Astron. Astrophys. 333, 753-761 (1998)

Inversion of shape statistics for small solar system bodies

K. Muinonen ^{1, 2} and J.S.V. Lagerros <sup>1

1</sup> Astronomical Observatory, Box 515, S-75120 Uppsala, Sweden (WWW: Http://www.astro.uu.se/)
² Observatory, P.O. Box 14, FIN-00014 University of Helsinki, Finland (WWW: http://www.astro.helsinki.fi/)

Received 10 December 1997 / Accepted 30 January 1998

Abstract

The irregular shapes of small solar system bodies are modelled by lognormal statistics, i.e., assuming that the shapes are realisations of the so-called Gaussian random sphere. The Gaussian sphere is fully described by the mean radius and the covariance function of the logarithmic radius. The stochastic shape is thus given by the covariance function, or the discrete spectrum of its Legendre coefficients. A maximum likelihood estimator is here provided for inverting the covariance function from three-dimensional sample shapes. The inverse method is applied to sophisticated shape data on altogether 14 small solar system bodies: the asteroids 4 Vesta , 243 Ida , 951 Gaspra , 1620 Geographos , 4179 Toutatis , and 4769 Castalia ; the Martian satellites Phobos and Deimos ; the Jovian satellite Amalthea ; the Saturnian satellites Hyperion , Epimetheus , Janus , and Prometheus ; and the Neptunian satellite Proteus . Inversion yields for the relative standard deviation of radius, shows that most of the spectral power lies in the second-degree spherical harmonics, and gives for the correlation angle. Even though the first results are promising, caution is recommended because the number of sample shapes is still small. Omitting one sample shape at a time and repeating the inversion shows that the results are not too sensitive to any one sample shape.

As an example application, thermal light curves are simulated for 1 000 Gaussian sample spheres in order to study the uncertainties in diameters and masses derived for asteroids. As compared to the Standard Thermal Model that assumes spherical asteroids, the irregular shape is shown to cause a 5 % systematic effect with 10 % scatter in diameter estimation whereas, in mass estimation, the respective numbers are larger at 17 % and 33 %.

Key words: minor planets, asteroids methods: analytical methods: statistical

Send offprint requests to: K. Muinonen

Contents

• 1. Introduction
• 2. Gaussian random sphere
  • 2.1. Statistical model
  • 2.2. Maximum likelihood estimator
• 3. Individual shape characteristics
  • 3.1. Translational invariants
  • 3.2. Intrinsic statistics
• 4. Results and discussion
  • 4.1. Irregular shapes of the solar system
  • 4.2. Maximum likelihood estimates
  • 4.3. Example application
• 5. Conclusion
• References

© European Southern Observatory (ESO) 1998

Online publication: April 20, 1998
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