ON BALLISTIC ACQUISITION OF SHORT PERIOD
OUT-OF-ECLIPTIC TRAJECTORIES
「弾道飛行による短周期の高黄道面傾斜角軌道への移行について」
Jun’ichiro Kawaguchi,* Yasuhiro Kawakatsu,† Mutsuko Morimoto‡
and Justin A. Atchison§
This paper presents new orbital synthesis results to achieve ballistic and short
period out-of ecliptic trajectories, instead of using electric propulsion or solar
sail acceleration. The strategy developed utilizes a Jovian gravity first, followed
by polar very high speed gravity assists by Earth or Venus. So far, the use of
very high speed gravity assists has been conceived not practically useful.
However, this paper presents those still effectively contribute to amending the
trajectories periods, and to acquiring small sized out-of-ecliptic ballistic
trajectories. The biggest advantage of this strategy is to reduce propellant mass
carried drastically.
本論文は，純弾道飛行にて，短周期の対黄道面高傾斜角軌道を実現する
手法について，とくに木星を利用する場合について述べる．
INTRODUCTION
ULYSSES spacecraft launched in 1990 successfully has observed solar polar region from
high solar latitude. It is well known that the trajectory of it first made use of a Jovian gravity
assist to attain a highly inclined orbit with respect to the ecliptic plane. Intensive scientific
demand in pursuing such highly inclined orbits has been shown to the orbit synthesis community.
The demand is not only in helio-physics observation but also in the astronomy that is eager to get
out of the solar system dust cocoon. It shall be stressed here that such scientific demand at the
same time requests the orbital period had better be as shortest as possible to have frequent
observation opportunities. This study was motivated by the helio-physics scientists who desire the
polar region observation of the Sun much more frequently than that performed by the Ulysses
spacecraft.
Recent studies about the nearest star, the Sun, has intrigued the solar physics scientists to
have more intimate and high latitude observation of it. The Solar Orbiter mission concept has
been investigated in Europe for years, and it assumes the trajectory strategy of using multi-Venus
gravity assist instead of the Jupiter. It is mainly due to the preference that science observation be
commenced as quickly as possible, and has tried to avoid extra flight period prior to it. The
trajectory synthesis for the Solar Orbiter was well performed to access the Sun very closely with
relatively higher latitude [1]. The Solar Probe+ mission has been studied at NASA to have a
similar observation of the Sun through also repetition of Venus swingbys. The purpose of the
Solar Probe+ mission is relatively to reduce the distance to the Sun rather than acquiring higher
solar latitude [2].
*
Professor, ISAS, Japan Aerospace Exploration Agency (JAXA), Sagamihara, Japan 229-8510.
Associate Professor, ISAS, Japan Aerospace Exploration Agency (JAXA), Sagamihara, Japan 229-8510.
‡
Project Researcher, JSPEC, ISAS, Japan Aerospace Exploration Agency (JAXA), Sagamihara, Japan 229-8510
§
Post-Graduate Student, Cornell University, Ithaca, New York, 14853.
†
The paper aims at finding suitable highly inclined orbits with short period which shall be
devised for the SOLAR-C mission of Japan Aerospace Exploration Agency (JAXA). The
SOLAR-C is the mission following its predecessor SOLAR-B ('Hinode') that has been orbiting on
a Sun Synchronous Orbit around the Earth, and made a great success in observing the nearest star,
the Sun by first detailed close-up of the surface structure. The solar physics community intends to
have much more new discoveries by putting an observatory on a highly inclined orbit with
respect to the ecliptic plane, while it should have a short period that enables the spacecraft to have
multiple observation opportunities during its mission duration. Besides, acquiring the orbit had
better not consume propellant to carry as much payload as possible. In conventional planetary
missions, these two requirements contradict with each other, and finding a solution has never
been successfully done so far. The orbit that the Ulysses mission adopted does not fit for this
purpose. To this end, an international workshop was held at JAXA on November 18th to 21st of
2008, when the idea this paper describes here was devised and presented.
Despite the successful orbit synthesis in both the Solar Orbiter and the Solar Probe+, the
solar latitude in them is not made very high. Besides, since the distance to the Sun is designed
very close, the observation period length is in turn diminished. And the heat flux problem occurs
from such close distance, and the heat shield protection mass increases significantly for them.
