Abstract

The macroscopic shapes, rotational states, and scattering parameters of atmosphereless bodies can be deduced from photometric measurements of total brightnesses in different viewing/illumination geometries. The problem is solved with nonlinear optimization techniques; the use of positive definite quantities effectively removes the apparent ill-posedness of the problem. Since the parameters of scattering laws such as the Hapke model cannot be unambiguously determined from photometric data only, we propose a simple empirical scattering model for the purpose. Our methods can obtain convex hull-like shapes even for strongly nonconvex objects; a conception of the major concavities can also be formed.

© Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |

  1. R.S.Hudson and S.J.Ostro 1999,“Physical Model of Asteroid 1620 Geographos from Radar and Optical Data,”Icarus 140 369-378 (1999). http://www.eecs.wsu.du/hudson/Research/Asteroids/index.htm
    [CrossRef]
  2. M. Kaasalainen, L. Lamberg, K. Lumme, and E. Bowell, ``Interpretation of lightcurves of atmosphereless bodies. I. General theory and new inversion schemes,' Astron. Astrophys. 259, 318-332 (1992).
  3. M. Kaasalainen and J. Torppa, ``Optimization methods for asteroid lightcurve inversion. I. Shape determination,' submitted to Icarus.
  4. M. Kaasalainen, J. Torppa, and K. Muinonen, ``Optimization methods for asteroid lightcurve inversion. II. The complete inverse problem,' submitted to Icarus.
  5. S. Kaasalainen, K. Muinonen, and J. Piironen 2000. ``A comparative study of the opposition effect of icy solar system objects,' J. Quant. Spect. Rad. Transf., in press.
  6. P. Magnusson and 46 colleagues, ``Photometric Observations and Modeling of Asteroid 1620 Geographos,' Icarus 123, 227-244 (1996).
    [CrossRef]
  7. K. Muinonen, ``Light scattering by axially symmetric Gaussian radom articles,' in Light Scattering by Nonspherical Particles: Halifax Contributions (G. Videen, Q. Fu, P. Chylek, Ed.), Army Research laboratory, Maryland, 91-94 (2000).
  8. W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, Numerical Recipes in Fortran (Cambridge University Press, Cambridge, 1994).
  9. P.C. Thomas and 11 colleagues, ``Mathilde: Size, Shape and Geology,' Icarus 140, 17-27 (1999).
    [CrossRef]
  10. J. Veverka and 32 colleagues, ``NEAR at Eros: Imaging and Spectral Results,' Science 289, 2088-2097 (2000). http://near-mirror.boulder.swri.edu/
    [CrossRef] [PubMed]

Other (10)

R.S.Hudson and S.J.Ostro 1999,“Physical Model of Asteroid 1620 Geographos from Radar and Optical Data,”Icarus 140 369-378 (1999). http://www.eecs.wsu.du/hudson/Research/Asteroids/index.htm
[CrossRef]

M. Kaasalainen, L. Lamberg, K. Lumme, and E. Bowell, ``Interpretation of lightcurves of atmosphereless bodies. I. General theory and new inversion schemes,' Astron. Astrophys. 259, 318-332 (1992).

M. Kaasalainen and J. Torppa, ``Optimization methods for asteroid lightcurve inversion. I. Shape determination,' submitted to Icarus.

M. Kaasalainen, J. Torppa, and K. Muinonen, ``Optimization methods for asteroid lightcurve inversion. II. The complete inverse problem,' submitted to Icarus.

S. Kaasalainen, K. Muinonen, and J. Piironen 2000. ``A comparative study of the opposition effect of icy solar system objects,' J. Quant. Spect. Rad. Transf., in press.

P. Magnusson and 46 colleagues, ``Photometric Observations and Modeling of Asteroid 1620 Geographos,' Icarus 123, 227-244 (1996).
[CrossRef]

K. Muinonen, ``Light scattering by axially symmetric Gaussian radom articles,' in Light Scattering by Nonspherical Particles: Halifax Contributions (G. Videen, Q. Fu, P. Chylek, Ed.), Army Research laboratory, Maryland, 91-94 (2000).

W.H. Press, B.P. Flannery, S.A. Teukolsky, and W.T. Vetterling, Numerical Recipes in Fortran (Cambridge University Press, Cambridge, 1994).

P.C. Thomas and 11 colleagues, ``Mathilde: Size, Shape and Geology,' Icarus 140, 17-27 (1999).
[CrossRef]

J. Veverka and 32 colleagues, ``NEAR at Eros: Imaging and Spectral Results,' Science 289, 2088-2097 (2000). http://near-mirror.boulder.swri.edu/
[CrossRef] [PubMed]

Supplementary Material (2)

» Media 1: MOV (669 KB)     
» Media 2: MOV (677 KB)     

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (2)

Fig. 1.
Fig. 1.

The shape model and a lightcurve of asteroid 6489 Golevka at two observing geometries [two movies (690 kB, 690 kB)].

Fig. 2.
Fig. 2.

The phase function f(α) for asteroid 433 Eros.

Equations (10)

Equations on this page are rendered with MathJax. Learn more.

d L = S ( μ , μ 0 ) ϖ d σ ,
L = A g ,
χ 2 = L A g 2
G ( ϑ , ψ ) = exp ( lm a lm Y l m ( ϑ , ψ ) ) ,
L ( E , E 0 ) = A + S G ( ϑ , ψ ) d σ ,
g j = G ( ϑ j , ψ j ) Δ σ j ,
χ rel 2 = i L ( i ) L - ( i ) A ( i ) g < A ( i ) g > 2 ,
S ( μ , μ 0 , α ) = f ( α ) [ S LS ( μ , μ 0 ) + c S L ( μ , μ 0 ) ]
= f ( α ) μ μ 0 ( 1 μ + μ 0 + c ) ,
f ( α ) = A 0 exp ( α D ) + k α + 1 ,

Metrics