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Small universal space platform: Mission capabilities
Pergamon PII:
Acta Asrronautrca Vol 39, No l-4. pp 181-188. 1996 CopyrIght II 1997 Pubbshed by Elsewer Saence Ltd Pruned m Great Bntam. All nghts reserved 0094-5765!96 $15.00 + 0.00 SO@‘Q5765(%)00135-X
SMALL UNIVERSAL SPACE PLATFORMz MISSION CAPABILITIES V. Baiebanov*, G. Fedotov**, V. Kim***, M. Konstantiuov**, V.Kostenko’, M. Pivovarov.*, V. Petukhov**, G. Popov***, A Sukhanov* *
** ***
Space Research Institute 0, Moscow, Russia Moscow Aviation Institute (MAI), Moscow, Russia Research Institute of Applied Mechanics and Electrodynamics of MAI (RUMI MAX),Moscow, Russia
ABSTIUCT 7he rcs&sof missionanalysi3for s.nA univ& space @tf6rm withplasmatbuster (SUSPPT)developedon base ofmodantechnologylcvdarepnsartedinthe~.Thesertsultsshowthatitis~ltto~SUSPVTorbit raising(tkomLEOtotheorbitofsomehund&oft&sands kmheightwiththechangeoforbit~aulWumto LEo),to~~thescientificpayloadtotfaeMoon~arbittoreachtfieEarth-Moonmd~-~tibpation point%nearsalth 8stcroid!s(_)* ie.torealkedi&rentkindsofinttx4ng~adoonmnerdrl mipsiona.Astheclectricpopulsion~~banchosenthe~~stationaryplasma~(s~~ m~ytimesflo~andusedinrpsoe.Ifigh~impubeof~tfuustaincombinationwiththe~sakranays atlowto reach highlevelof space transportahon ’ systan efficiency.For example,SUSPPT,whichinitialmass is 2002% kg in the LEO, can deliver 30-70 kg scientificpayloadto a near-Earthasteroid. CopyrIght
NOMENCLATURE SUSPPT
Tl
small-space platfolm
with plasma
T2
thruster
LEO SS SIM EPM SPP SPT MO
Ml
low Earth orbit SeWice systems scientific instlumcnts’ module electric propulsion module solar power plant stationary plasma thruster initialmassinthe LEO kg spacuxaf& mass after spading up to parabolic velocity kg final SpaCeClY&‘S ma3s kg required mass of the xenon kg mass of the SS, structure, and SIM kg
T
TIU
to
N, c V
v, a
P W
181
c 1997 Pubhshed
duration
by Elsewx
ScienceLtd
of the
geocentric spiraling motion duration of the heliocentric arc duration of the transfer ftom LEOto asteroid total duration of theallbumarcs start e@och of the heliocentric arc Xe-tanks spec& mass electrical power of SPP position vector v&or of velocity vdocity increment of the heliocentic arc thrust acceleration adjoint vector exhaust velocity of SPT
&YS
days
days
days
kW E/S
lU/S m/S2
UdS
182
Low-cost
planetary
1. INTRODUCTION. Modern state of teclmology allows to use light lowa scientific payload to solve many space research problem. Required mass of such payload can be a few tens of kilos and cost can be a few millions dollars. This kind of payload, which is delivemdtothetargetregionofspacebysmall space vehicle, can effectively study space plasma, Moon, near-Earth asteroids, comets, planets of the Solar system etc. Small spacecrafl have a good commercial prospective. They can be part of the telecommunication navigation and Eaithmonitoting space systems. Modern technology achievements allows to realize light low-cost space vehicle, based on light solar arrays and electric propulsion engines. One of the most reliable, tested, and high-wormance engines is Russian stationary plasma thrusters (SPT). High specific impulse of these engines allows to applicate near identical space vehicles to di&rent missions. It allows to realize project of the small uGvemal space platform with plasma thruster (SUSPPT). The key new technologies, which are used in the SUSPPT, are follows: l The SPT, having unique performance and many times proven in space: - Morethan50SPTs~beenflown in space without faihrres. - SPT have thrust efficiency -5O?h in the most interest@ range of specific impulse I,r,=1500-2000 s. - ThelargeSPTlifetimeiscon&ed by7OOOhoursgroundtestinRussia and-6ooohoumgroundtestatJPL - TherelsRus&n/Amulcanjolnt companydmlopingtheeledric pmpulsionsubsys&msonbaseof SPT and US power pmcess& unit. . ThcUSpowersupplysystem,basedon ultralight flexible solar arrays. l The Ruasian or US launch whicles. High specific impulse of SPT allows to reach high mass efficiency of the SUSPPT. It allows to fulfill the missions which are impossible for comrcntional Low thrust
0 l l
cl-m&d
propulsion
systans.
and long opemtion time allow todeemasethcmeehanicalloads; to extend possiities of the orbit ccmtro~ tore&QalmostcitGularolbitsorseriesof almostcimularorbitnofdiffemntaltlnX@
mwons
to control effectively relative satellites positions in the constellation for a long duration. This paper presents examples of magnetoshere research scientific mission and scientific mission to the near-Earth asteroids, which could be realized by SUSPPT.
