W elcome to the 15th Workshop on JAXA
Astrodynamics and Flight Mechanics
Contents
------------------------------------------------------Map Session Schedule
Session Detail
17:15 17:45 u Formation Flight and Intelligent
Traffic System?v
*J. Kawaguchi (JAXA)
A?|?P?P?L
u Dynamic Deployment of Solar Sail
Membrane with Bending Stiffness?v
*K. Nakaya, O. Mori, Y. Tsuda, T. Saiki,
T. Y amamoto (JAXA)
?a?|?P?P?L
u Stabilizing Nonlinear Control of
Spacecraft at Capturing and Docking
Phase?v
*A. Ito, Y. Ikeda, T. Kida, T. Nagashio
(The University of
Electro-Communications)
?b?|?P?P?L
18:00
~
19:00
Small Party
A‰???z Conference Room A
A?|?P
?u Design of Reference ??Lissajous Trajectories around the L2 Point in the Sun-Earth System?v
*M. Utashima (JAXA)
Since both halo and Lissajous orbits around L2 point in the Sun-Earth system are unstable, orbital maintenance maneuvers at several month intervals are necessary. If an attitude subsystem does not
cause large disturbances, however, the orbits can be maintained with a yearly V of about 1 m/s based on
orbit determination errors and maneuver errors. In order to perform orbital maintenance, a reference
trajectory with zero V must be designed in advance under a precise model of perturbations. In Europe
and the United States, a zero V reference trajectory is designed by numerically obtaining a solution with
the matching conditions of positions and velocities between half-period orbits from an initial trajectory
derived by a third- or higher-order analytical solution. The method above has a problem in that
higher-order analytical solutions are required. This paper presents a new method for the design of zero
V reference Lissajous trajectories in which the Sequential Quadratic Programming (SQP) method is
applied and the higher-order analytical solutions are not necessary.
?u‘?—z-’n?…?n L2“_?ü?è?ì???T?W?…???€?O“1?ì?Y?v?v
JAXA?j
??‰ì“??1—R?i
???T?W?…?O“1?a?n???[?O“1?í?s?à’è?è?????é?”?–?????u?ì?O“1?????§???a?K?{??? ?è?A?3?
???ê?é’??]?·?é—l?é?????§???a?s?è?í????￠?é?B
‰￠?????í?A
‰o???V?[???ì???€?O“1?e‘O?à?á???Y?v?μ???¨???A
?ü?^‰e???ˉ?e?g—p?μ?????T
–{?_?????í?A
3???è???ì????‰e?í‰e??‰?ú’l???μ?????€?O“1?a?ì???3?ê???￠?é?a?A
?W?…???€?O“1?e????·?é?V?μ?￠??–@?e?q?×?é?B
A?|?Q
?u Low-Thrust Periodic Orbits in the Restricted Three-Body Problem?v
*M. Morimoto (The Graduate University for Advanced Studies), H. Y amakawa, K. Uesugi
(JAXA)
Lagrange points in the restricted three-body problem are the equilibrium points by the gravity of the
two primary bodies and centrifugal force in the rotating frame. Many studies for Lagrange points have
been investigated in the past. This study is focused on the periodic orbit around non-equiriblium point
in the rotating frame utilizing continuous low thrust propulsion.
?v
?u’á?…—í?…?i?e—?—p?μ???ü??O“1?é???·?é??l?@
?A?R?ì?G?A????–M???i
JAXA?j
???X–{–r?q?i‘??¤‘??E‰@?j
‰F’??@?a?A‘?—z?¨????’n?…?????ì?d—í?ì?Y‰e???e??ˉ?é??‰?’è?μ?????ì’T???@?ì‰^“??í?A?O‘ì–a‘è?é?B’T???@?ì??—ê?e?[?????μ?C‘?—z??’n?…?a???ì?¤’??S?e‰~‰^“???‰?“]?·??‰?’è?μ???§?à?R‘ì–a‘è?é?’T???@?ì‰^“??é???￠???l?@?·?é?B‘?—z?e’??S???μ?A?t?a“_?????2?é??’è?·?é?μ???à?W?n???á?á???A ‘è?í?A‘?—z??’n?…?e??’è?μ??‰?“]?à?W?n???\???3?ê??B?O‘ì–a‘è‰o???í?A“?“V‘ì?ì?d—í???A‰?“]?à?W?n?é(?‰?O?‰?“?W?…“_?j?a‘??Y?μ?A???ì“_?é?¨?ˉ?é?‰?O“1?í?A?±?ê?ü???é?”‘??-?¤????鉓?S—í?ì’T?è???￠“_
A?|?R
?u Design of Small Circular Halo Orbit around L2?v
*K. Tarao (The University of T okyo), J. Kawaguchi (JAXA)
The Sun-Earth L2 libration point is conceived the best point for the astronomy, since it maintains not only
constant distance from Sun and Earth but geometry with them. This paper describes a new control
method for realizing small circular Halo orbits around the L2 point. First, a control law is mathematically
obtained from linear equations of motion in restricted three body problem. And next, the station keeping
strategy is verified using real ephemeris. Required thrust for the strategy is small, and it’s realized even
by solar sail.
?u L2“_?ü?è?ì??‰~?n???[?O“1?Y?v?v
?A?ì??~?ê?Y?i J AXA?j
??‘?—…”??N‘??i“?‘??E?H?E‰@?j
‘?—z―
L1 “_???è?à—L—???? ?é?B??
?ì?????k?Q“_?ü?ó?ì?O“1?í?A???O?ü“V??‰q?ˉ?a?O?f?ˉ’T???ì?????ì?N?E?I“_???μ???ì‰F’??`?ì?
