EVOLUTION OF THE APHOPHIS ORBIT AND POSSIBLE USE OF THE ASTEROID

1
EVOLUTION OF THE APHOPHIS ORBIT AND POSSIBLE USE
OF THE ASTEROID
Joseph J. Smulsky1 and Yaroslav J. Smulsky2 1
Institute of Earths Cryosphere Siberian Branch
of RAS (Tyumen), E-mail Jsmulsky_at_mail.ru,
webpage http//www.smul1.newmail.ru/. 2
Institute of Thermophysics of SB PAS
(Novosibirsk). Correction data 26.09.2009

• The International Conference AsteroidComet
  Hazard 2009, September 21 25, 2009,
• St. Petersburg.

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 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.

4
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 from
epoch of November 30.0, 2008
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 ? 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 T0. 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.
Longitude of ascending node
Eccentricity
Argument of perihelion
Inclination
Period
Major semiaxis
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 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
Aphophiss 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. ??????? ?.?., ??????
?.?., ???? ?.?., ??????? ?.?. ???????? ????????
??????????? ????????? // ??????????? ??????????
2007// ????????? ????????????? ??????????? 3-7
???????? 2007 ?. ?. ???????. ????????????? ?????
??????????????? ? ??????-?????????????
???????????? ???????????? ???????? ???? ??????? ?
???????? ?????????? ???. ?. ???????, 2008 ?., ?.
25-33. 3. ????????? ?.?., ???????? ?.?.,
????????? ?.?. ????????????? ??????? ??????????
????????? ?????? ???????????? ? ?????????
??????????? // ??? ??, ?. 38 -43. 4. ?????????
?.?., ?????????? ?.?., ???????? ?.?., ?????????
?.?. ???????? ??????????? ?????????? ??????
????????? ??????, ?????????????? ????????????
??????????? // ??? ??, ?. 59-64. 5. ??????? ?.?.,
??????? ?.?., ?????? ?.?. ? ????????? ??????????
AC? 99942 ?????? ? ?????? // ??? ??, ?. 33
38. 6. ?????? ?.?. ???????? ?.?. ????????
????????? ??????? ???????? ????????? 99942 ??????
// ??? ??, ?. 48 54.
20
7. ?????? ?.?., ??????? ?.?., ???????? ?.?.
??????? ??? ????? ?????????? ? ??????? ?????????
???????? ????????? 99942 ?pophis//
??????????????? ? ?????????? ???????? ???????????
????????. ????????? VI ????????????? ???????
???????????, ??????????? 130-????? ????????
???????????????? ???????????? ? 40-????? ???
?????????? ?????????? ? ???????? ????????
???????????????? ????????????. ?????, 30 ????????
2 ??????? 2008 ?. 2008 ?. ?. 417-418. 8.
??????? ?.?. ??????????? ????????? ??????
?????????????? ????????? ???????? ??????????,
???????????? ? ?????? // ??? ??, ??? ? 4, ?.
54-59. 9. ??????? ?.?., ?????? ?.?. ??????
???????? ????????? ?????? ????????? ?????? // ???
??, ?. 44 48. 10. Smulsky J.J. Optimization of
Passive Orbit with the Use of Gravity Maneuver //
Cosmic Research, 2008, Vol. 46, No. 5, pp.
456464. http//www.ikz.ru/smulski/Papers/COSR456
.PDF.
21
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/s
mulski/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.

22
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 .