1 EVOLUTION OF THE APHOPHIS ORBIT AND POSSIBLE USE OF THE ASTEROID The International Conference «Asteroid–Comet Hazard – 2009», September 21 – 25, 2009, St. Petersburg. Joseph J. Smulsky1 and Yaroslav J. Smulsky2 1 Institute of Earth’s Cryosphere Siberian Branch of RAS (Tyumen), E-mail: [email protected], webpage: http://www.smul1.newmail.ru/. 2 Institute of Thermophysics of SB PAS (Novosibirsk). Correction data 26.09.2009
2 The report contents 1. Introduction and dynamics of the Aphophis approaches 2. Evolution of the Aphophis orbit parameters 3. Possible uses of Aphophis-satellite 4. Trajectory of the Aphophis at approach to the Earth 5. Transformation of the Aphophis in the satellite 6. Transformation of the Aphophis in the satellite with a necessary direction of orbiting 7. Conclusions 8. Gratitude 9. References 10. Some information
3 1. Introduction and dynamics of the Aphophis approaches In a number of works, for example [1-9], is shown, that asteroid Aphophis on April 13, 2029 will pass on distance of 38000 km from the centre of the Earth and because of essential change of the orbit the further prediction of its movement becomes impossible. However there is some probability of encounter it with the Earth in 2036. We have analyzed the publications and have established, that the uncertainty in the Aphophis trajectory are caused by the imperfection of methods of its computing. By a new numerical method  we have integrated the differential equations of movement of Aphophis, planets, the Moon and the Sun and have investigated evolution of its orbit. At April 13, 2029 the Aphophis will pass on distance RminA = 38907 km from the Earth centre and during 1000 years it will not passes so close.
4 Fig. 1. The Aphophis approaches in during time ?T on minimal distance Rmin in km with Solar system bodies: Mars (Ma), Earth (Ea), Moon (Mo), Venus (Ve) and Mercury (Me); a - ?T = 1 year; b - ?T = 10 years. T, cyr is time in Julian centuries from epoch of November 30.0, 2008 TA = 13 Ap 2029 yr RminA = 38907 km TE =10 Oc 2586 yr RminE = 74003 km Approaches of Apophis to the Earth TB= 13 Ap 2067 yr RminB = 622231 km
5 2. Evolution of the Aphophis orbit The change of parameters of an orbit Aphophis was investigated on an interval -100 years ? +100 years from epoch of November 30.0, 2008. As it is visible from fig. 2, the eccentricity е of the Aphophis orbit changes non-uniformly. There are jumps or breaks of eccentricity. One of significant breaks is observed at the time TA of April 13, 2029, when Aphophis approaches with the Earth on smallest distance RminA. The second essential jump of eccentricity occurs at approach to the Earth at the time TB of April 13, 2067 on distance of 622231 km. The longitude of ascending node ? is less subject to breaks. Other elements of an orbit ie, ?e, P and a have significant breaks at the time (TA) of the closest passage of Aphophis at the Earth.
6 Fig. 2. Evolution of the Aphophis orbit elements under influence of planets, Moon and Sun: 1 – by integrating of the movement equations; 2 is results observation at T=0. Angular parameters: ?, ie, ?e are given in degrees, major semiaxis a is in AU, and period P – in days. T, cyr is time in sidereal centuries; A and B are the moments of time. Eccentricity Inclination Major semiaxis Longitude of ascending node Argument of perihelion Period
7 On the graphics of the fig. 2 the dash line gives the orbit elements on the data JPL (USA). They coincide with orbit elements at time T = 0, which received at integrating of the equations. It testifies the reliability of the executed calculations. The moment of approach of Aphophis with the Earth of April 13, 2029 at 21 hours 45'47'‘ of times on Greenwich and distance RminA, computed by us, coincides with results received in other works. For example, in work  it is resulted to within one minute: 21 hours 45' UTC and geocentric distance of approach is given in a range from 5.62 up to 6.3 radiuses of the Earth, i.e. the distance, received by us, in 6.1 radiuses of the Earth is in this range. The coincidence of computing results, which is executed by various methods, testifies to reliability of this event. At breaks of elements of an orbit, which is submitted in a fig. 2, the usually used methods of computing do not allow to define asteroid movement after approach it with the Earth. Our method is deprived of these lacks, and, as it was already noted, we have calculated movement asteroid during 1000 years. Such Aphophis’s approaches to the Earth any more will not be.