Halo?O“1?a?ì???±???e
L2“_‰??è?é???3?è‰~?`?ì
—p?a?l?|???ê???￠?é?B–{?_?????í?A?V?μ?￠?§??–@?é???è
?|?·?B?ü???‰???é?A‰~?§?à?O‘ì–a‘è?é?¨?ˉ?é??`‰??3?ê????’??????—??_“I?é?§??‘￥?e“±?-?B???ì?“1—v‘f?e—p?￠???O“1?§????–@?e?????·?é?B?O“1?§???é?K—v?è?…—í?í?\?a???3?-?A?\?[?‰?[?Z?C??? ?è?A‘????à—p“I?è?§????–@??? ?é?B
A?|?S
?u Optimization of Trajectories between the Earth to the L2 Point?v
*S. Aida (The University of T okyo), M. Matsumoto, Y. Kawakatsu, J. Kawaguchi (JAXA)
Optimization of trajectories from the earth to the sun-earth L2 point is discussed, supposing their applications to missions around L2, such as deep-space ports and infrared astronomical satellites. The
problem of compromising between short transit times and small ??V, which is proportional to the amount
of fuel consumption, is considered in detail. Transfers are studied in some cases, free-fall trajectories,
multi-impulse trajectories using chemical thrust, and trajectories using a lunar swing-by. We discuss each
case from the perspective of transit times, ??V, and Isp.
?u LEO-L2“_???ì—A‘—?O“1??“K‰??v
JAXA?j
?A??–{“1?O?A?ì???N?O?A?ì??~?ê?Y?i
??‘?“c?ê‰??i“?‘??E?H?E‰@?j
LEO?|L2“_???ì—A‘—?O“1?ì??“K
L2“_?ü?è?é?¨?ˉ?é?[‰F’??`?A???O?ü“V??‰q?ˉ?è???ì?~?b?V???“?e‘z’è?μ?A
V?????ì?????ì?O“1“?“ü?p??“?“ü‘?“x?ì??
‰??e?s?á???B–{?¤?????í?A?ü??‰??w?…?i?e—p?￠??—A‘—?é???￠????
Isp?ì???￠“d?C?…?i?e—?—p?μ??—A‘—?O“1?e??“￠?·“K‰??e??“￠?·?é?B???é?A‰??w?…?i???ì??“￠??‰ê?e?3?é?μ??
Isp?è???ì“_????—A‘—?O“1?e?]‰??μ?A?X?é‰??w?…?i??“d
V?E”ò?s?????E?…?i?n?ì
?é?B?e—A‘—?ì?ê???é???￠????
?C?…?i?é???é—A‘—?e”??r?·?é?B
A?|?T
?u Orbital Dynamics of Solar Photon Thrusters?v
*H. Y amakawa (JAXA?j
The idea of utilizing large sheets of reflecting material for a spacecraft, which uses positively the radiation
pressure from the sun, has been in the literature since the days of the early space pioneers. This solar
sailing concept has long been considered for a diverse range of future mission applications, and recent
advances in the light material made this concept realistic. This conventional flat solar sail suffers from a
loss of efficiency due to the cosine squared reduction in solar radiation pressure force magnitude as the
Sun aspect angle increases. When it comes to the transverse component of force tangent to the solar sail
orbit, only 38 % of the available solar radiation pressure force is of use when the sail orientation is optimized. However, by separating the functions of collecting and directing the solar radiation, significant performance improvements over conventional flat solar sails are possible. This concept is called solar
photon thruster, which was proposed in the Soviet literature and reinvented by R. L. Forward in 1989.
This paper focuses on the orbital dynamics of solar photon thrusters by comparing with the conventional
flat solar sails.
?u?\?[?‰?[?t?H?g?“?X?‰?X?^?ì?O“1?_?C?i?~?N?X?v
???R?ì?G?i JAXA?j
‘????è–?–ê??‘?—z???”????μ???…?i—í?e“??é?l?|???é???￠???í‰F’??J”-?ìêt–??ú???è’????3?ê???￠???B?±?ì?\?[?‰?[?Z?C???ì?R?“?Z?v?g?í??”N?ì?y—ê?è?T—??ì“o?ê?é???á????‘ì‰??μ????? ?é?B??–ê?^?ì?\???ì–a‘è“_?ì?P?????μ???A–@?ü???ì‘?—z?é‘??·?é?p“x?ì—]?·?ì“????é”?—á?μ???…?i—í?ì‘????3?a’á????±???a?“?°???ê??B?±?ì’Z???e‰???·?×?-?A?W???@”\??”????@”\?e“?—§?é?§???·?é?\?[?‰?[?t?H?g?“??^?ì?T”O?a???\?A?ì‰è?w?ò?é???á??’????3?ê?A
1989”N?é?íF orward?é???á????’????3?ê???B–{?_???í?A?±
?ì?\?[?‰?[?t?H?g?“?X?‰?X?^?e“??ú?μ??’T???@?ì?O“1?_?C?i?~?N?X?é???￠???l?@?μ???à?ì??? ?A?|?U
?u Preliminary Analysis of Interplanetary Transfer Trajectory Using Libration Points?v
*K. Nakamiya (The Graduate University for Advanced Studies), H. Y amakawa (JAXA)
This study presents an approach to obtain a low energy interplanetary transfer trajectory for the
spacecraft using the libration points, where solar gravity, planetary gravity and centrifugal force in the
Sun-planet system are balanced in the restricted three-body problem (R3BP). Firstly the libration point of
the Sun-Departure (Arrival) planet system is set as the departure (arrival) point of the spacecraft. Then,
the relation between the departure (arrival) velocity and the movable region of the spacecraft (i.e. the
maximum and the minimum heliocentric distance) is searched by numerical calculation, changing the
departure (arrival) velocity and mass ratio of the primary bodies. Then a low energy interplanetary
transfer based on these results is suggested. Finally, the effectiveness of this approach is discussed and
compared with the previous works.
