An Orbit Plan of AKATSUKI to Avoid Long Eclipse on Venus Orbit
Yasuhiro Kawakatsu (ISAS)
Abstract
AKATSUKI, the Japanese Venus explorer, is now on its way to re-encounter Venus in 2015. However, due to a
malfunction in the propulsion system, AKATSUKI can be only injected into an orbit much higher than that originally planned. It causes an issue of long eclipse, which is the main topic of this paper. This paper introduces an
orbit design strategy to avoid the long eclipse. An example of design result is shown as well.
金星周回軌道上での長期間日陰の回避を考慮した「あかつき」の一軌道計画
川勝康弘 （ISAS）
摘要
金星探査機「あかつき」は、2015 年の金星再会合を目指し、惑星間軌道を航行中である。しかし、事故により主
エンジンが使用できなくなったため、投入後の金星周回軌道が当初計画より大きくなる見込みであり、いくつかの
課題が生じている。本論文では、その一つ、長期間日陰の回避を考慮した軌道計画方法についての一考察結
果を紹介する。
AKATSUKI into the orbit around Venus by use of RCS.
However, the apocenter of the resulting orbit (about 50
Venus radius ( Rv )) is much higher than that of the originally planned scientific observation orbit (about 13).
The mission objective of AKATSUKI is to investigate
the climate and atmospheric phenomena of Venus. Fortunately, most of the scientific instruments are healthy,
and once it starts the operation at Venus, it is expected to
achieve most of its scientific objectives. The operational
orbit around Venus is chosen to meet this objective, and
is set near to the equatorial plane of Venus, which is near
to the orbit plane of Venus as well. The spacecraft system
design is optimized to this orbit condition, and if it is
located on the orbit highly inclined to this plane, the observation period is strongly constrained, which results in
the serious degradation of the science outputs. Accordingly, we are to inject AKTSUKI into a low inclined orbit as we planned in the beginning.
The combination of the higher apocenter and the low
inclination causes a couple of issues to be considered in
its orbit operation around Venus. One of them is rapid
1. Introduction
AKATSUKI, the Japanese Venus explorer, was successfully launched in May, 2010 to investigate the climate and atmospheric phenomena of the Venus. It was
originally planned to be injected into the orbit around
Venus in December, 2010, at its first approach to Venus.
However, due to a malfunction in the propulsion system,
the orbit injection was failed and AKATSUKI escaped
Venus into an interplanetary orbit. We made up the orbit
plan to reencounter the Venus, and successfully performed deep space maneuvers in November, 2011. Now,
AKATSUKI is on its way to reencounter Venus in November, 2015 (Fig. 1).
The test maneuvers conducted prior to the deep space
maneuvers show that the bipropellant orbit maneuver
engine (OME) is already out of use. Now, the only
available propulsion system onboard is the monopropellant reaction control system (RCS). Although the performance (thrust and specific impulse) of RCS is lower
than that of OME, it is estimated that we can inject
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this paper is briefly introduced. It is an important precondition for the discussion proper setting of the initial
condition. In the second subsection, the requirements on
the orbit around Venus are defined with respect to the
orbit inclination and the eclipse duration. Finally, the
problem is defined concisely for the following discussion.
drop of the pericenter due to solar gravity perturbation. A
method was proposed by the author to cope with this
issue and presented in Ref. 2. Another issue is long
eclipse, which is the major topic of this paper.
The capacity of the onboard battery permits the eclipse
duration shorter than 90 minutes. As a matter of course,
the condition was met in the originally planned orbit.
However, the new orbit around Venus is larger than the
original one and its orbital motion is slower. It makes it
severe to suppress the length of the eclipse duration. The
limitation in the orbit maneuver capability and the requirement on the low inclination strongly constrain the
design space of the orbit. The solar gravity perturbs the
orbit gradually, which does not permit to maintain good
geometrical condition for long years.
The objective of this paper is to introduce an orbit design method to avoid the long eclipse under this situation.
The basic concept of the method is the combination of
phase control and proper setting of the initial condition.
In this paper, the former is clarified in in major.
The paper is composed in the following manner. In the
first section above, the background and the objective of
the paper is briefly introduced. In the next coming second section, the problem setting is defined. The profile of
the interplanetary flight assumed in this paper is briefly
introduced as a precondition of the discussion. The requirements on the orbit design (inclination, eclipse duration) are defined in this section as well. In the third section, the aspect of long eclipse is introduced using an
example. The concept of phase control is introduced in
this section as well, and the effectiveness and limitation
of the method is clarified. Finally, the findings in the
discussion are summarized in the conclusion.
