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Fast Geometric Method for Calculating Accurate Minimum Orbit Intersection Distances

Wiśniowski T., Rickman H.

Acta Astronomica

2013

Vol. 63, No. 2

293--307

We present a new method to compute Minimum Orbit Intersection Distances (MOIDs) for arbitrary pairs of heliocentric orbits and compare it with Giovanni Gronchi's algebraic method. Our procedure is numerical and iterative, and the MOID configuration is found by geometric scanning and tuning. A basic element is the meridional plane, used for initial scanning, which contains one of the objects and is perpendicular to the orbital plane of the other. Our method also relies on an efficient tuning technique in order to zoom in on the MOID configuration, starting from the first approximation found by scanning. We work with high accuracy and take special care to avoid the risk of missing the MOID, which is inherent to our type of approach. We demonstrate that our method is both fast, reliable and flexible. It is freely available and its source Fortran code downloadable via our web page.

Behavior of Jupiter Non-Trojan Co-Orbitals

Wajer P., Królikowska M.

Acta Astronomica

2012

Vol. 62, No. 1

113--131

Searching for the non-Trojan Jupiter co-orbitals we have numerically integrated orbits of 3160 asteroids and 24 comets discovered by October 2010 and situated within and close to the planet co-orbital region. Using this sample we have been able to select eight asteroids and three comets and analyze their orbital behavior in a great detail. Among them we have identified five new Jupiter co-orbitals: (241944) 2002 CU147, 2006 S.A.387, 2006 QL39, 2007 GH6, and 200P/Larsen, as well as we have analyzed six previously identified co-orbitals: (118624) 2000 HR24, 2006 UG185, 2001 QQ199, 2004 AE9, P/2003 WC7 LINEAR-CATALINA and P/2002 AR2 LINEAR. (241944) 2002 CU147 is currently on a quasi-satellite orbit with repeatable transitions into the tadpole state. Similar behavior shows 2007 GH6 which additionally librates in a compound tadpole-quasi-satellite orbit. 2006 QL39 and 2000P/Larsen are the co-orbitals of Jupiter which are temporarily moving in a horseshoe orbit occasionally interrupted by a quasi-satellite behavior. 2006 S.A.387 is moving in a pure horseshoe orbit. Orbits of the latter three objects are unstable and according to our calculations, these objects will leave the horseshoe state in a few hundred years. Two asteroids, 2001 QQ199 and 2004 AE9, are long-lived quasi-satellites of Jupiter. They will remain in this state for a few thousand years at least. The comets P/2002 AR2 LINEAR and P/2003 WC7 LINEAR-CATALINA are also quasi-satellites of Jupiter. However, the non-gravitational effects may be significant in the motion of these comets. We have shown that P/2003 WC7 is moving in a quasi-satellite orbit and will stay in this regime to at least 2500 year. Asteroid (118624) 2000 HR24 will be temporarily captured in a quasi-satellite orbit near 2050 and we have identified another one object which shows similar behavior - the asteroid 2006 UG185, although, its guiding center encloses the origin, it is not a quasi-satellite. The orbits of these two objects can be accurately calculated for a few hundred years forward and backward.

A Combined Method to Compute the Proximities of Asteroids

Šegan S., Milisavljević S., Marčeta D.

Acta Astronomica

2011

Vol. 61, No. 3

275--283

We describe a simple and efficient numerical-analytical method to find all of the proximities and critical points of the distance function in the case of two elliptical orbits with a common focus. Our method is based on the solutions of Simovljević's (1974) graphical method and on the transcendent equations developed by Lazović (1993). The method is tested on 2 997 576 pairs of asteroid orbits and compared with the algebraic and polynomial solutions of Gronchi (2005). The model with four proximities was obtained by Gronchi (2002) only by applying the method of random samples, i.e., after many simulations and trials with various values of elliptical elements. We found real pairs with four proximities.