0
SPACE UNIVERSAL SMALL 2. STATIONARY PLATFORM WITH PLASMA THRUSTER The main fm of the SUSPPT (see Fig. 1) are prese&d in the table 1. The required propellant (xenon) mass and required area of the solar arrays depend on mission scenario. Table 1. IGllIMax( Inilialma!3s,lcg 150 300. Lifetime, hours
Required power, W Efilciency (including
SF-r-70
SPT-100
3000 700 0.4 -
7ooo 1500 0.45
The main advantages of the SUSPPT in the comparison with conventional spacecrafts are follow: l highvelocityincrement(approx by 5 times higher in comparison with chemical propulsion system with the same mass), &rease range of givingthepossibilityto missionsessentially.
SUSPPT orbit remains near&cular up to a hundreds of thousands kilometers when it moves along spiral& tmjectory around the Earth to trarlsffl into the high-altitude orbit or to escape. It can be interesting for many missions. The main deficiency of the SUSPPT is longtime (a few months) insertion into the target orbit. This deficiency isn’t essential in many cases.
l
Low-cost planetary mIssIons
Asteroid
183
/ PlasMa
Pa&ad
-t Total
Mass
s/c
Xenon Mass, up bnw Mass. KQ Thruster , SPT-100 Powr
-Sotar
.%-stems ad c Scientific
,
WQ
, 2 Unit 5
W
PfmeCs,
E4uhent
300 114 30 60md 1700
Mass .q_
131
Pa-load Mass,~cs 1 25
A
Fig. 1 SUSPPT can realize the following maneafter insertion into the LEO: 1. Delivery into the high-altitude circular orbit (up to hundreds of thousands km). It is possible: - change orbit plane simultaneous&, -retnmtotheLEOaftermissionfinish. 2. Insertion into the satellite orbit around the Moon. 3. Insertion to the vicinity of the Earth-Moon and Sun-Earth lib&ion points.
4. Near-Earth asteroid rendezvous (including 5.
landing) and flyby. Venus/Mars missions.
3. M.4GNETOSHERE REBL4RaI MISSIONS. SUSPTT capables to pe&rm detailed study of the main magnetosphere boundaries, including near-Earth shock wave, inner boundary of the plasma layer and plasmapause (see F&.2). It is necessary to provide spacecraft motion along the selected boundary to provide such study. Optimal target
Fig. 2
184
Low-cost planetary missions
orbit of the spacecraft is near-circular one. The spacecraft retains in the boundary vicinity in this case for a long time. There are two interesting possibilities, which can be realized. The first one is concluded in the detailed study of the boundary structure when the boundaxy is stationary or it slowly moves with rfxpect to
spacecraft. The second possibility is collecting of the numerous cross-sections of the boundary structure when boundary quickly moves with respect to spacecraft. Both possibilities are realized many times using proposed orbit. Initial spacecraft orbit is formed in the vicinity of the mean plasmapause position.Spacecraftretainsfor a few months in this orbit and it collects numerous data concerning plasmapause parameters. Then SUSPTI delivem spacecraft into the orbit in the vicinity of the inner plasmapause boundary. Then spacecraft is delivered into the orbit in the magnetopause vicinity and later it is inserted into the orbit in the vicinity of the shock wave. The collection of experimental data, which can be obtained during SUSPPT magnetosphere mission, essentially exceeds collection which can be obtained duting conventional magnetosphere mission The spacecraft crosses boundaryathighangleinthecomhentiona mission New quality is achiewd due to following: 0 the number of boundary intersections is increased when boundary moves with respectto satellite; l spacecraft retains inside boundary layer structurefor a long time when boundary is Stationary. So, there are realized a few missions inside proposed one. Each of these missions can give more experimental data in -W comparison with conventional magnetosphere mission. An example of magnetosphere mission sCientiticpayloadispresentedinthetable2. 4. NEAR-EPTH ASTEROID MISSION. The purpose of the investigation is to estimate minimal mass of the SUSPPT in the LEO that allows to feach some nearEarth asteroids. There LIZ considered asteroid rendezvous and flyby missions. It is supposed that rtndczvous mission includes landing on the asteroid surface to c8n-y out its direct scientific rcseareh.