?u?O?‰?“?W?…“_?e—?—p?μ???f?ˉ???ú?s?ì—\”??l?@?v
?A?R?ì?G?i JAXA?j
??’??{???÷?i‘??¤‘??E‰@?j
–{?¤???ì–ú“I?í?A‘?—z?n?ì?f?ˉ???é???????￠?é?d—í?ê?ì—í?w“I“á???e?????μ???A???è?-?è?￠?G??ú”R—??j???ì‰F’?’T???@?ì?f?ˉ???ú?s?e‰?”\?é?·?é?±????? ?é?B?è‘O?????A?f?ˉ???ú?s?é?K—v?è
L1?A L2?j????é“I?é—?—p?·?é?±???é???è?A
?í?????è?G?l???M?[?i‘?“x?j?ì?t‰á???A‘?—z?n?ì“à?O?f?ˉ???ì?ú?s?a—e?????è?é??????? ?é?B???
?i?R
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?ü???A
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–{?¤?????í?A
‰F’?’T???@?ì?o”-?i“?’…?j“_?e‘?—z?|’n?…?i“?’…?f?ˉ?j?n?ì?‰?O?‰?“?W?…“_???μ???A???ì???ì?o”-?i“?‘?“x??’T???@?a?ú“?‰?”\?è—ì???i‘?—z????‰F’?’T???@?ü???ì??‘??——￡???????——￡?j?ì???W?e’2?????±?ì“á???e??—p?μ???A???è??—|“I?è‰F’?’T???@?ì?f?ˉ???ú?s?è–@?e’???μ?A–{?è–@?ì—L?????e‘??ì?”??r?μ?è?a???l?@?·?é?B
A?|?V
?u Orbital maneuvers from the Sun-Earth L2 point?v
*M. Matsumoto, J. Kawaguchi (JAXA)
In this paper, we consider orbital maneuvers from the Sun-Earth L2 point. As the first step, impulsive
maneuvers from the L2 point are examined, and using these results, low-thrust maneuvers are designed.
?u‘?—z?|’n?…L2“_?????ì’n?…’E?o?O“1?é???·?é?¤???v
JAXA?j
????–{“1?O?A?ì??~?ê?Y?i
L2“_?e”-
L2“_?e?[‰F’??`???μ??‘z’è?μ?A’á?…—í?…?i?@???e“??ú?μ??‰F’??@?é???é
–{?u‰‰???í?A‘?—z?|’n?…?n
L2“_?????ì?C?“?p???X”ò
’…’n???μ???[‰F’?‰??ò?V?X?e?€?e?l?|?A???ì’E?o?O“1?e?_???é?B–{?¤?????í?ü???A
?s?e‘z’è?μ?A‰~?§?à3‘ì–a‘è‰o?é?¨?ˉ?é’E?o?O“1?é???￠???l?@?e?s?￠?A???ì“á???e?ü???????B?3???é?A????X”ò?s?ì??‰ê?e??é’á?…—í’E?o?O“1?ì??“￠?e?s?á???B
A?|?W
?u Practical Analytic Solution of Relative Motion between Formation Flying Satellites with
Different Ballistic Coefficients in Near-Circular Reference Orbit?v
*T. Y amamoto (JAXA?j
Formation flying of multiple satellites is an evolving technology with many possible applications, such as
long baseline interferometry, synthetic aperture radar, simultaneous measurement of magnetic field at
different points, and so on. T o achieve these formation flying missions, precise control of relative motion
between multiple satellites is required. And the equation describing the relative motion is needed. So the
study of the orbit dynamics for the formation flying has become active recently. Hill's equation is suitable
for the analysis of the rendezvous problem. Because it needs relatively short-term operation and there are
frequent thrust firings. However, the equation can not be accurate for long-term orbit maintenance such
as formation flying missions. Because it assumes the Earth is spherically symmetric. Actually, several
external forces cause perturbation to the orbit of each satellite which comprises the formation. The
analytic solution for the relative motion of the formation flying satellites which considers the main secular perturbations and difference of the ballistic coefficients is proposed in this paper. The solution is practical
and useful for the mission analysis and design of formation flying missions in the near-circular orbit.
?u?ù?è?é’e“1?W?”?e?????t?H?[???[?V???“?t?‰?C?g‰q?ˉ?ì‰~?O“1?é?¨?ˉ?é‘?‘?‰^“?‰e??è?v
Hill??’???ìClohessy-Wiltshire‰e?a—L????? ?é?a?A?t?H ?[???[?V???“?t?‰?C?g?~?b?V???“?é?¨?￠??’·?ú??‘?‘?“I?è?ê’u?e?????μ‘±?ˉ?é????é?í?ó?C’??R?a?d—í?
2‰q?ˉ?ì’e“1?W?”?ì?·???A?d—í?é???é??“?—í?ì?·?é??“?—í?ì?·?ì??—^?a‘????-?A?s?\?a??? ?é?B–{?u‰‰???í?A
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A?|?X
?u Control of Relative Position Change in Formation Flying?v
*K. Y amada (Nagoya University), S. Y oshikawa, T. Shima (Mitsubishi Electric Co.)
This paper proposes the basic method for constructing a formation flying. It proposes a trajectory design
of minimum-fuel consumption for spacecraft relative position change. Numerical studies of the formation construction are executed in order to verify the trajectory control.
