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The Potentially Hazardous Asteroid (410777) 2009 FD

Wlodarczyk I.

Acta Astronomica

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2015

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Vol. 65, No. 2

215--231

EN

The asteroid (410777) 2009 FD is placed at the top of the JPL NASA Sentry Risk Table. We show that the predicted probability of the potential impact of the asteroid (410777) 2009 FD in fact depends on (i): used methods of selection and weighing of observational data, (ii): adopted dynamical model with included non-gravitational effects in the motion of asteroid based on cometary approach, and considerably weaker depends on (iii): the used model of the Solar System with different number of massive asteroids as potential perturbers. We computed impact solutions of the asteroid (410777) 2009 FD based on its 296 optical observations from February 24, 2009 to April 02, 2014 and one radar observation from April 07, 2014. We used the freely available ORBFIT Software Package and studied the future evolution of the orbit of (410777) 2009 FD searching for close approaches with the Earth and for the possible impacts up to the year 2200. According to our study the impacts are possible in the years: 2185, 2186, 2190, 2191, 2192, 2194, 2196, and 2198, provided the non-gravitational parameter A2 in the range of (-46.0,+3.0)×10-15 a.u./d2, with the gap between (-25.0,-11.0)×10-15 a.u./d2.

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

A Combined Method to Compute the Proximities of Asteroids

Šegan S., Milisavljević S., Marčeta D.

Acta Astronomica

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2011

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Vol. 61, No. 3

275--283

EN

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.

4

Librations with Mass Transfer in the Sun-Jupiter System

Horedt G. P., Oproiu T.

Acta Astronomica

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2005

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Vol. 55, No. 3

321--329

EN

Trojan-type motion is analytically and numerically studied under mass transfer between the primaries with conservation of their total orbital angular momentum. We prove theoretically and numerically our new result that angular libration widths change as m1/4, (m - Jupiter mass) if they are throughout smaller than about 60°. Numerical examples show that for initial libration widths larger than about 60°, the Trojan is ultimately driven out of the libration domain, becoming an ordinary asteroid, if Jupiter's transferred mass increases by a factor less than about two. Certain processes occurring in our solar system and in extrasolar planetary systems lead to a decrease of the Trojan's libration amplitude, while other processes lead to an increase, respectively.

5

2060 Chiron - Chaotic Dynamical Evolution and its Implications

Gabryszewski R.

Acta Astronomica

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2002

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Vol. 52, No. 3

305--216

EN

2060 Chiron - one of the Centaurs orbiting chaotically among the giant planets - is treated as an asteroid and a comet (95P/Chiron) as well. Since the day of the discovery many papers have discussed its past and future fate. In this paper a possibility of Chiron's dynamical evolution to different cometary orbital types is studied. An ensemble of orbital elements was used to describe Chiron's dynamics in terms of probability. The ensemble was generated using a unique scheme of elements creation. Dispersion of elements obtained by this method is much smaller compared to ranges obtained by varying the original elements in the ellipsoid of their mean errors. The chaos in Chiron's dynamical evolution can be seen in 5 to 9 kyrs, although the dispersion of orbital elements is small. Halley type orbits are the rarest noticed orbital types but the number of these objects is three times greater than the number of apparent Halley type comets. The variations of probability of different cometary orbits as a function of time is also presented. The rate of HTC orbit production is only four times lower than the production rate of JFCs after the first 50 kyrs of integration. Remarks on the small body transportation mechanisms are also included.

6

Prediction of the Motion of Asteroids and Comets Over Long Intervals of Time

Włodarczyk I.

Acta Astronomica

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2001

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Vol. 51, No. 4

357--376

EN

Difference of the mean anomalies of two starting orbits of a minor planet or a comet which only differ by an error of calculating of one of the orbital elements grows rapidly with time. This means that it is almost impossible to predict behavior of minor planets or comets on the orbit outside the period of time called the time of stability in our work. The time of stability for some selected minor planets and comets are given. For some minor planets and comets the time of stability is surprisingly short, about several hundreds years only.

7

On the Small Asteroid 1994 GV

Sitarski G.

Acta Astronomica

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2000

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Vol. 50, No. 3

417--419

EN

Minor planet 1994 GV was observed during only three days but it passed near the Earth and ran over the 28-degree arc on the sky. The orbit of this minor planet crosses the Earth orbit in the descending node. It appeared that according to this nominal orbit determined from the three-day observation arc, a very close approach of the asteroid to the Earth to within 0.000114 a.u. could happen in April 2008. However, our investigations of 600 randomly selected orbits as well as a search of the impact orbit excluded a possibility of a collision of 1994 GV with the Earth.

8

Motion of the Dangerous Asteroid 1997 XF11

Sitarski G.