It is supposed that spacecraft consists of l EPM based on the SPT-1OOlJ; l SPP based on light solar arrays3 (its specific mass is equal to 16 kg&W); l service systems (SS) (control system, guidance and pointing system, communication system, landing system etc.) and structure; l scientific instruments module (SIM). It is supposed that SUSPP’I should include landing (docking) system in case of the rendezvous mission. Table 2
1
1.5
3 wave comDonalts
clxlult meter
M~of lcllmntdenaity
2 1
2
57
I
4.1. Model of the SUSPPT. Pammetas of the main SUSPPI’ systems were chosen corresponding to modern state of art. Their masses are pmented in the Table 3. Mass of the SS and structure supposed difk in cases of rtndezvous and flyby missions. Required eleetrical power to supply EPM based on SPT-100 is 1.35 kW. It is assumed that total peak required electrical power is equal to 1.5 kW. So, mass of the SPP equal to 1.5 kWxl6 kg&W = 24 kg. EPM consists of two SPT-
Low-cost
100 (the second SPT is standby one), power converter, and propellant supply system. Required mass of the propellant (xenon) A& is evaluated based on trajectory optimization problem. Mass of the tanks is proportional to A.&. Specific tanks’ mass ai is 0.13.
I
Table 3. Mass of the main onboard systems System M=, kg I SIM 15 1 SO(rendezvous) ss & Stlucture 40 (flyby)
4.2. Mission scenario and assumDtioas. It is supposed that EPM engages in the LEO. The altitude of the LEO is equal to 400 km. The SUSPPT moves along spiraling trajectory to achieve parabolic geocentric velocity due to transversal thrust a.cceluation_ It was assumed that thrust is constant. It was not considu-ed the possibility to use a coast arcs in this phase of the mission. Heliocentric arc of the trajectory was optimkxl to choose thrust direction and thrust switching function. Geocentric asymptotic velocity assumed equal to 0. It was used method of the zero-radius gravity spheres with the “zero junction” of the geocentric and heliocentric arcs. Docking of the SUSPPT and asteroid was not considaed especially. It was assumed that mass consumption due to this docking maneuver includes in the mass of the landing system. It is necessary to note several assumptions in addition to above-mentioned ones. AMultirevolutional spiraling geocentric trajectory crosses iran-Allen belts. So, it may take place a sign&ant solar array degradation. In addition, output SPP power decreases due to Othtr ~vironmental factors. These effects were not taking into account in this investigation. It was not taking into account coast arcs of the geocentric
planetary
185
mlsslons
trajectory during eclipses. It was assumed that surface of the solar array is perpendicular to the sunlight during all bum arcs. also
There were checked all known near-Barth asteroids. Preliminary estimations of the required propellant consumption were carried out only for asteroids, which could appear easy-to-reached ones. Detailed investigation of the mission to the asteroid was carried if preliminary estimation shows possibility to reach it. 4.3. Mathematical statement. &ocentric spiraling trajectory was calculated under the assumption that thrust direction is transversal. Initial value problem was soived for every chosen set of the main mission parameters (initial mass MO and exhaust velocity w). There were obtained duration of geocenttic arc TI and spacecraft’s mass in the beginning of the heliocentric arc MI as a result. Heliocentric arc was optimized. Pontryagin’s maximum principle was used to reduce optimal control problem to the two point boundary value problem. This problem was solved by modified Newton’s method. Controlling functions are switching function S(it equals to 1 if SPT is running and equals to 0 otherwise) and angles a and B of the thrust direction (a is angle between thrust and plane of the spacecraft’s osculating orbit, and pis angle between vector of the spacecraWs position r and the thrust projection on the same plane). Start ru and final tf epochs of the heliocentric arc were assumed fixed ones (the parametric optimization was used to search their optimal conditions are follow: rE(fO),
V(lO)
=
values).
Boundary
vE(fO),
r(fO)
=
r(tf)
= rdlf),
v(ff)
= v&f)
r(cf)
= r&f),
p&f)
= 0
(rendezvous), (flyby),
where re, vE - position and velocity of the Barth, r,, V~- position and velocity of the asteroid, pv= (Pv~ PKQJ$, Equations of optimal motion in spherical coordinates are as follows4:
the
Low-cost planetary misslons
186
dr v I* t= VA
fi
dt= tcoscp’ dq
v,
dV -$
= k(V;
x=7,
@A -z-=7
VA
+ V,’ - l/r) + 6a pR
/py
,
100
0 (v, %cp-vJ+~~
PJP”
9
200
300
400
T Wwl Fig.4. Optimal control (1989ML rendezvous) where r, 4 4, are heliocentric distance, longitude and latitude; V’, VA, V, are components of spacecraft’s velocity; pyn p n PL P c p yrrP ‘/2,P VPa
~mpon~~
of the pi
fi=ld; s_
V dP I=~(-P,Sinrp-V.p,+V;p,,), dt rcosl(p 1 V ( hPvA+V,P,
1 VrPv,r(
function of the time, and it does not depend on heliocentric distance: a-(t). 4 4 Results Some numerical results are 2-k presented in the tables.