?u‰F’??@?ì‘?‘??ê’u???X?ì?§???é???￠???v
?A?g‰í?í“??A“??x–??i?O?H“d?@?j
???R“c???F?i–?‘??E?H?j
?t?H?[???[?V???“?t?‰?C?g???í?C???”?ì‰F’??@?a?~?b?V???“?ì–ú“I?é‰??????t?H?[???[?V???“??é???X?·?é?±???a?K—v??? ?é?D‰F’??@?a?t?H?[???[?V???“?ì?`‘??e???X?·?é?????ì?C?á”??…–ò—ê?e??·?é?O“1???X‘￥?é???￠????“￠?μ?C?”’l?V?~?…???[?V???“???ì”??r?e?s?¤?D
A?|?P?O
?u Piecewise Linear-Quadratic Control for Clustering Spacecraft?v
*H. Umehara (NICT)
The onboard control system by multiple spacecraft requires (A) near-miss avoidance, (B) fuel-cost minimization, and (C) computation reduction. Formulating the potential-function guidance [1] and the
penalty-function guidance [2] overcame the respective two requirements: (A) and (C), and (A) and (B).
However, all the three requirements are still unsolved. The linear dynamical system with a piecewise
quadratic penalty function is therefore defined for reducing iterative computation load. By referring the
dynamical behavior, we will consider the guidance design into the global optimum state.
?u???”???ú‰F’??@?ì???a?ü?`?Q???§???v
NICT?j
??”~?′?L–??i
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[1]???í?|?e?“?V??
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(A) ?j?A?~?X‰?”?A(B) ”R”?’á???A(C) ?v?Z?‰‰×?y???A??? ?é?B
(A)
?l?H‰q?ˉ???a‰?‘z“I?è??—í‘??Y?ì—p?e?·?é???ì???¤?è?A‘±?…—í?e—^?|?é?±?????A ?????”—U“±–@?e?\’z?μ???B
[2]???í?y?i???e?B??
?¨????
(C) ?e‰???3?1???B?μ???μ?A??—í‘??Y?ì—p?ì?????ì?§??”R—??e‘??-?K—v???μ???B
?”—U“±–@?e“±“ü?μ?A?ó‘????”?é?¤–e?è???”?ó????‰q?ˉ???é‘??Y?ì—p?e“-???1?é???¤?è??“K?§??‘￥?e—^?|???
(B) ?e‰???3?1???B?μ???μ?A”????v?Z—ê?a‘??-?K—v???è?á???B?–‘O?é??“K?O ?±?ê?é???á???A
(A) ?¨????
?Y?v?·?é????é?í–a‘è???í?è???è?￠?a?A‰q?ˉ?a?I?“?{?[?h???????§??‘￥?e?????é????é?í?A?v?Z?‰
(A) (B) (C) ?e“ˉ???é‰e???3?1?é?????é?í?A?y?i???e?B???”?????|?e?“?V???????”???í?d—v?è‰?‘è???è?é?B
?′“n?μ?e?·?é?¤???a?K—v??? ?é?B???±???A–{?e???í?A???”?@?O“1?§???e’P??‰??3?1???ü?`?n?é?A?”e?E”R”?’á???e–í?μ?????a?ü?`?Q???§???e‰á?|??—í?w?n?e?l?|???B??????“K‰e?ì‘??Y?e???e?ü?????A?-”????v?Z??‘?????“K‰e?é—U“±?·?é????l?@?·?é?B
A?|?P?P
?u Study on Formation Flight Control and Information Propagation Structur?v
*T. Saiki (JAXA)
In formation flight missions, the feedback control with the relative information between the members is
effective in order to keep the formation strictly and to avoid the collisions. In such formation maintenance
control, the local control law (control gain, etc.) of each spacecraft and the information propagation
structure of the formation determine the behavior of the formation. In this study, the information
propagation structure of the formation is focused on and how the information propagation structure
influences the behavior of the formation is investigated. And the method for constructing the information
propagation structure is shown.
?u?ò‘à”ò?s?é?¨?ˉ?é??“`’B?\‘￠???Q?ì?§?????é???·?é?¤???v
JAXA?j
???2”??F???i
?e‰F’??@?a‘?‘?????—?—p?μ???§???e?s?á???Q?ì?`?ó??????·?é????é?í?C?e‰F’??@?ì???[?J???è?§????à?é?C?e‰F’??@?a???ì‰F’??@?ì‘?‘????????ì’?“x—?—p?·?é?????￠?¤‘?‘?????ì??“????W?a?C?Q?ì?“???§?????e??’è?·?é?D–{?¤?????í?C?±?ì‘?‘?????ì??“????W?e??“`’B?\‘￠???????C???“`’B?\‘￠?a?Q?ì?????é—^?|?é‰e???e’è—ê“I?é?]‰??·?é?D?ü???C?§?????é—D?ê??Q?ì?\’z–@?e’???·?é?D
A?|?P?Q
?u Application of Ballistic Capture Trajectory for Jovian Outpost Establishment?v
*Ridanto Eko Poetro, Hiroshi Hirayama, T etsuo Y asaka?i Kyushu University?j
Future exploration and exploitation of Jovian system is expected. Establishment of an outpost in Jovian
system will ensure maximum benefit of the exploration with capability for extending the exploration to
outer solar system and beyond. Outpost base around Callisto is tentatively selected to avoid the Jupiter’s
main radiation belt. Since multiple missions required for the outpost establishment, the establishment trajectories must be optimized. Multiple gravity assists or low thrust propulsion is expected to be
employed for the Jupiter en route trajectory. Braking using galilean satellites prior to Jupiter insertion,
followed by multiple galilean satellites resonance hopping for step by step apojove reduction are assumed
to be taken as Callisto en route trajectory. This approach already save much V compare to a direct
trajectory scenario, but still leave a quite big V for final orbit insertion. Final approach to Callisto along
a trajectory on the weak stability boundary of Callisto with respect to Jupiter is examined. Numerical
study of Callisto ballistic capture linked to an arriving joviocentric trajectory, with and without other
galilean satellites effect, is performed for construction of an optimum final insertion maneuver.
