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On Estimating Non-Uniform Density Distributions Using N Nearest Neighbors

Woźniak P. R., Kruszewski A.

Acta Astronomica

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2012

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Vol. 62, No. 4

409--417

EN

We consider density estimators based on the nearest neighbors method applied to discrete point distributions in spaces of arbitrary dimensionality. If the density is constant, the volume of a hypersphere centered at a random location is proportional to the expected number of points falling within the hypersphere radius. The distance to the N-th nearest neighbor alone is then a sufficient statistic for the density. In the non-uniform case the proportionality is distorted. We model this distortion by normalizing hypersphere volumes to the largest one and expressing the resulting distribution in terms of the Legendre polynomials. Using Monte Carlo simulations we show that this approach can be used to effectively address the trade-off between smoothing bias and estimator variance for sparsely sampled distributions.

2

Behavior of Jupiter Non-Trojan Co-Orbitals

Wajer P., Królikowska M.

Acta Astronomica

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2012

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Vol. 62, No. 1

113--131

EN

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.

3

On the Dynamical Evolution of Scattered Disk Objects Outside the Planetary System

Gabryszewski R., Rickman H.

Acta Astronomica

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2010

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Vol. 60, No. 4

373--385

EN

We report the results of dynamical simulations, covering Gyr timescales, of fictitious Scattered Disk Objects as a follow-up to an earlier study. Our dynamical model is similar in that it does not include external agents like passing stars or the Galactic tide. Only the four giant planets are explicitly treated as perturbers. We analyze the random-walk behavior of the inverse semi-major axis by means of a simplified circular restricted 3-body problem as an approximate analogue. Our results concerning the role of resonant effects and the transfer efficiency into the orbital energy domain of the inner Oort Cloud are in broad agreement with the earlier papers, and we confirm the important role of external objects (with perihelia beyond Neptune's orbit) in feeding the Oort Cloud. We estimate the efficiency of this transfer to be even somewhat higher than previously found.

4

Local Group Velocity Versus Gravity: Nonlinear Effects

Ciecieląg P., Chodorowski M., Kudlicki A.

Acta Astronomica

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2001

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Vol. 51, No. 2

103--115

EN

We use numerical simulations to study the relation between the velocity of the Local Group (LG) and its gravitational acceleration. This relation serves as a test for the kinematic origin of the CMB dipole and as a method for estimating β≡Ω0.6/b. We calculate the misalignment angle between the two vectors and compare it to the observed value for the PSCz survey. The latter value is beyond the upper limit of the 90% confidence interval for the angle; therefore, the nonlinear effects are unlikely to be responsible for the whole observed misalignment. We also study the relation between the amplitudes of the LG velocity and gravity vectors. In an Ω=1 Universe, the smoothed gravity of the LG turns out to be a biased low estimator of the LG (unsmoothed) velocity. In an Ω=0.3 Universe, the estimator is biased high. The discussed biases are, however, only a few per cent, thus the linear theory works to good accuracy. The gravity-based estimator of the LG velocity has also a scatter that limits the precision of the estimate of β in the LG velocity-gravity comparisons. The random error of β due to nonlinear effects amounts to several per cent.