) -P,.
P. - Wc.P, -V,P,
intervals between optimal launch dates often are difkred from time inten& between adjacent asteroid-Earth oppositions. These difkrences are &used by relativay high eccentricity of asteroids orbits. For example, time interval between adjacent oppositions of asteroid 1989ML is 3.4 year, but time in~al between adjacent optimal launch dates is 7 year. These intervals equal to 1.6 and 8 year respectively in case of asteroid 3908. Thexe are different optimal within time transfkrs these intervals, which have diRering forins of the control functions and differing number of the bum arcs. An example of optimal trajectory and control are presented in the Figures 3 and 4. This example corresponds to last row of the table 4 (1989ML rendezvous mission). Heliocentric arc includes three bum arcs. Spacecraft tives to the asteroid in the vicinity of the descending node of its orbit.
Time
tg?),
dp,=_E* dt w’ PA = con!%
Fig.3.
@=Pv+Pd
It is assumed that acceleration a is known
+
dP, -=dt
ifA>a,
-I 0, ifA>O,
+V,‘tgcpX
dPvr dt=r
1
Optimal heliocentric trajectory of the 1989ML rendezvous mission (the last row of table 2).
Low-cost
planetary
187
mlsslons
Table 4 Main wnnmeters
of the rendezvous missions
Spacecraft’s mass at the BOM M, = 250 kg 15.690 km/” Exhaust velocity of the SPT Ml00
Table 5
dezvousrmsslans . .
Spacecraft’s mass at the BOM M, = 200 kg Asteroid 1 / MI,
w,km/s
kg
Vs,
buts
Mr, kg
M., kg
+ M,,
T-1. TI,
k,Q
days
T,
'&a,
t,
day3 day3
days
ddmm.yy
360
272
15.12.04
Eros, 15.690 Eros, 17.650 17.650 3908,
! 129.9
7.06
83.6
116.4
Sf.4
163
135.4
6.96
92.0
108.0
34.0
135.4
6.7?
93.0
107.0 1 35.0
15.12.04 168 i 360 528 283 ! 168 ’ 220 I 388 I 280 1 05.06.04
4660, 15.690 4660,
129.9
5.67
91.1
108.9
33.0
129.9
5.20
93.9
106.1
129.9
4.59
97.5
, 129.9
3.90
101.8
15.690 1989UQ, 15.690 1989ML.
523
313
254
15.10..01
36.1
163 i 150 I 163 360
523
248
15.08.01
102.5
40.2
163
400
563
239
15.11.03
98.2
45.0
163
420
583
257
01.07.02
15.690 1
J Table 6 Main wxrameters of the flvbv missions
Exhaust velocity of the SPT Ml00
15.690 k&s
1 1989ML 1 200 1 130.01 1.29 1 120.0 ( 80.0 1 65.6 1 163 1 328 ( 491 1 191 1 01.10.02
Obtained 5. CONCLUSION. results allow to state that required initial spacecraws mass in the LEO MOis not less than 250 kg in case of rendezvous mission. It is mass that allows to deliver useful mass MP (SW, SS, and structure) about SO-67 kg to the asteroid’s vicinity.
Decreasing A4, to 200 kg leads to decreasing MP to 25-45 kg. This MP does not allow to provide scientific research of the asteroid, in our opinion. On the other hand, increasing of the specifc impulse and transfer time allow to increase I&,. So, increasing of exhaust velocity from 15690 m/s to 17650 m/s allows to increase MP by a lo-15 kg.
188
Low-cost
planetary
References.
PI Rober A. S., at al.
“State of Work on Electrical Thrusters in USSR”, Proc. of
the 22nd International Electric Propulsion Conference, Viareggio , Italy, October, 199 1. PI Brophy J. R., at al. “Performance of the Stationary
Plasma Thruster: SPT-100”,
AI&+92-3155, July, 1992. PI Loeb H.W. “Nuclear or Solar Plants for Advanced interplanetary
EP-Missions?‘,
missions
Papers of the 3rd Russian-German conference on electric propulsion and their technical applications, Stuttgart, 1994, pp.ws-P14. Efunov G.B., Konstantinov M. S., Petukhov V. G., Fedotov G.G. “investigation of Pluto Hyby Possibility by means of Solar Powered Electric Propulsion”, preprint, Inst. Appl.