A?|?P?R
?u Orbital Characteristics of V enus Explorer PLANET-C?v
*N.Ishii, H. Y amakawa (JAXA)
In this paper, orbital properties and characteristics of Earth to V enus transfer orbits are summarized for
the purpose of ensuring launch opportunities of V enus exploring mission, PLANET-C. From the
viewpoint of backup scenario, identically designed spacecraft was assumed to be launched by the same configuration of M-V vehicle. T otal amount of velocity correction to V enus capture as well as required
weight of propulsion fuel was also evaluated.
PLANET-C?O“1?v‰??v
JAXA?j
???????M–??A?R?ì?G?i
(PLANET-C)?ì‘????°?E?B?“?h?E?ì?m???¨?????o?b?N?A?b?v?E?B?“?h?E?ì?m???e–ú“I ?à?ˉ’T???@
2010”N‘????°?¨???????ê?è?~?ì?à?ˉ‰????O“1?ì“á’￥?é???￠???q?×?é?B“ˉ?ê?Y?v?ì’T???@?e“ˉ?ê?d—l?ì‘????P?b?g??‘??????°?é?–?e????é‘????°?????ì??“￠?e?s?￠?A?à?ˉ?ü‰?O“1“?“ü?ü???é?K—v???3?ê?‘?“x?§—ê?¨????“??ú”R—??d—ê?ì?…?Z?e?s?á???B
A?|?P?S
?u Orbit Design and Simulation for ASTROD I?v
*Xia Yan?i Purple Mountain Observatory, Chinese Academy of Sciences?j,
Tang Chien -Jen?i Department of Physics, Tsing Hua University?j,
Ni Wei –Tou(Purple Mountain Observatory, Chinese Academy of Sciences?j,
Li Guang – Yu?i Purple Mountain Observatory, Chinese Academy of Sciences?j
As a first step of ASTROD (Astrodynamical Space Test of Relativity using Optical Devices), ASTROD I is
to have one spacecraft launched to a solar orbit to range optically with ground stations to test the experimental schemes for ASTROD and to meet important scientific goals. These scientific goals include
an improvement in measuring solar-system parameters, a better precision in solar-system dynamics,
improved tests of relativistic gravity and the fundamental laws of spacetime, and a slightly better
sensitivity for detecting gravitational waves as compared to Doppler tracking of spacecraft using radio
waves. This paper presents the orbit design and orbit simulation for ASTROD I. The spacecraft is
designed to enter the solar orbit from a low earth-orbit and to encounter Venus twice to receive
gravity-assistance for achieving shorter periods for making the relativistic Shapiro time delay sooner.
Five-hundred sets of the orbit data were simulated using a simple noise model and fitted with 23 parameters of relativistic parameters, celestial-body masses, solar quadrupole parameter, and spacecraft
initial position and velocity parameters. From these simulations and fittings, the uncertainty of the
relativistic parameters gama and beta are estimated to be about 10 . The uncertainties of the masses
of celestial bodies including the 3 big asteroids can be improved considerably.
A?|?P?T
?u EFFICIENT ORBIT INTEGRATION BY MANIFOLD CORRECTION METHOD?v
*T. Fukushima(National Astronomical Observatory of Japan)
The manifold correction method (Nacozy 1971, Murrison 1989)or the projection method (Hairer et al.
2002) is a meta-method tointegrate a dynamical system with some conserved quantities. Atevery
integration step, it modifies the integrated solution so as to lie on a manifold defined by the quantities,
which is assumed to contain the true solution. We extended the method to be applicable to a more
general case where the quantities are no longer constant (Fukushima
2003a,b,c,2004a,b,c,d,e,f,2005a,b,c,d). To do this, we follow the time development of the quantities and
use a sort of coordinate transformation to maintain the consistency between the integrated variables
and the quantities. Typical methods of correction are certain geometric transformation such as a scaling,
a rotation, or a general linear transformation. The simplest example is the single scaling method for the gravitational two-body problem under perturbations. The method adopts the Kepler energy, K = T - U,
as the quasi-conserved quantity, which is a constant when unperturbed. We numerically integrate the
position, x, and the velocity, v, as (x, v) -> (sx, sv ), at every integration step. We determine the scale
factor, s, by solving an associated cubic equation. by Newton method starting from a trivial initial guess,
s_0=1. Thus integrated solution show a linear error growth w.r.t. time. The applicability of the
manifold correction method is independent on the kind of integrators or on the nature of perturbations.
Also it is applicable to perturbed harmonic oscillators. As an example, we also applied the method to
the two-body problems regularized by the Kustaanheimo-Stiefel (KS) transformation.
?u‘?—l‘ì?a?3?é???é?—|“I?è?O“1???a?v
????“?“o?u?v?i?‘—§“V??‘??j
‘?—l‘ì?a?3???í???^?”’l???a–@?ì?ê????? ?é?B“V‘ì?ì?O“1‰^“??e?”’l?V?~?…???[?V???“?·?é????A“V‘ì?’u?E‘?“x?è???O“1‰^“??e?L?q?·?é?ì?é?K—v?????à?è“?—§???a?ì????”-“W?e’????·?é?ì?a’ê—á??? ?é?‘ì?a?3–@???í?A“?‘ì–a‘è?ì?ê???ì??‘?—ê??? ?é?G?l???M?[???a?a?p‰^“?—ê?x?N?g???è???ê’u‘?“x?ì???”-“W?à?1?1??’????·?é?B?”’l???a?a??à???? ?ê???A?±?ê??”?“?—§?è?”—ê???ê’u?E‘?“x?ì???W???í??é?í????? ?é?a?A?à???í?A???¤?è???è?￠?B‘?—l‘ì?a?3–@???í?A?±?ì?á?￠?a?à?s?μ???”’l???a????￠?é???l?|?A?á?￠?a–3?-?è?é???¤?é?ê’u?E‘?“x?e?X?P?[?????·?a‰?“]“??ì?Q?[?W???·?é???è????2???é?a?3?·?é?B?a?3???ì?”’l‰e?í?A?^?ì‰e??ü?T?i“??G?l???M?[–ê?è???ì?j‘?—l‘ì???é?ú?é??‘z’è????A‘?—l‘ì?a?3???????B?Q”N?ù??‘O?é“?‘ì–a‘è?ì?G?l???M?[???a?e”“?—§—ê???μ??’P?ê?X?P?[?????·?
