Transcript Теория относительности и реальность

EVOLUTION OF THE APHOPHIS ORBIT AND
POSSIBLE USE OF THE ASTEROID
Joseph J. Smulsky1 and Yaroslav J. Smulsky2
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).
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Correction data 26.09.2009
The International Conference «Asteroid–Comet
Hazard – 2009», September 21 – 25, 2009,
St. Petersburg.
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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
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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 [10] 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.
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Approaches
of Apophis
to the Earth
TA = 13 Ap 2029 yr
RminA = 38907 km
TB= 13 Ap 2067 yr
RminB = 622231 km
TE =10 Oc 2586 yr
RminE = 74003 km
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
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from epoch of November 30.0, 2008
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, ωe, P and a have significant breaks at
the time (TA) of the closest passage of Aphophis at the Earth.
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Longitude
of ascending node
Eccentricity
Inclination
Major semiaxis
Argument
of perihelion
Period
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, ωe 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.
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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 [1] 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.
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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.
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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.
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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.
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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.
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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.
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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.
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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).
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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.
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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.
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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.
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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.
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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.
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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 [4], 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.
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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/Ev
Ma100m4t2.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 .