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The study of gravitational potential of a binary asteroid

The study of gravitational potential of a binary asteroid. Zheleznov Nikolay ( Institute of Applied Astronomy of RAS, Saint-Petersburg, Russia) znb@ipa.nw.ru. Binary asteroids. Ida&Dactyl ( http://www.johnstonsarchive.net/astro/asteroidmoons.html ).

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The study of gravitational potential of a binary asteroid

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  1. The study of gravitational potential of a binary asteroid Zheleznov Nikolay (Institute of Applied Astronomy of RAS, Saint-Petersburg, Russia) znb@ipa.nw.ru

  2. Binary asteroids Ida&Dactyl (http://www.johnstonsarchive.net/astro/asteroidmoons.html) Artist's representation of binary asteroid (617) Patroclus Credit: Lynette Cook and W. M. Keck Observatory (http://www.keckobservatory.org)

  3. The coordinate systems

  4. The prograde motion equations The rotational motion equationsThe Poisson's ratios

  5. The rotational motion equations Euler’s kinematical equations

  6. The projections of the forces moments

  7. The development of spherical functions series

  8. 4th harmonics

  9. 4th harmonics for forces moment Total 18 members

  10. The scheme of dividing of triaxial ellipsoid by central sphere and cubes

  11. The coordinates of point masses

  12. The force function

  13. The projections of the forces moment

  14. The integrals of energy and of squares

  15. The data of binary asteroid 1996 FG3 Primary: 0.772 х 0.738 х 0.710 km Density of the bodies: ρ=1.024 g/sm3 Satellite orbit: M= 260=183= 78i= 117 e=0.07 a=2.187 km Époque: JD = 2451164.678 Satellite: 0.260 х 0.224 х 0.224 km

  16. The number of elementary masses in the ellipsoids in depending on n

  17. The system energy integral v the dividing order of central sphere of the Primary

  18. Comparison of results(integrating by Everhard method on ~2.5 Satellite revolutions) n for Primary = 15 n for Satellite = 14 time for U4-integrating ~ few seconds time for p.m.-integrating ~ 1 day!

  19. Comparison of results(integrating by Everhard method on ~10 Satellite revolutions) n for Primary = 15 n for Satellite = 14 time for U4-integrating ~ few seconds time for p.m.-integrating ~ 4 day!

  20. The satellite orbits calculated by U4- and p.m.-integrating

  21. Conclusions • The representation of force function as the sum of attractions of point masses is more perspective method; • This method demands very lot of time for integrating; • In order to reduce calculation time it is necessary to modify method by following possible ways: 1) by more compact dispositions of cubes; 2) to refuse from only even number of cubes; • It is possible to develop a similar method for real bodies in future

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