Mathem., Russia Academy of Sciences, 1994, N25.
Acta Asrronautrca Vol 39, No l-4. pp 181-188. 1996 CopyrIght II 1997 Pubbshed by Elsewer Saence Ltd Pruned m Great Bntam. All nghts reserved 0094-5765!96 $15.00 + 0.00 SO@‘Q5765(%)00135-X
SMALL UNIVERSAL SPACE PLATFORMz MISSION CAPABILITIES V. Baiebanov*, G. Fedotov**, V. Kim***, M. Konstantiuov**, V.Kostenko’, M. Pivovarov.*, V. Petukhov**, G. Popov***, A Sukhanov* *
** ***
Space Research Institute 0, Moscow, Russia Moscow Aviation Institute (MAI), Moscow, Russia Research Institute of Applied Mechanics and Electrodynamics of MAI (RUMI MAX),Moscow, Russia
ABSTIUCT 7he rcs&sof missionanalysi3for s.nA univ& space @tf6rm withplasmatbuster (SUSPPT)developedon base ofmodantechnologylcvdarepnsartedinthe~.Thesertsultsshowthatitis~ltto~SUSPVTorbit raising(tkomLEOtotheorbitofsomehund&oft&sands kmheightwiththechangeoforbit~aulWumto LEo),to~~thescientificpayloadtotfaeMoon~arbittoreachtfieEarth-Moonmd~-~tibpation point%nearsalth 8stcroid!s(_)* ie.torealkedi&rentkindsofinttx4ng~adoonmnerdrl mipsiona.Astheclectricpopulsion~~banchosenthe~~stationaryplasma~(s~~ m~ytimesflo~andusedinrpsoe.Ifigh~impubeof~tfuustaincombinationwiththe~sakranays atlowto reach highlevelof space transportahon ’ systan efficiency.For example,SUSPPT,whichinitialmass is 2002% kg in the LEO, can deliver 30-70 kg scientificpayloadto a near-Earthasteroid. CopyrIght
NOMENCLATURE SUSPPT
Tl
small-space platfolm
with plasma
T2
thruster
LEO SS SIM EPM SPP SPT MO
Ml
low Earth orbit SeWice systems scientific instlumcnts’ module electric propulsion module solar power plant stationary plasma thruster initialmassinthe LEO kg spacuxaf& mass after spading up to parabolic velocity kg final SpaCeClY&‘S ma3s kg required mass of the xenon kg mass of the SS, structure, and SIM kg
T
TIU
to
N, c V
v, a
P W
181
c 1997 Pubhshed
duration
by Elsewx
ScienceLtd
of the
geocentric spiraling motion duration of the heliocentric arc duration of the transfer ftom LEOto asteroid total duration of theallbumarcs start e@och of the heliocentric arc Xe-tanks spec& mass electrical power of SPP position vector v&or of velocity vdocity increment of the heliocentic arc thrust acceleration adjoint vector exhaust velocity of SPT
&YS
days
days
days
kW E/S
lU/S m/S2
UdS
182
Low-cost
planetary
1. INTRODUCTION. Modern state of teclmology allows to use light lowa scientific payload to solve many space research problem. Required mass of such payload can be a few tens of kilos and cost can be a few millions dollars. This kind of payload, which is delivemdtothetargetregionofspacebysmall space vehicle, can effectively study space plasma, Moon, near-Earth asteroids, comets, planets of the Solar system etc. Small spacecrafl have a good commercial prospective. They can be part of the telecommunication navigation and Eaithmonitoting space systems. Modern technology achievements allows to realize light low-cost space vehicle, based on light solar arrays and electric propulsion engines. One of the most reliable, tested, and high-wormance engines is Russian stationary plasma thrusters (SPT). High specific impulse of these engines allows to applicate near identical space vehicles to di&rent missions. It allows to realize project of the small uGvemal space platform with plasma thruster (SUSPPT). The key new technologies, which are used in the SUSPPT, are follows: l The SPT, having unique performance and many times proven in space: - Morethan50SPTs~beenflown in space without faihrres. - SPT have thrust efficiency -5O?h in the most interest@ range of specific impulse I,r,=1500-2000 s. - ThelargeSPTlifetimeiscon&ed by7OOOhoursgroundtestinRussia and-6ooohoumgroundtestatJPL - TherelsRus&n/Amulcanjolnt companydmlopingtheeledric pmpulsionsubsys&msonbaseof SPT and US power pmcess& unit. . ThcUSpowersupplysystem,basedon ultralight flexible solar arrays. l The Ruasian or US launch whicles. High specific impulse of SPT allows to reach high mass efficiency of the SUSPPT. It allows to fulfill the missions which are impossible for comrcntional Low thrust
0 l l
cl-m&d
propulsion
systans.