2.1 Interplanetary Flight Profile
AKATSUKI is going to reencounter Venus in November, 2015. It is natural to inject AKATSUKI into the
orbit around Venus at this first opportunity. However, the
change of situation prevents us from adopting this simple
procedure. If it is adopted, the higher apocenter of the
orbit around Venus results in rapid drop of the pericenter
due to solar gravity perturbation. A couple of methods
are proposed to overcome this issue.
The interplanetary flight profile assumed in this paper
is based on the method proposed and presented by the
author in Ref. 2, which uses a Venus swingby (VSB) and
a Venus synchronous orbit (VSO) (Fig. 2). The rapid
drop of pericenter results from undesirable geometrical
relation between the orbit and the Sun, which is originated from the AKATSUKI’s approach direction to Venus. The concept of the method is to inject AKATSUKI
into VSO (1:1 Venus resonant orbit) by way of VSB at its
first Venus reencounter, which results in the approach
from desirable direction at its second Venus reencounter
one Venus year later (Fig. 3). Please find the detail of the
method in the reference.
There is one degree of freedom in choosing VSO.
However, in case of AKATSUKI, the low inclination
requirement on its orbit around Venus constrains the
VSO to those lie nearby the orbit plane of Venus. As a
result, two groups of VSOs are available for this method,
and they are named “leading orbit” and “trailing orbit”
(and colored orange and green) in Fig. 2. Between them,
“trailing orbit” case assumed as the interplanetary flight
2. Problem Definition
To be provided in this section is the definition of the
problem to be discussed in this paper. In the first subsection, the profile of the interplanetary flight assumed in
2
To satisfy these two requirements simultaneously is
the necessary condition for AKATSUKI’s safe and satisfactory operation on its orbit around Venus. And to
maintain this condition as long as possible is the goal of
this study. Under this serious situation of AKATSUKI,
there is no clear criterion on the period of the condition
maintenance. However, I want to provide the number “2
Earth years” as a reference, which was planned in the
beginning of the mission.
profile in this paper.
Now, the possible apocenter of the orbit around Venus
is much higher than that originally planned. Under this
situation, for the sake of maximizing the science outputs,
we give priority to inject AKATSUKI into lower (and
short period) orbit as possible. Accordingly, we are to use
most of the remaining propellant at VOI, which is equivalent to approximately 270m/s of v . As a result, only
small maneuvers for orbit adjustment are acceptable after
VOI (approximately 20m/s of v in total).
2.3 Summary of the Problem Definition
The problem definition is summarized as follows.
2.2 Requirements on the Orbit around Venus
The mission objective of AKATSUKI is to investigate
the climate and atmospheric phenomena of Venus. The
operational orbit around Venus is chosen to meet this
objective, and is set near to the equatorial plane of Venus,
which is near to the orbit plane of Venus. The spacecraft
system is designed to this orbit condition. The y axis of
the body is directed perpendicular to the orbit plane, and
the spacecraft rotates slowly around the y axis in accordance with its orbital motion. The location of major
components, such as scientific instruments, solar array
paddle, radiation panel, reaction wheels, is set based on
this configuration. This configuration requires the spacecraft to be placed in low latitude region to observe Venus.
Otherwise it cannot direct the science instruments to Venus. Hence, if it is located on the highly inclined orbit,
the observation period is strongly constrained, which
results in the serious degradation of the science outputs.
From this aspect, 13deg. is set as the upper limit for the
orbit inclination, which is defined with respect to the
orbit plane of Venus.
The length of eclipse is constrained from the capacity
of the onboard battery. It constrains the duration of total
eclipse (umbra) to be shorter than 90min. In actual, the
length of partial eclipse (penumbra) should be considered
as well, however, it is not dealt with in this paper due to
the lack of information on its criterion.
Maintain the conditions below as long as possible
• orbit inclination ( imax )
< 13deg.
• eclipse duration ( decl )
< 90min.
under the conditions
• use the sequence of VSB/VSO as the interplanetary flight profile.
• use only small adjustment maneuvers after VOI.
3. Long Eclipse and its Shortening by Phase Control
In this section, the aspect of long eclipse is introduced
and its characteristic is investigated. The effect of
changing orbit period is clarified, and is applied to
shorten eclipse duration as the concept of “phase control”. In the first subsection, an orbit example is used to
show the profile of the orbit and eclipse. Well known
“solar direction fixed rotational coordinate frame” is
used to explain the characteristics of the phenomenon.