8 3. Possible uses of Aphophis-satellite Many pioneers of astronautics, for example, K.E. Ciolkovsky, Yu.V. Kondratyuk etc., the development of near-Earth cosmonautics are dreamed with the help of the large manned satellites. However, the delivery of such large masses from the Earth represents the serious technical and ecological problem. Therefore due to a happy case the arising opportunity to transform asteroid Aphophis in the satellite of the Earth and then in manned station represents significant interest. It can be used for many targets, namely: as permanent orbital station, as the basis for the space lift, as "shuttle" for delivery of cargoes to the Moon and on the contrary. In last case the satellite should have the elongate orbit with perihelion radius closing to radius of the geostationary orbit and with apogee radius, which is coming nearer to perihelion radius of lunar orbit. In this case the cargoes from the geostationary orbit in perihelion would be shifted on the Aphophis-satellite, and then in apogee these cargoes could be delivered to the Moon. These two applications are possible, if the satellite movement coincides on the direction with the Earth rotation and with the Moon orbital moving.
9 4. Trajectory of the Aphophis at approach to the Earth We shall consider the features of the Aphophis trajectory at approach to the Earth. Fig. 3. Trajectories of the Aphophis (Ap, blue) and of the Earth (E, red) in barycentric equatorial system of coordinates yx during 2 years: Ap0 and E0 are initial points of the Aphophis and of the Earth; Apf is the final point of the Aphophis trajectory; Ape is the point of approach (encounter) of the Aphophis with the Earth; coordinates x and y are given in AU.
10 Fig. 4. Results of integration of the movement differential equations of planets, Moon, Sun and asteroid. There is the Aphophis movement during 2 years. In this interval it approaches to the Earth at April 13, 2029. View on the side of South Pole.
11 Fig. 5. The Aphophis trajectory (1) is in the geocentric equatorial system of coordinates yrxr: a is in usual scale, b is in increased scale at the moment of Aphophis approach to the Earth (2); 3 is the Aphophis position at the moment of its approaching to the Earth after correction of its trajectory (velocity diminution with factor of k = 0.9992) in point Ap1; coordinates xr and yr are given in AU.
12 Fig. 6. A plot before approach Aphophis with the Earth in coordinates relatively the Sun. Fig. 7. A plot before approach Aphophis with the Earth in coordinates relatively the Earth.
13 5. Transformation of the Aphophis in the satellite We executed researches on the transformation of the Aphophis in the satellite. The velocity of the Earth satellite on a circular orbit at distance Rmin is equal ?cE = 3.2 km/sec. To transform asteroid in the satellite it is necessary its velocity in a point of approach ?AE = 7.39 km/sec to do near ?cE. At reduction of Aphophis velocity till 3.89 km/sec it reforms in the satellite of the Earth with sidereal cycle time 2.344 days. However the satellite orbiting occurs against rotation of the Earth. Fig. 8. The satellite Aphophis orbits around of the Earth in the opposite direction to movement of the Moon.
14 6. Transformation of the Aphophis in the satellite with a necessary direction of orbiting For transformation Aphophis in the satellite with a necessary direction of its orbiting, it is necessary at 0.443 years before to Aphophis approach with the Earth to lower its velocity on 2.54 m/sec. Fig. 9. A plot before approach of Aphophis with the Earth after correction of velocity at 0.443 years before approach (in coordinates relatively the Earth).
15 If at approach to the Earth the asteroid velocity yet will be reduced on 3.5 km/sec, it reforms in the satellite with the same direction of orbiting as the Moon. Our researches have shown that the orbit of the satellite is steady. Therefore it can carry out the task long time. Fig. 10. The satellite Aphophis orbits around of the Earth in the same direction as the Moon.
16 The reduction of body velocity, which mass is 30 millions tones, on 3.5 km/sec now represents a serious scientific and technical problem. But the experience of creation of the first artificial satellite of the Earth testifies if the society allots such task, it will be successfully realized in during remnant 20 years.
17 7. Conclusions 1. As a result of the analysis it have be established, that of uncertainty in a trajectory Aphophis are caused by methods imperfections of its computing. 2. By method deprived of these lacks the differential equations of movement of Aphophis, planets, Moon and Sun are be integrated numerically at span of 1000 years. 3. The Aphophis will pass near the Earth on distance of 6.1 terrestrial radiuses from its centre at 21 hours 45' on Greenwich of April 13, 2029. It will be the closest passage of Aphophis at the Earth in nearest 1000 years 4. The calculations of reform of the Aphophis in the satellite are executed. Such satellite can perform various tasks for the further reclamation of cosmic space.