Acta Astronomica

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1999

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Vol. 49, No. 1

103--112

EN

Minor planet 1997 XF11, discovered in December 1997, is moving in the heliocentric orbit which almost intersects the Earth orbit. In October 2028 the asteroid will approach the Earth to within 0.006 a.u. We improved the asteroid's orbit on the base of 151 astrometric observations from 1990-1998. To investigate the long-term motion of the asteroid we randomly selected 500 sets of orbital elements and numerically integrated the equations of motion by the recurrent power series. We followed evolution of minimum distances between orbits of 1997 XF11 and the Earth for moments of consecutive passages of the asteroid through its descending node. We found that only in 2042 the minimum distance between orbits of both planets could be smaller than the Earth radius. However, the asteroid will pass through its descending node in July 2042 while a collision with the Earth could happen during the October encounter. After 2042 the minimum distance between orbits of both planets will be permanently growing up, and hence we estimate that during the next several thousand years collision with the Earth will be impossible. We also investigated the asteroid's motion before 1990. We found that past close approaches of 1997 XF11 to the Earth occurred in 1971 to within 0.032 a.u. and in 1957 to within 0.015 a.u. We calculated ephemerides of the asteroid for those past approaches aiming at finding some old observations of the minor planet. We have also studied accuracy of prediction of the future motion of 1997 XF11 based, however, on 142 observations of the asteroid from 1997/98 only. We found that in that case possibility of collision during 2030-2050, although possible, is completely unpredictable.

9

How to Find an Impact Orbit for the Earth-Asteroid Collision

Sitarski G.

Acta Astronomica

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1999

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Vol. 49, No. 3

421--431

EN

The Earth-crossing asteroids can approach the Earth at dangerously small distances. If the observation arc of a single apparition orbit is short the determined orbital elements and hence a prediction of the future encounter with the Earth are uncertain. We presented the method of finding an impact orbit by the least squares correction with the "forced" equality constraints. As a solution we obtain: (i) initial values of rectangular coordinates and velocity components (and hence the orbital elements) allowing the asteroid to collide with the Earth, and (ii) the minimum value of the \it rms residual resulting from the impact orbit. The latter value is very important since it may serve as a kind of measure of probability of the collision, and in any case it allows us to exclude a possibility of the expected catastrophe. We performed computations of the impact orbits for two asteroids: 1997 XF11 and 1999 AN10. We found two impact orbits for hypothetical collisions of 1997 XF11 with the Earth in 2028 and 2033, and four orbits for 1999 AN10 colliding with the Earth in 2027, 2034, 2036, and 2039. Based on the 101 observations of 1999 AN10 from 1999 Jan. 13 - May 16, we show that its collision with the Earth in 2027 is impossible, but in 2039 it would be more probable. We made also a numerical simulation of the fictitious asteroid which would certainly collide with the Earth. We show that in this case we can easily find the impact orbit, and the rms value evidently does not allow us to exclude a possibility of the collision.

10

Motion of the Minor Planet 4179 Toutatis: Can We Predict Its Collision with the Earth?

Sitarski G.

Acta Astronomica

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1998

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Vol. 48, No. 3

547--561

EN

Minor planet 4179 Toutatis is an Apollo type object with a very small orbit inclination (i=0°.47), hence it has a possibility to approach closely the Earth (an encounter to within 0.01 a.u. is expected in 2004) and might be a good candidate for a future collision with the Earth. We collected 640 astrometric observations of Toutatis from the period 1934-1997 to improve the orbit. We had to include a nongravitational term into equations of motion expressed by a secular change a of the semi-major axis a of the Toutatis orbit to obtain a fully satisfactory solution of the orbit determination. A value a=-0.16×10-10 is two orders smaller than that determined in the case of short-period comets with known nongravitational effects. To investigate the long-term motion of Toutatis we numerically integrated the equations of motion by recurrent power series taking into account perturbations caused by the eight planets from Mercury to Neptun, treating the Earth and Moon as separate bodies, and also by the four biggest asteroids. We randomly varied the orbital elements to examine the Toutatis' motion for a number of different orbits. We present a new method of the random orbit selection which allows us to find a set of different orbits but representing well all the observations used for the orbit correction. Our results confirm a conclusion found by other authors that Toutatis orbit is exceptionally chaotic. Therefore, we are not able to predict the motion of Toutatis further than for 300 years. However, our integrations spanning 1500 years showed that the evolution of position of the descending node of Toutatis' orbit might go also in such a direction that the orbits of Toutatis and of the Earth would intersect in the future. Hence a possibility of the Toutatis-Earth collision is not excluded but it is completely unpredictable. To investigate conditions of a hypothetical collision of a minor planet with the Earth we made the following numerical simulation. Based on the Toutatis' orbit we deduced such orbital elements for a fictitious minor planet "Fatum" that a shape of the orbit was very similar to that of Toutatis, but we knew in advance that "Fatum" would certainly collide with the Earth in September 2004 and we calculated values of the impact parameters. We created a set of 638 artificial observations of "Fatum" in 1988-1997 for the same dates and with the same random observational errors like those of Toutatis. Then we corrected the "Fatum's" orbit for different observational intervals to examine the exactness of the impact prediction in 2004. We found that in 1993 we would be sure that the collision is inevitable, and in 1997 we could determine an impact area on the Earth's surface in range of a square of 100×100 km. We show that if we knew the impact date so early we could undertake an action to avoid the collision by trying to change the "Fatum's" heliocentric velocity only by one cm/sec.