The effect of changing the orbit period is discussed qualitatively in this context. The quantitative evaluation of
the effect on eclipse duration is introduced in the beginning of the second subsection. The effect is utilized to
shorten eclipse duration as the concept of “phase control”, which is the major topic of this paper. The effectiveness and limitation of the phase control is discussed
in this subsection.
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theme here (the eclipse profile) is small.
Fig. 4 shows the profile of long eclipse (longer than
30min) experienced in one Venus year. A bar corresponds
to a single eclipse. Its horizontal location of the bar
means the center time of the eclipse, and the height of
the bar means the length of the eclipse duration. The
eclipse cycle is not uniform and has a strong peak (over
500min) in the middle of the profile (about a half Venus
year from VOI). In the profile, 7 eclipses have the duration longer than 90min. Hence, this example orbit obviously violates the requirement.
Fig. 5 shows the orbit profile projected on the xy
plane of the solar direction fixed rotational coordinate
frame. The frame is popular in the field of interplanetary
mission analysis. Its x axis is in the direction of Venus
viewed from the Sun, z axis is in the direction of the
orbit angular momentum of Venus, and y axis is defined to form a right-handed system. The origin of the
frame is Venus. Since Venus revolves around the Sun in a
counterclockwise direction, the inertial fixed orbit revolves clockwise in the frame once in a Venus year. On
the other hand, the direction of the Sun is fixed to  x
direction, and accordingly, the shadow of Venus extends
to  x direction (note that the shadow is described in a
cylinder model, and it is not true in the far distance from
Venus). The eclipse duration get longer in case that the
shadow intersects with the apocenter side of the orbit
where the orbital motion is slower. The apocenter of the
orbit initially located in  x direction of Venus revolves
to  x direction in a half Venus year. In this area, the
apocenter side of the orbit passes through the shadow
which results in long eclipse. This is the reason why the
peak of eclipse duration is observed in the middle of the
profile, about a half Venus year from VOI.
Fig. 6 (a) shows a closes up of the previous figure
around the extremely long eclipses. That is, 8th (182min),
9th (543min), and 10th (235min) long eclipse in Fig. 4.
Thick black lines on the orbit denote the eclipse sections,
which is calculated and described based on a conic model of Venus shadow. In Fig. 6 (b), the same information is
3.1 Long Eclipse on the Orbit around Venus
In order to provide an overview of the long eclipse
phenomenon, an example of an orbit profile around Venus is presented. The orbit is the sequel of the interplanetary flight path presented in Fig. 2 as “trailing orbit”.
The sequence of events in the interplanetary flight is
listed in Tab. 1, where v is velocity increment, and
rp , B are the pericenter radius and the argument of
ballistic parameter at the Venus approaches respectively.
The terminal of the sequence provides the initial condition of the orbit around Venus. The initial values of
orbital elements are listed in Tab. 2. The subscript ‘0’
means that the values are of the initial point. The elements to determine the orientation of the orbit, i ,  ,
and  are measured from an inertial frame defined
based on the orbit of Venus at J2000.0. Its Z axis is in
the direction of the orbit angular momentum, X axis in
the direction of Venus viewed from the solar system
barycenter, and Y axis is defined to form a
right-handed system. The orbit is propagated for one
Venus year (about 225 days) from the initial condition. In
actual, a small pericenter raising maneuver is required in
order to avoid the spacecraft’s crashing on the surface of
Venus, however, it is neglected here. Its effect on the
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projected on the yz plane of the same coordinate frame.
The shadow of Venus in a cylinder model is described as
a circle in this projection. Dots on the eclipse sections are
marked for every 30min.
These two figures well indicate the complexity inherent in the eclipse analysis of an inclined long elliptic
orbit. For example, the geometrical length of an eclipse
section cannot be easily determined from either of the
views because of the three dimensional structure of the
orbit and the Venus’s shadow. The estimation of the
eclipse duration is more difficult, since the difference of
the orbit velocity by the position must be additionally
taken into account. Hence, numerical simulations are
practically the only effective way to analyze the eclipse
in an inclined long elliptic orbit quantitatively.
On the other hand, meaningful qualitative analysis is
possible by use of these figures. As an example, I want to
discuss the effect of slightly changing the orbit period.