18 8. Gratitude The authors express gratitude to T.Yu. Galushuna and V.G. Pol’, that they have given materials on the Aphophis asteroid. We express gratitude too to the experts of Jet Propulsion Laboratory (JPL) of USA, from which sites we used the initial conditions for integration. The Edward Bowell site (ftp://ftp.lowell.edu/pub/elgb/) has helped us to understand all features of the data on asteroids and to avoid mistakes at their use.
19 9. References 1. Georgini J.D., Benner L.A.M., Ostro S.I., Nolan H.C., Busch M.W. Predicting the Earth encounters of (99942) Apophis // Icarus. 2008 v.193, pp. 1-19. 2. Рыхлова Л.В., Шустов Б.М., Поль В.Г., Суханов К.Г. Насущные проблемы астероидной опасности // Околоземная астрономия 2007// Материалы международной конференции 3-7 сентября 2007 г. п. Терскол. Международный центр астрономических и медико-экологических исследований Национальной академии наук Украины и Институт астрономии РАН. г. Нальчик, 2008 г., с. 25-33. 3. Емельянов В.А., Меркушев Ю.К., Барабанов С.И. Периодичность сеансов наблюдения астероида Апофис космическими и наземными телескопами // Там же, с. 38 -43. 4. Емельянов В.А., Лукьященко В.И., Меркушев Ю.К., Успенский Г.Р. Точность определение параметров орбиты астероида Апофис, обеспечиваемая космическими телескопами // Там же, с. 59-64. 5. Соколов Л.Л., Башаков А.А., Питьев Н.П. О возможных сближениях ACЗ 99942 Апофис с Землей // Там же, с. 33 – 38. 6. Быкова Л.Е. Галушина Т.Ю. Эволюция вероятной области движения астероида 99942 Апофис // Там же, с. 48 – 54.
20 7. Быкова Л.Е., Батурин А.П., Галушина Т.Ю. Опасные для Земли траектории в области возможных движений астероида 99942 Аpophis// Фундаментальные и прикладные проблемы современной механики. Материалы VI Всероссийской научной конференции, посвященной 130-летию Томского государственного университета и 40-летию НИИ Прикладной Математики и Механики Томского государственного университета. Томск, 30 сентября – 2 октября 2008 г. – 2008 г. – С. 417-418. 8. Смирнов Е.А. Современные численные методы интегрирования уравнений движения астероидов, сближающихся с Землей // Там же, что и , с. 54-59. 9. Ивашкин В.В., Стихно К.А. Анализ проблемы коррекции орбиты астероида Апофис // там же, с. 44 – 48. 10. Smulsky J.J. Optimization of Passive Orbit with the Use of Gravity Maneuver // Cosmic Research, 2008, Vol. 46, No. 5, pp. 456–464. http://www.ikz.ru/~smulski/Papers/COSR456.PDF.
10. Some information 1. Computing results of the movement differential equations of planets, Moon, Sun and planets orbit evolution at span 100 mln. years are accessible on site: http://www.ikz.ru/~smulski/Data/OrbtData/. 2. Now there are several our books: 2.1. Smulsky J.J. 2004. The Theory of Interaction. - Ekaterinburg, Russia: Publishing house "Cultural Information Bank". – 304 p. (In English). http://www.ikz.ru/~smulski/TVEnA5_2.pdf. 2.2. Grebenikov E.A., Smulsky J.J. Evolution of the Mars Orbit on Time Span in Hundred Millions Years / Reports on Applied Mathematics. Russian Academy of Sciences: A.A. Dorodnicyn Computing Center. Moscow. - 2007. 63 p. (In Russian). http://www.ikz.ru/~smulski/Papers/EvMa100m4t2.pdf.
3. Our two language (Russian-English) book: Melnikov V.P., Smulsky J.J. ASTRONOMICAL THEORY OF ICE AGES: NEW APPROXIMATIONS. SOLUTIONS AND CHALLENGES, 180 p., which was edited by Prof. Eugeny A.Grebenikov. : http://www.ikz.ru/~smulski/Papers/AsThAnE.pdf .