From both the observation length and the heat flux points of views, the trajectory sought had
better be highly inclined while the distance to the Sun be kept beyond a certain distance,
preferably around Earth distance.
Many investigations have been performed so far as to the orbit alteration syntheses via
solar sailing. Actually, pure photon sail propulsion is perfect in terms of propellant consumption,
if the cruise period is enough long. However, the authors think such photon sail is useful only for
smaller spacecraft that have ultra low ballistic coefficient in terms of solar radiation pressure.
And the authors also think solar sails, if appear, will had better make use of hybrid propulsion
(Solar Power Sail) taking the advantage of large membrane solar cell technology driving ultra
high performance electric propulsion combined with photon propulsion. For instance, if 50% of
mass can be devoted for the propulsion system element, such the mass of ultra high Isp electric
propulsion well replaces that of the sail membrane mass plus the associated mechanism mass.
About the Application to larger spacecraft, pure photon sails are less advantageous over
either of Electric Propulsion or hybrid Solar Power Sail Propulsion. Developing and application
of pure photon sail may not be demanded when the flight period is evaluated from the mission
analysis point of view. Besides, high resolution telescopic observation does not fit for the
spacecraft that carries large flexible parts and always changes its attitude. As a result, typical
photon solar sail technology was given up for the application to the SOLAR-C mission. However,
what this paper presents does not rely even on the use of Solar Power Technology, either, since
the method presented here does not assume any scheduled delta-V at all, and it successfully
results in, as it were, the most optimized mission configuration in terms of propellant
consumption.
The gravity assist, in other words, swingby that this paper adopts is not special but
literally conventional. However, this technique does not seem to have been introduced for
acquiring the short period out-of-ecliptic trajectory by now. It is primarily due to a-priori
conception as to 1) High velocity swingby cannot bend its velocity direction and not effectively
useful, 2) Swingbys have been conceived as the means to make the velocity direction aligned or
normal with respect to the revolution orbital velocity direction of the planet used, and 3) Ballistic
swingby that occurs at the same location does not provide any orbital energy gain.
Fig. 1a Gravity Assist Geometry
Fig. 1b Repetition of Gravity Assists
The in-and-out velocity geometry is drawn in Fig. 1a, when the spacecraft makes an
Earth swingby after the inclination is made erect by the Jovian gravity assist. Note the horizontal
axis corresponds to the ecliptic plane, and vertically out-of-ecliptic axis is taken. The purpose of
the swingby here is to make the resulted velocity VF smaller that that of the original velocity V0.
It is accomplished by bending the relative velocity VREL relative to the Earth, by . It shall be
noted that this process never reduces the inclination angle, rather makes the inclination even
higher. The repetition of this process is possible, if the resulted orbital velocity VF is tuned to
have synchronism with respect to the revolution period of the Earth. This multiple process is
drawn in Fig. 1b. As in the usual ballistic gravity assist process, the relative velocity with respect
to the Earth is preserved throughout this trajectory alteration, and no propellant is required.
In the SOLAR-C mission, common to the Solar Probe+ and the Solar Orbiter, what is of
significance is in the 1) Resolution in polar region of the Sun. Both reduction of the distance to
the Sun and higher solar latitude contribute to enhance the resolution. However, there seem two
other important parameters: 2) Heat Flux impact to both the spacecraft and the sensors, 3)
Observation Period. Both the heat flux and the angular velocity of the orbit are inversely
proportional to the square of the distance to the Sun. And the latter two requirements results in the
same specification. This implies the enhancement of the resolution shall be pursued by making
the inclination higher maintaining the distance form the Sun above a certain limit. The method
proposed here can comply with these requirements.
The trajectory sequences this paper presents are summarized as follows:
[1] Strategy-1 (Seq.-1)
C3: 106 km2/s2, 78deg, 1 (1.0) AU in 13 years, 73 deg, 1.1 AU in 10 years.
[2] Strategy-2 (Seq.-2)
C3: 90 km2/s2, 39deg, 1 (1.0) AU in 7 years.