(Fukushima
?·?é’P?X?P?[??–@?é???è?A
?R???3??“?“?‘ì–a‘è?ì?”’l???a???·?a?€“I?é???-?·?é?±???e????μ??
2003a)?a?A???ì???A?‰?v?‰?X???a?A?O“1?p‰^“?—ê?x?N?g???è??“?‘ì–a‘è?ì??‘?—ê?e???X??’?‰á?μ??[?W???·?à‘o‘??X?P?[?????·?A?R???3‰?“]?è?????G‰??·?é?±???é???è?A?O“1???a?ì??“x?ü???(Fukushima 2003b,c,2004a)?B?μ???μ?A?I–-?è???”???·?e?s?¤?±???é???è?A?v?Z–@?ì??”\?e’á‰o?3?1?é?±?-?v?Z—ê?a’á??‰?”\??? ?é?±???é?C?????A??“x?í‘?“x?ì?è—a?a?ê’u?x?N?g???ì??–ê‰??è???A??{?·?±???é???è?A”???é?V?“?v??????????”\?è?è–@??? ?é?O“1?o“x–@?é“?’B?μ??
(Fukushima 2004b,c,d,e)?B
KS???·?ì???é?A???·???ì??“?’2?a?U“??q–a‘è?é‘??μ?3???é?A
HALCA?è??—￡?S—|?a‘????￠?O“1?ì?ê???é?í
(Fukushima 2004f,2005a,b,c)?B
‘?—l‘ì?a?3?e?{?·?±???é???è?A
“ˉ—l?ì?€“I?è??“x?ü???e’B???·?é?±???a??????
A?|?P?U
?u Autonomous Localization System of Planetary Lander?v
*S. Higo (The University of T okyo)
Recently, the investigation of asteroids is attracted because it will clarify the origin and the formative
process of our solar system. T o get the knowledge of internal aspects of asteroids, in-site observation by
landers and rovers is most promising. Precise localization of rover over asteroid surface is required for its navigation. Most asteroids are very small that positioning methods on Earth, Moon and Mars are not appropriate. In this paper, a new positioning method is proposed using Range measurement between the
rover and the orbiter. Formalization and simulation analysis are also conducted which shows the
efficiency of the proposed model.
?u???f?ˉ’T???@?ì?ê’u“ˉ’è?ì??—￥‰??v
??”ì???3?a???i“?‘??E?H?E‰@?j
‰??X?ì‘?—z?n?ì?N?1?ì“??e‰??–????·???3?ê????f?ˉ?í?A??’T???a?n?ü?á???????è??? ?é?B???f??ê’u“ˉ’è?í?A’??a?”?S???[?g?????￠?¤???3?3???|?A’n???a??–ê?a‰??ˉ???ì?ê’u“ˉ’è?è–@?e—?—p?·?é??￠?B??”-?\???í?A???f?ˉ???ì’T???@?é???￠???A???à“I?è“??ú?@?í?ì?§–??i?d?3?A?§“x?j?e?l—??μ?
A?|?P?V
?u HAYABUSA Orbit Determination Analysis just before the Rendezvous with Itokawa?v
*T. Ohnishi (Fujitsu Co Ltd) M. Y oshikawa, T. Kato, T. Ichikawa (JAXA)
Hayabusa will have an operation gap for two weeks before arrival to Itokawa because of conjunction.
Orbit determination will be performed using radiometric data on coasting period both before and after the conjunction, but observed data noise will increase around the conjunction because of influence by solar
plasma, so we have to take it into account on our orbit determination analysis. We evaluate the amount of
Doppler noise for Nozomi conjunction, and adopt it to Hayabusa by considering difference of bands the spacecrafts use.
?u???f?ˉ“?’…’?‘O?ì?u?í?a???3?v?O“1??’è??“x‰e?í?v
??‘??? —2?j?i?x?m’ê?j?g?ì?^?A‰á“? —2“??A?s?ì?×?i
JAXA?j
?u?í?a???3?v?ì?O“1???í???f?ˉ“?’…?ì’?‘O?é??‰^—p?ú???a‘??Y?·?é?B??‘O?????í‘?—z?v?‰?Y?}?ì
?u?í?a???3?v??‰^
???h?b?v?‰?[?ì?m?C?Y???x???a‘?‘??·?é?B’??ò???í?u?ì???Y?v?é?¨?ˉ?é??‰^—p?ì?o?±?????A —p???ì?h?b?v?‰?[?m?C?Y?ì—\‘a’l?e?????A?O“1??’è‰e?í?e?s?è?á???B?ü???A??‰^—p–??ˉ?é?í???w??e?1—p?μ???O“1??’è?à—\’è?3?ê???￠?é?B?±?ê?é???·?é??“￠?ó?μ?é???￠???à?????·?é?B
A?|?P?W
?u Status Report on VLBI application for Space Navigation for HAYABUSA?v
*M. Sekido, R. Ichikawa, T. Kondo, H. Takeuchi, Y. Koyama, E. Kawai (National Institute
of Information and Communications T echnology) M. Y oshikawa, N. Mochizuki, T. Kato T.
Ichikawa Y. Murata, H. Hirabayashi (JAXA), T. Ohnish (Fujitsu Co Ltd), Y. Tamura, Q.