and long opemtion time allow todeemasethcmeehanicalloads; to extend possiities of the orbit ccmtro~ tore&QalmostcitGularolbitsorseriesof almostcimularorbitnofdiffemntaltlnX@
mwons
to control effectively relative satellites positions in the constellation for a long duration. This paper presents examples of magnetoshere research scientific mission and scientific mission to the near-Earth asteroids, which could be realized by SUSPPT.
0
SPACE UNIVERSAL SMALL 2. STATIONARY PLATFORM WITH PLASMA THRUSTER The main fm of the SUSPPT (see Fig. 1) are prese&d in the table 1. The required propellant (xenon) mass and required area of the solar arrays depend on mission scenario. Table 1. IGllIMax( Inilialma!3s,lcg 150 300. Lifetime, hours
Required power, W Efilciency (including
SF-r-70
SPT-100
3000 700 0.4 -
7ooo 1500 0.45
The main advantages of the SUSPPT in the comparison with conventional spacecrafts are follow: l highvelocityincrement(approx by 5 times higher in comparison with chemical propulsion system with the same mass), &rease range of givingthepossibilityto missionsessentially.
SUSPPT orbit remains near&cular up to a hundreds of thousands kilometers when it moves along spiral& tmjectory around the Earth to trarlsffl into the high-altitude orbit or to escape. It can be interesting for many missions. The main deficiency of the SUSPPT is longtime (a few months) insertion into the target orbit. This deficiency isn’t essential in many cases.
l
Low-cost planetary mIssIons
Asteroid
183
/ PlasMa
Pa&ad
-t Total
Mass
s/c
Xenon Mass, up bnw Mass. KQ Thruster , SPT-100 Powr
-Sotar
.%-stems ad c Scientific
,
WQ
, 2 Unit 5
W
PfmeCs,
E4uhent
300 114 30 60md 1700
Mass .q_
131
Pa-load Mass,~cs 1 25
A
Fig. 1 SUSPPT can realize the following maneafter insertion into the LEO: 1. Delivery into the high-altitude circular orbit (up to hundreds of thousands km). It is possible: - change orbit plane simultaneous&, -retnmtotheLEOaftermissionfinish. 2. Insertion into the satellite orbit around the Moon. 3. Insertion to the vicinity of the Earth-Moon and Sun-Earth lib&ion points.
4. Near-Earth asteroid rendezvous (including 5.
landing) and flyby. Venus/Mars missions.
3. M.4GNETOSHERE REBL4RaI MISSIONS. SUSPTT capables to pe&rm detailed study of the main magnetosphere boundaries, including near-Earth shock wave, inner boundary of the plasma layer and plasmapause (see F&.2). It is necessary to provide spacecraft motion along the selected boundary to provide such study. Optimal target
Fig. 2
184
Low-cost planetary missions
orbit of the spacecraft is near-circular one. The spacecraft retains in the boundary vicinity in this case for a long time. There are two interesting possibilities, which can be realized. The first one is concluded in the detailed study of the boundary structure when the boundaxy is stationary or it slowly moves with rfxpect to
spacecraft. The second possibility is collecting of the numerous cross-sections of the boundary structure when boundary quickly moves with respect to spacecraft. Both possibilities are realized many times using proposed orbit. Initial spacecraft orbit is formed in the vicinity of the mean plasmapause position.Spacecraftretainsfor a few months in this orbit and it collects numerous data concerning plasmapause parameters. Then SUSPTI delivem spacecraft into the orbit in the vicinity of the inner plasmapause boundary. Then spacecraft is delivered into the orbit in the magnetopause vicinity and later it is inserted into the orbit in the vicinity of the shock wave. The collection of experimental data, which can be obtained during SUSPPT magnetosphere mission, essentially exceeds collection which can be obtained duting conventional magnetosphere mission The spacecraft crosses boundaryathighangleinthecomhentiona mission New quality is achiewd due to following: 0 the number of boundary intersections is increased when boundary moves with respectto satellite; l spacecraft retains inside boundary layer structurefor a long time when boundary is Stationary. So, there are realized a few missions inside proposed one. Each of these missions can give more experimental data in -W comparison with conventional magnetosphere mission. An example of magnetosphere mission sCientiticpayloadispresentedinthetable2. 4. NEAR-EPTH ASTEROID MISSION. The purpose of the investigation is to estimate minimal mass of the SUSPPT in the LEO that allows to feach some nearEarth asteroids. There LIZ considered asteroid rendezvous and flyby missions. It is supposed that rtndczvous mission includes landing on the asteroid surface to c8n-y out its direct scientific rcseareh.