[3] Strategy-2+, -2+U(pper) (Seq.-2+, Seq.-2+U)
C3: 90 km2/s2, 39deg, 1AU in 7 years, 41 deg, 0.52 (0.7) AU in 8 years,
41 deg, 0.26 (0.4) AU in 10 years.
[4] Strategy-2+V(enus) (Seq.-2+V)
C3: 90 km2/s2, 49deg, 1AU in 11 years, 45 deg, 1.6 (1.0) AU in 8 years,
50 deg, 0.9 (0.8) AU in 13 years.
The distance numbers above indicate the aphelion / perihelion distance. Note the other
aphelion / perihelion distance is not shown but 1 AU, since the spacecraft makes swingbys with
the Earth. [Aphelion distance when perihelion is at Earth distance (1AU), or perihelion distance
when aphelion is at Earth distance (1AU).] And the numbers in parentheses the distance of semilatus rectum that represents the distance between the spacecraft and the Sun when the spacecraft
passes over the Sun. Except Strategy-2+U, the next chapter describes the details of them, while
the chapter 3 will lead to the discussion on Seq.-2+U.
The Table-1 below lists the most primitive idea about synchronized Earth swingbys that
reduce the aphelion distance at the cost of propellant mass. Here, the swingby altitude is taken
1,000 km beyond the surface, and here is assumed the 3 km/s delta-V is applied at perigee
passage. As circled, when the inclination takes 80 to 85 degrees, the resulted orbital period is
reduced down to 2 years from the period of Earth-Jupiter ellipse. Note still aphelion distance is a
little far than 2 AU.
This is itself an idea to attain the short period out-of-ecliptic trajectory via the
combination of Earth gravity assist and the propulsion. This is known as a Powered Swingby
technology. Both tables suggest shortening the period to 2 years with very high inclination
requires 3 km/s delta-V, in which fuel occupies almost two thirds of the spacecraft. It is hardly
practical and the results assuming the propulsive means were given up fro the SOLAR-C mission.
Table-1 Use of a Single Powered Earth Swingby
BALLISTIC TRAJECTORY ALTERATION - REPETITION OF GRAVITY ASSISTS
As the previous chapter described, what this study pursues is a ballistic multiple
synchronized swingby to accomplish making the period shorter while the inclination is retained
still high. When the delta-V amount is set zero with the swingby altitude retained as 1,000 km,
the resulted orbital parameters are listed in Table-2.
Table-2 Use of Ballistic Gravity Assist for Synchronization
There are found two special inclination angles, 30.24 and 64.85 degrees, both of which
result in the synchronous orbit with respect to the Earth. The orbital periods are 2 years and three
years sharp, and the spacecraft will make another encounter with the Earth again. Corresponding
aphelion distances are 2.2 and 3.2 AU much shorter than the Jupiter's distance. Even by these
scenarios up to this point, the strategies look enough attractive since the process is propellant free
with shorter period resulted. However, as for the polar observation of especially the Sun, they still
suffer from few observation opportunities, even though the chance of observation is much
frequent in this strategy than that in Ulysses. Here is an idea about making the spacecraft swingby
again so that the resulted orbit can further have synchronism with the Earth.
The control means to adjust the period is the swingby altitude as well as the delta-V
performed at the swingby, in other words, powered swingby. In this example, fortunately no
delta-V is required, but adjusting swingby radius (altitude) suffices to control the orbital period
resulted. Note the inclination angle becomes even higher, reaching to 73 degrees in the end. Seq.2+ ends in the inclination of 39 degrees and the perihelion distance is reduced to 0.27 AU. These
illustrations show that these multiple ballistic synchronized swingbys efficiently converts the
orbit energy originally possessed by the Jupiter to the inclination angle, with small delta-V
amount. These analyses are based on circular ephemeris as for the planets, and the discussion is
simplified, while later illustration will refer to the actual planetary ephemeris.
