scheeres, D. J. (1999). Satellite dynamics about asteroids: Computing Poincaré maps for the general case. Hamiltonian Systems with Three or More Degrees of Freedom (pp. 554–557). Springer, Dordrecht

  • Scheeres, D., Broschart, S., Ostro, S., & Benner, L. The dynamical environment about asteroid 25143 Itokawa, target of the Hayabusa mission. In AIAA/AAS Astrodynamics Specialist Conference and Exhibit (p. 4864) (2004)

  • Scheeres, D., Gaskell, R., Abe, S., Barnouin-Jha, O., Hashimoto, T., Kawaguchi, J. I., et al. The actual dynamical environment about Itokawa. In AIAA/AAS Astrodynamics Specialist Conference and Exhibit (p. 6661) (2006)

  • Song, Y., Cheng, L., Gong, S.: Fast estimation of gravitational field of irregular asteroids based on deep neural network and its application. Adv. Astronaut. Sci. 168, 1721–1735 (2019)

    Google Scholar 

  • Stein, M.L.: Interpolation of Spatial Data: Some Theory for Kriging. Springer Science & Business Media, Heidelberg (1999)

    Book  MATH  Google Scholar 

  • Takahashi, Y., Scheeres, D.J., Werner, R.A.: Surface gravitational fields for asteroids and comets. J. Guid. Control. Dyn. 36(2), 362–374 (2013)

    Article  ADS  Google Scholar 

  • Tsuda, Y., Yoshikawa, M., Abe, M., Minamino, H., Nakazawa, S.: System design of the Hayabusa 2—Asteroid sample return mission to 1999 JU3. Acta Astronaut. 91, 356–362 (2013)

    Article  ADS  Google Scholar 

  • Werner, R.A.: The gravitational potential of a homogeneous polyhedron or don’t cut corners. Celest. Mech. Dyn. Astron. 59(3), 253–278 (1994)

    Article  ADS  MATH  Google Scholar 

  • Werner, R.A., Scheeres, D.J.: Exterior gravitation of a polyhedron derived and compared with harmonic and mascon gravitation representations of asteroid 4769 Castalia. Celest. Mech. Dyn. Astron. 65(3), 313–344 (1996)

    ADS  MATH  Google Scholar 

  • Yeomans, D.K., Antreasian, P.G., Barriot, J.P., Chesley, S.R., Dunham, D.W., Farquhar, R.W., et al.: Radio science results during the NEAR-Shoemaker spacecraft rendezvous with Eros. Science 289(5487), 2085–2088 (2000)

    Article  ADS  Google Scholar 

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Funding

This research is supported by the Beijing Municipal Science and Technology Commission (Z181100002918004), Space Science Pre-Research Project (XDA15014900), Civil Aerospace Pre-Research Project (Grant No. kjsp2020020101). The corresponding author is supported by the Youth Innovation Promotion Association CAS.

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Authors and Affiliations

  1. National Space Science Center, Chinese Academy of Sciences, No.1 Nanertiao, Zhongguancun, Haidian District, Beijing, People’s Republic of China

    Shidong Zhang & Mingtao Li

  2. University of Chinese Academy of Sciences, No.19 (A) Yuquan Road, Shijingshan District, Beijing, People’s Republic of China

    Shidong Zhang & Mingtao Li

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  1. Shidong Zhang
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  2. Mingtao Li
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Correspondence to Mingtao Li.

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Zhang, S., Li, M. A fast method of estimating the gravitational acceleration of asteroids with irregular shapes. Celest Mech Dyn Astron 135, 2 (2023). https://doi.org/10.1007/s10569-022-10117-0

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  • DOI: https://doi.org/10.1007/s10569-022-10117-0

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