It is supposed that spacecraft consists of l EPM based on the SPT-1OOlJ; l SPP based on light solar arrays3 (its specific mass is equal to 16 kg&W); l service systems (SS) (control system, guidance and pointing system, communication system, landing system etc.) and structure; l scientific instruments module (SIM). It is supposed that SUSPP’I should include landing (docking) system in case of the rendezvous mission. Table 2
1
1.5
3 wave comDonalts
clxlult meter
M~of lcllmntdenaity
2 1
2
57
I
4.1. Model of the SUSPPT. Pammetas of the main SUSPPI’ systems were chosen corresponding to modern state of art. Their masses are pmented in the Table 3. Mass of the SS and structure supposed difk in cases of rtndezvous and flyby missions. Required eleetrical power to supply EPM based on SPT-100 is 1.35 kW. It is assumed that total peak required electrical power is equal to 1.5 kW. So, mass of the SPP equal to 1.5 kWxl6 kg&W = 24 kg. EPM consists of two SPT-
Low-cost
100 (the second SPT is standby one), power converter, and propellant supply system. Required mass of the propellant (xenon) A& is evaluated based on trajectory optimization problem. Mass of the tanks is proportional to A.&. Specific tanks’ mass ai is 0.13.
I
Table 3. Mass of the main onboard systems System M=, kg I SIM 15 1 SO(rendezvous) ss & Stlucture 40 (flyby)
4.2. Mission scenario and assumDtioas. It is supposed that EPM engages in the LEO. The altitude of the LEO is equal to 400 km. The SUSPPT moves along spiraling trajectory to achieve parabolic geocentric velocity due to transversal thrust a.cceluation_ It was assumed that thrust is constant. It was not considu-ed the possibility to use a coast arcs in this phase of the mission. Heliocentric arc of the trajectory was optimkxl to choose thrust direction and thrust switching function. Geocentric asymptotic velocity assumed equal to 0. It was used method of the zero-radius gravity spheres with the “zero junction” of the geocentric and heliocentric arcs. Docking of the SUSPPT and asteroid was not considaed especially. It was assumed that mass consumption due to this docking maneuver includes in the mass of the landing system. It is necessary to note several assumptions in addition to above-mentioned ones. AMultirevolutional spiraling geocentric trajectory crosses iran-Allen belts. So, it may take place a sign&ant solar array degradation. In addition, output SPP power decreases due to Othtr ~vironmental factors. These effects were not taking into account in this investigation. It was not taking into account coast arcs of the geocentric
planetary
185
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trajectory during eclipses. It was assumed that surface of the solar array is perpendicular to the sunlight during all bum arcs. also
There were checked all known near-Barth asteroids. Preliminary estimations of the required propellant consumption were carried out only for asteroids, which could appear easy-to-reached ones. Detailed investigation of the mission to the asteroid was carried if preliminary estimation shows possibility to reach it. 4.3. Mathematical statement. &ocentric spiraling trajectory was calculated under the assumption that thrust direction is transversal. Initial value problem was soived for every chosen set of the main mission parameters (initial mass MO and exhaust velocity w). There were obtained duration of geocenttic arc TI and spacecraft’s mass in the beginning of the heliocentric arc MI as a result. Heliocentric arc was optimized. Pontryagin’s maximum principle was used to reduce optimal control problem to the two point boundary value problem. This problem was solved by modified Newton’s method. Controlling functions are switching function S(it equals to 1 if SPT is running and equals to 0 otherwise) and angles a and B of the thrust direction (a is angle between thrust and plane of the spacecraft’s osculating orbit, and pis angle between vector of the spacecraWs position r and the thrust projection on the same plane). Start ru and final tf epochs of the heliocentric arc were assumed fixed ones (the parametric optimization was used to search their optimal conditions are follow: rE(fO),
V(lO)
=
values).