Distance to Sun
Distance to Earth
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1.2E+09
1.0E+09
8.0E+08
6.0E+08
4.0E+08
2.0E+08
0.0E+00
Fig.-2 Scenario A_Ballsitic-1: Distance to Sun and Earth for 78deg, 1AU
Fig. 3 Strategy A-Ballistic-1
The orbit synthesis is performed through a conventional patched conics approach
technique, referring to the actual ephemeris incorporated. Fig. 3 above shows the history of the
distance to the Sun in Seq.-1. As it represents the distance to the Sun is kept 1 AU beyond 13
years later after launch, and the distance to the Earth periodically takes zero when the spacecraft
makes swingbys with the Earth. Fig. 4 presents the bird view of the trajectory.
Table-3 Use of Venus instead of Earth
Fig. 4 Use of Venus instead of Earth
Table-4 Summary of Ecliptic Inclination, Aphelion Distance History
Red line shows the loci of the Jupiter and green line draws the Earth orbit. Light blue line
is the equinox nodal line. Seq.-1 computed results in no scheduled delta-Vs and the flight is
purely ballistic as the preliminary analysis concluded. Fig. 5 shows the history of the distance to
the Sun in Seq.-2.Similar technique is also applicable assuming the gravity assist by Venus. The
velocity sensitivity to the orbital period is higher than that in Earth gravity assist, and the initial
inclination rises up steep quickly, if Venus is used.
Rotation Coordinate
Inertial View
1 109
1 109
5 108
5 108
Jupiter
Earth
0
0
-5 108
-5 108
Spacecraft
-1 109
-1 109
-5 108
0
5 108
1 109
Fig. 5a Inertial Plot for Seq.-2+U Orbit
-1 109
-1 109
-5 108
0
5 108
Fig. 5b Rotation Plot for Seq.-2+U Orbit
1 109
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50
40
30
20
10
0
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Solar Latitude
As easily extended, there might be further idea to use Venus for the Seq.-2+U that takes
upper flight path beyond the ecliptic plane after the Jupiter swingby. The merit anticipated is, first
of all, increased frequency in observing the polar region of the Sun from high elevation angle.
Actually, there exists such a sequence, and here it is designated as Seq.-2+UV. The details are
similarly taken as to the discussion so far. In Fig. 6, similarly, the history of the solar latitude and
the resolution index are drawn. The solar latitude reaches to 50 degrees or higher in ten years.
This sequence is one of the best realizations of the technique developed in this paper.
Date
Fig. 6 Solar Latitude in Seq.-2+UV
While expected so beneficial, this sequence results in not significantly good scenario.
First of all, as the perihelion distance diminishes down to the Venus distance, the swingby
velocity at Jupiter needs to be higher than those discussed by now. This leads to the higher launch
energy that reduces the spacecraft mass. Therefore, from payload amount point of view, this
sequence is not advantageous over the others. And the swingby altitude restriction at Venus and
the reencounter periodic constraints prevent the sequence from taking efficiently reduction of
aphelion distance, and it results in not significantly frequent observation of the polar region of the
Sun during short flight period. Since the distance to the Sun is reduced to the Venus distance
lower than Earth orbit, high resolution index figure is anticipated. The figure may be improved
slightly, however, the difference is not significant. Besides, it should be stressed that there is the
big technical hurdle in this sequence relating to the navigation issue.
Fig. 7 Orbital Illustration of Seq.-2+UV
The swingby requires precise altitude control, as discussed. If the spacecraft approaches to the
Earth, the distance is enough close to have a satisfactorily high navigation accuracy even though
the approach speed is high and data length available reduces. However, as to the high speed
swingby at Venus is very difficult. This is simply accounted for by looking at the distance from
the ground stations. Via the Delta-VLBI technique, if enough data length is assured with slower
approach speed, the contemporary navigation accuracy provides the navigation accuracy of about
a few nano-radians that correspond to a few to several kilometers in terms of swing by altitude.
However, since the approach speed is very high in this sequence, enough delta-VLBI data amount
may not be available. And also the Venus position accuracy itself needs to be enhanced, since
there is no station on the Venus. If a certain Venus orbiter is available, the accuracy may be
increased, however, it is too challenging and the sequences with Earth swingbys are found more
practically feasible. The bird view of the trajectory is drawn in Fig. 7.