LIU, F. Kikuchi (NAOJ) K. Fujisawa (Y amaguchi University), H. Takaba (Gifu University),
K. Takashima (Geographical Survey Institute)
Joint use of very long baseline interferometry, which has high angular resolution, with conventional rand
and range rate observation is expected to enhance the accuracy of orbit determination of spacecraft in the
deep space. For the purpose to support the orbit determination of spacecraft HA Y ABUSA, Japanese
research institutes working with VLBI: ISAS/JAXA, NICT, NAOJ, GSI, and universities: Y amaguchi and
Gufu, are collaborating on VLBI application for orbit determination. Measurement precision of group
delay observable depends on signal bandwidth and signal to noise ratio. We have performed several VLBI observations to examined preferable signal types (telemetry and range signal) and cases of using different
types of antenna on the spacecraft (HGA and MGA), so far. At the end of May 2005, switching VLBI observations for HA Y ABUSA and nearby quasor were performed by participation of domestic VLBI
stations: Usuda 64m(ISAS), Kashima 34m(NICT), Tsukuba 32m(GSI), Mizusawa 20m(NAOJ), Chichijima 10m (GSI), Aira 10m(GSI), and Shintotsukawa 3.8m (GSI). The observations were almost
successful and observed data are now under the correlation processing. HA Y ABUSA is going into the final
stage to approach to the asteroid “ITOKA W A” in this summer. We are planning to organize some VLBI
sessions in this season and wish to demonstrate the effectiveness of the VLBI observation on spacecraft navigation. Current status of our research will be reported in this presentation
HA Y ABUSA?ìVLBI??‘a― ―
?A???R‘×?O?A?ì??‰h???i???’ê?M?¤???@?\?j
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?[?g??‘a???1—p?·?é?±???é???è?[‰F’?’T???@?ì?O“1??’è??“x?e”–“I?é?ü???3?1?é?±???a?????ü?ê???￠?
ISAS/JAXA,NICT?A
VLBI???A?¤???@????? ?é
HA Y ABUSA?ì?O“1??’è?e?x‰??·?×?-?A
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VLBI?e”??‘ì?ì?O“1
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?|—??P?O???A?V?\’??ì?R?D?W???i?‘“y’n—?‰@?j?ì?A?“?e?i?Q???à?{?μ???B???ê???ê?ì??????HA Y ABUSA???à?é?ù?ú—??D?è‘????a“????ê???¨?è?A???Y?A–{“y?ì??‘a???f?[?^?ì‘?????—??e?i???
6??––?y??
HA Y ABUSA?u?C?g?J???v?ú???é?ü?ˉ???A
?u’n?ì?f?[?^?ì—A‘—?e‘ò?á???￠?é???±????? ?é?B?????A
VLBI??‘a?ì?O“1??’è???ì—L?????e?|?μ???￠????
VLBI??‘a?e?v‰??μ???¨?è?A
7??––?ì???“?W?v‘a?é? ?í?1??
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A?|?P?X
?u Perturbation Analysis of Sun-Synchronous Orbit between Planets?v
*S. Nishimaki, K. Kuroshima (The University of T okyo), T. Saiki, J. Kawaguchi (JAXA)
The Cart Wheel orbit is a kind of sun-synchronous orbit around the Earth for astronomy satellites. Considering the disturbance of the Earth gravity, the period of the in-plane motion and out-of plane
motion vary and trajectory becomes Lissajous. In this study, a transition of the orbit is analytically shown.
?u?f?ˉ??‘?—z“ˉ?ú?O“1?ì??“?‰e?í?v
????–q?C???A??“??c?q?i“?‘??E?H?E‰@?j
?A?2”??F???A?ì??~?ê?Y?i JAXA?j
)?????Y??
2?@?ì‰F
(Hill?ì?à?W?n
2???ì‰F’??@?eCart-Wheel?O“1???????ê??à?ì?é“?“ü?·?é???C‰?“]?à?W?n
’??@?ì‘?‘??O“1?í?C?ü??a?O“1‰^“??ì?ü???“??μ?￠‰~?O“1???è?é?D?ü???C‘?‘?‰^“??ì?O“1–ê?í‰?“]?n?é????‰??μ?è?￠?D?±?ì???¤?è?O“1?e?C‘?—z’??S?n?ì?f?ˉ???é?g‘??μ—?—p?·?é?±?????C’T???@?e’n?…?[?—‘?—z“ˉ?ú?O“1?é“?“ü?·?é?±???a‰?”\???è?é?D’n?…?d—í?a?è?￠?ê???é?í?C?±?ì???¤?è?f?ˉ??‘?—z“ˉ?í?????3?ê??a?C?à???í?C‰F’??@?ì?O“1?í’n?…?ì?d—í?ì‰e???e?¤?ˉ??‰??·?é?D–{?¤???í?C’n?…??é’?–ú?μ?C‰F’??@?ì?O“1?ì??‰??ì—l?q?e‰?í“I?é?????à?é?±???e–ú“I???·?é?D
A?|?Q?O
?u Eccentricity of an Asteroid’s Orbit for the Minimum Fuel Exploration?v
*S. Ueno, T. Kobayashi, S. Koga (Yokohama Nat. University)
Exploration to asteroid in the solar system has been focused by space scientists because asteroids have
different features from large planets. The target asteroid is usually not specified. Calculation of trajectory
to asteroid is also interest problem for space engineers because it is necessary to select target asteroid and
to design trajectory simultaneously. The purpose of this paper is to provide the technical information for
in this paper. The target asteroid’s orbit is elliptic in the earth’s orbital plane. The explorer is under
influence of only the gravitational acceleration of the sun. Impulse approximation adopts the calculation
in this paper. The minimum fuel trajectories are selected to minimize the summation of ?Vs at the
departure from the earth and at the arrival to the asteroid.Orbital energy is given as a function of
semi-major axis, thus the relation between eccentricity and ?V are shown numerically. The results show
that ‘critical eccentricity’is a significant parameter. Critical eccentricity, e CR, is defined as an eccentricity
when the elliptic orbit tangents the circular orbit. When the eccentricity is less than the critical eccentricity, two orbits do not across each other. The other hand, the eccentricity is larger than e CR, there
are two cross points on each orbits.The total ?V also depends on the relative position of the earth and the
target asteroid at the departure time of explorer. The minimum ?V at the best departure time can be
calculated for given eccentricity. While the eccentricity is less than e CR, the value of minimum ?V does not
depend on eccentricity largely. The other hand, in the region of eccentricity is larger than e CR, the value of
minimum ?V is increasing as the eccentricity is increasing. Thus it can be said that the better candidates
for searching are asteroids whose eccentricities are less than e CR. However, the value of minimum ?V
changes depending on the departure time in the case of small eccentricity. It means that large additional
?V is necessary when the departure time is delayed by some reason. Finally, it is concluded that the best
candidate is an asteroid whose eccentricity is e CR.