The orbit period can be changed by small maneuver at
the pericenter. If the orbit period is extended, the intervals between the orbits in Fig. 5 are stretched, and each
orbit revolves clockwise in the figure. Its effect on the
eclipse duration can be discussed in Fig. 6 (a) by revolving the orbits clockwise (or equivalently revolving the
shadow counterclockwise). To focus on the longest
eclipse (#9), the revolution shortens the eclipse section
slightly, and moves the section near to the pericenter
where the orbital velocity is faster. The both effects lead
to the shortening of the eclipse duration. In Fig. 6 (b), the
revolution moves the orbit to the right hand side (or
equivalently moves the shadow to the left hand side).
This motion raises the eclipse section slightly to  z
direction where the radius of the shadow is slight shorter.
It leads to the shortening of the eclipse duration as well.
From the analyses using Fig. 5 and 6, at least qualitatively speaking, we can conclude that the change of the
orbit period is effective to shorten the eclipse duration.
3.2 Phase Control to Suppress Eclipse Duration
Following the qualitative discussion in the previous
subsection, the effect of changing the orbit period is
evaluated quantitatively by way of numerical simulations.
Using the initial condition listed on Tab. 2, a small acceleration maneuver is imposed at the initial pericenter
(i.e. the beginning of the propagation). Since the deceleration maneuver for VOI is performed just before, the
addition of a small acceleration maneuver is equivalent
to the small reduction of the VOI v , which results in
the slight extension of the orbit period. The orbit is
propagated for one Venus year, and the duration of the
longest eclipse is recorded. The results for various
(from 0 to 10m/s) of the maneuver are plotted in Fig. 7.
Obviously, the longest eclipse duration strongly depends on the v imposed, or in other words, on the
orbit period. For example, the longest eclipse duration of
543min in Fig. 4 (which coincides with the value at v
of 0 in Fig. 7) is reduced by 170min by merely adding
2m/s of v at the initial pericenter. Fig. 8 shows the
eclipse profile of this minimum case. From this result, it
is concluded that the change of the orbit period is seri-
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ously effective to shorten the eclipse duration. The
method is called “phase control” hereafter.
Although the longest eclipse duration is largely reduced by use of phase control, the result also indicates
the limitation of the method. Fig. 8 shows that the phase
optimized orbit still has 8 eclipses whose duration is
longer than 90min. That is, the phase control is necessary,
but not sufficient. This limitation of the method is determined from the initial condition of the orbit which is
defined in Tab. 2. In order to achieve further shortening
of the eclipse duration, proper setting of the initial condition is necessary.
5. Conclusion
AKATSUKI, the Japanese Venus explorer, once failed
to inject itself into an orbit around Venus in 2010.
AKATSUKI is now on its way to re-encounter Venus in
2015. However, due to a malfunction in the propulsion
system, AKATSUKI can be only injected into the orbit
much higher than that originally planned. It causes a
couple of issues to be considered in its orbit design
around Venus. One of which is long eclipse, which is the
main topic of this paper. An orbit design method is exploited to avoid the long eclipse under this situation. The
basic concept of the method is the combination of phase
control and proper setting of the initial condition. The
former is clarified in this paper in major, and its effective
ness is shown quantitatively. The results also show that
the only use of phase control is not sufficient to satisfy
mission requirements. It is necessary to further shorten
the eclipse duration by proper setting of the initial condition.
References
[1] Sakao, T., Solar-C Study Team. : Overview of the
next Solar Observation Mission following ‘HINODE’,
The 8th ISAS Space Science Symposium, 2008, S2-18.
[2] Macdonald M., Hughes G., McInnes C., et al. : Solar
Polar Orbiter: A Solar Sail Technology Reference Study,
Journal of Spacecraft and Rockets, Vol. 43 (2006), pp.
960-972.
[1] Nakamura M., Imamura T., Ishii N., et al. : Overview
of Venus Orbiter Akatsuki, Earth, Planets and Space, Vol.
63 (2011), pp. 443-457.
[2] Kawakatsu Y., Campagnola S., Hirose C., Ishii N. :
An Orbit Plan toward AKATSUKI Venus Re-encounter
and Orbit Injection, Advances in the Astronautical Sciences, Vol. 143 (2012), pp. 1535-1547.
[3] Hirose C., Ishii N., Kawakatsu Y., Ukai C., Terada
H. : The Trajectory Control Strategies for AKATSUKI
Re-insertion into the Venus orbit, 23rd International
Symposium on Space Flight Dynamics (2012).
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