CONCLUDING REMARKS
This paper so far has discussed about the orbit synthesis results through devising the
multiple ballistic synchronized gravity assist technique for out-of-ecliptic trajectories. The gravity
assist is provided by either the Earth or the Venus. What this paper presented is a special
sequence excluding almost any scheduled delta-V and it is ballistic. No investigation has ever
looked at this beneficial aspect by now. Most of past researches assumed: High speed swingby
can not bend the velocity direction a lot, and has assumed such swingby is practically useless.
And while in-plane swingby has been studied to alter the orbital velocity, out-of-plane swingby
has not been thought to control the velocity magnitude efficiently. There has been a notion that
conventional low speed swingbys performed at the same position, even if repeated more than
once, may not be practically utilized since no velocity gain is expected, and that that qualitative
discussion also holds in high-speed swingbys. This paper presented an idea to have a new path to
the short-period, out-of-ecliptic trajectories through purely ballistic sequences breaking these
notions. It starts from a kind of extended Delta-V Jovian Gravity Assist, which amplifies the
launch investment, in other words, the launch delta-V added to the Earth revolution velocity,
several times when it re-encounters with the Earth. The energy surplus is the primary energy
source to lower the aphelion distance that results in shorter semi-major axes length, at the same
time leads to shorter period around the Sun. In this strategy, the orbital velocity is reduced by the
Earth or the Venus gravity assists at the cost of inclination angle that is made steeper against
anticipation. It is a bi-product of this method. Most of the swingby applications have looked at
how the outgoing velocity (V_infinity) be aligned or normal to the revolution velocity direction
of the celestial body used for the gravity assist. However, the strategy developed here devises a
new method of reducing the orbital velocity by taking the advantage of laying out the outgoing
escape velocity rather normal to the spacecraft's orbital velocity so that the resulted orbital
velocity can be diminished efficiently. In the past, most of investigations have been concentrated
to the use of propulsion represented by electric and photon propulsion means in order to make the
inclination higher, while the distance to the Sun is assumed retained. In those methods, there is no
ballistic orbital energy surplus and propulsion investment is essential. What this paper presents is
a new way in which the initial investment is poured to make the spacecraft fly for Jupiter, so that
the Delta-V Jovian Gravity Assist can amplify the initial investment several times. The repetition
of multiple ballistic synchronized swingbys efficiently spends the energy surplus gradually. It
should be stressed here that the inclination angle is rather made steep through the process as a
biproduct. When the spacecraft configuration is analyzed, in most of planetary spacecraft,
propulsion element including propellant occupies the major portion of the mass of the spacecraft
and typically the mass fraction concerning the payload is usually limited down to 10% or so. It is
completely different from that in case of satellites in low Earth orbit, in which the payload mass
fraction sometimes exceeds 30% or more for those applications. The difference observed is due to
the orbit amendment cost performed to make the spacecraft into orbiters or landers from
reconnaissance flight. In the new sequences developed here, surprisingly the orbit synthesis is
devised with no scheduled delta-V, and the spacecraft does not have to carry a lot of propellant
aboard, and the propulsion is not a big mass driver any more. Therefore, even though the
sequence presented here is a planetary mission, the payload mass fraction will reach even to 30%
or more, which is hardly expected for the past investigations trying to utilize the propulsion to
make the orbital plane inclination higher. This is the biggest advantage extracted through the
sequence of the paper.
As discussed in the previous chapters, from the heat flux and observation duration points
of views, the distance to the Sun is not arbitrarily taken short, but is constrained maintained above
a certain distance. As a consequence, in order that the polar observation can be done, the
inclination angle or solar latitude has to be made higher simply.
The paper discussed another sequence with higher elevation once beyond the Jupiter
gravity assist, if the ascending node of the trajectory is chosen appropriately. The sequence Seq.2+U in this paper provides 45 degrees solar latitude in seven years with almost no propellant
consumption. In this paper, the advantage of the rotation axis direction of the Sun is combined
with the use of Venus. It is designated Seq.-2+UV, one of the best realizations in the applications.
It makes 50 degrees in terms of solar latitude in 10 years, and higher than 50 degrees later, only
through purely ballistic flights.
The sequence presented adopts conventional and classical ballistic swingbys, however,
there is found a new and practical path to achieve the out-of-ecliptic flight that has been
conceived a hard mission so far.
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