?u????”R—?’T???O“1?e—^?|?é???f?ˉ?O“1?ì—￡?S—|“á???v
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V–a‘è?e?μ?¤?B–ú?W???f?ˉ?O“1?ì?O“1’·”??a?a“ˉ?ê??? ?ê
?ê??–ê“à?é‘??Y?μ?A?C?“?p???X???—?e—p?￠??????
V—ê?a?ù?è?é?ì???A–{”-?\???í
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—￡?S—|?é’?–ú?μ???X?ü?’2?×???B???ì??‰ê?A?o”-?·?é’n?…?O“1???ú?·?é???f?ˉ?O“1?e—^?|?é—￡?S—|?????V—ê?a?‰?ú????ì??‘????a?ù?è?é?X?ü?a?|?3?ê???ì???????·?é?B
A?|?Q?P
?u Trajectory Analysis of Post-Hayabusa Asteroid Explorer Mission?v
*Y. Kawakatsu, H. Y amakawa, M. Abe (JAXA)
Reported in this paper is the status of the trajectory analysis of the asteroid explorer mission now under
study in JAXA/ISAS. In the previous symposium, we have reported the results of the preliminary
analysis to select the candidates of the target asteroids and the exploration sequence. The global search of
the targets and sequences in the space of the combinations of the ballistic trajectories and planetary
swing-bys successfully made clear the mission candidates suited our objective. Following the preliminary
analysis, the more detailed trajectory analysis is performed assuming the usage of electric propulsion,
and the results of which are reported in this paper.
?u???ú???f?ˉ’T???~?b?V???“?ì?O“1?v‰??ì??“￠?ó?μ?v
JAXA?j
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–{”-?\???í?A???ú???f?ˉ’T???~?b?V???“?ì??“￠?ì’????i?????￠?é?O“1?v‰??ì??“￠?ó?μ?e????·?é?B?”
E-?VEGA?ì?g—p?e‘z’è?μ???O“1?v‰?
?e??“￠?μ???ì???A???ì??‰ê?e????·?é?B
A?|?Q?Q
?u Mission Analysis of Asteroid Flyby Exploration by Miniature Asteroid Interceptors?v
*Y. Kawakatsu, O.Mori (JAXA)
Reported in this paper is the result of the mission analysis of asteroid flyby missions using miniature
asteroid interceptors. Two types of mission concept are considered. The first is a mission concept with an
interceptor boosted from GTO (geostationary transfer orbit) by small solid rocket motor (assuming the
piggy back launch of geostationary satellite). The second is a mission concept with four interceptors
loaded on a mother carrier spacecraft, launched together and released on orbit to target four different asteroids. The results of the trajectory analysis and operation sequence investigation are reported in the
paper.
?u???^’T???@?C?“?^?Z?v?^?é???é???f?ˉ?t
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–{”-?\???í?A
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?i?Q?j???^‘????@‘ì?é???è???”?ì?C?“?^?Z?v?^?e“ˉ???é‘??????°??C?“?^?Z?v?^?e‘????è?3?1?é?~?b?V???“?A
?~?b?V???“?A?ì?Q???ì?~?b?V???“?`‘??e‘z’è?μ?A?O“1?v‰??A‰^—p?V?i???I“??e??“￠?μ????‰ê?e????·
B‰???z Conference Room B
B?|?P
?u Tether Controlled Deployment Characteristics of Rotationally Skew Fold Membrane for
Spinning Solar Sail?v
*H. Furuya, Y. Inoue (T okyo Institute of T echnology)
The dynamic properties of the rotationally skew fold membrane are experimentally examined for
spinning deployment. Also, the deployment control mechanism with tether is proposed to avoid the
quick deployment. Finally, the deployment characteristics of uncontrolled and controlled deployment of
the rotationally skew fold membrane are discussed.
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?u Static Deployment Experiment of Large Membrane for Solar Sail Spacecraft?v
*O. Mori (JAXA), T. Nakano, K. Tarao (The University of T okyo), T. Saiki, Y. Tsuda, J. Kawaguchi (JAXA)
This paper shows the deployment of large membrane for solar sail spacecraft. The static deployment is
proposed with due consideration of the dynamic deployment of relatively small membrane using spinning
table and S-310 sounding rocket. In May 2005, we performed the experiment using a balloon to deploy
the membrane of 20m diameter statically. The detail results of the experiment are reported in this paper.
We also propose the experiment on the ice rink in order to demonstrate the deployment of larger membrane.
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?u Dynamics Analysis of Solar Sail Membrane Using Improved Multi-Particle?v
*Y. Tsuda, O. Mori (JAXA)
The improved multi-particle model, a fast yet rationally accurate computational method for solving the
dynamis of a thin flexible structure, is applied to the solar sail spacecraft planned in ISAS/JAXA. Some
numerical results and the comparison with the rocket and spin table experiments are shown in the