Boundary
vE(fO),
r(fO)
=
r(tf)
= rdlf),
v(ff)
= v&f)
r(cf)
= r&f),
p&f)
= 0
(rendezvous), (flyby),
where re, vE - position and velocity of the Barth, r,, V~- position and velocity of the asteroid, pv= (Pv~ PKQJ$, Equations of optimal motion in spherical coordinates are as follows4:
the
Low-cost planetary misslons
186
dr v I* t= VA
fi
dt= tcoscp’ dq
v,
dV -$
= k(V;
x=7,
@A -z-=7
VA
+ V,’ - l/r) + 6a pR
/py
,
100
0 (v, %cp-vJ+~~
PJP”
9
200
300
400
T Wwl Fig.4. Optimal control (1989ML rendezvous) where r, 4 4, are heliocentric distance, longitude and latitude; V’, VA, V, are components of spacecraft’s velocity; pyn p n PL P c p yrrP ‘/2,P VPa
~mpon~~
of the pi
fi=ld; s_
V dP I=~(-P,Sinrp-V.p,+V;p,,), dt rcosl(p 1 V ( hPvA+V,P,
1 VrPv,r(
function of the time, and it does not depend on heliocentric distance: a-(t). 4 4 Results Some numerical results are 2-k presented in the tables.
) -P,.
P. - Wc.P, -V,P,
intervals between optimal launch dates often are difkred from time inten& between adjacent asteroid-Earth oppositions. These difkrences are &used by relativay high eccentricity of asteroids orbits. For example, time interval between adjacent oppositions of asteroid 1989ML is 3.4 year, but time in~al between adjacent optimal launch dates is 7 year. These intervals equal to 1.6 and 8 year respectively in case of asteroid 3908. Thexe are different optimal within time transfkrs these intervals, which have diRering forins of the control functions and differing number of the bum arcs. An example of optimal trajectory and control are presented in the Figures 3 and 4. This example corresponds to last row of the table 4 (1989ML rendezvous mission). Heliocentric arc includes three bum arcs. Spacecraft tives to the asteroid in the vicinity of the descending node of its orbit.
Time
tg?),
dp,=_E* dt w’ PA = con!%
Fig.3.
@=Pv+Pd
It is assumed that acceleration a is known
+
dP, -=dt
ifA>a,
-I 0, ifA>O,
+V,‘tgcpX
dPvr dt=r
1
Optimal heliocentric trajectory of the 1989ML rendezvous mission (the last row of table 2).
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187
mlsslons
Table 4 Main wnnmeters
of the rendezvous missions
Spacecraft’s mass at the BOM M, = 250 kg 15.690 km/” Exhaust velocity of the SPT Ml00
Table 5
dezvousrmsslans . .
Spacecraft’s mass at the BOM M, = 200 kg Asteroid 1 / MI,
w,km/s
kg
Vs,
buts
Mr, kg
M., kg
+ M,,
T-1. TI,
k,Q
days
T,
'&a,
t,
day3 day3
days
ddmm.yy
360
272
15.12.04
Eros, 15.690 Eros, 17.650 17.650 3908,
! 129.9
7.06
83.6
116.4
Sf.4
163
135.4
6.96
92.0
108.0
34.0
135.4
6.7?
93.0
107.0 1 35.0
15.12.04 168 i 360 528 283 ! 168 ’ 220 I 388 I 280 1 05.06.04
4660, 15.690 4660,
129.9
5.67
91.1
108.9
33.0
129.9
5.20
93.9
106.1
129.9
4.59
97.5
, 129.9
3.90
101.8
15.690 1989UQ, 15.690 1989ML.
523
313
254
15.10..01
36.1
163 i 150 I 163 360
523
248
15.08.01
102.5
40.2
163
400
563
239
15.11.03
98.2
45.0
163
420
583
257
01.07.02
15.690 1
J Table 6 Main wxrameters of the flvbv missions
Exhaust velocity of the SPT Ml00
15.690 k&s
1 1989ML 1 200 1 130.01 1.29 1 120.0 ( 80.0 1 65.6 1 163 1 328 ( 491 1 191 1 01.10.02
Obtained 5. CONCLUSION. results allow to state that required initial spacecraws mass in the LEO MOis not less than 250 kg in case of rendezvous mission. It is mass that allows to deliver useful mass MP (SW, SS, and structure) about SO-67 kg to the asteroid’s vicinity.
Decreasing A4, to 200 kg leads to decreasing MP to 25-45 kg. This MP does not allow to provide scientific research of the asteroid, in our opinion. On the other hand, increasing of the specifc impulse and transfer time allow to increase I&,. So, increasing of exhaust velocity from 15690 m/s to 17650 m/s allows to increase MP by a lo-15 kg.
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Low-cost
planetary
References.
PI Rober A. S., at al.
“State of Work on Electrical Thrusters in USSR”, Proc. of
the 22nd International Electric Propulsion Conference, Viareggio , Italy, October, 199 1. PI Brophy J. R., at al. “Performance of the Stationary
Plasma Thruster: SPT-100”,
AI&+92-3155, July, 1992. PI Loeb H.W. “Nuclear or Solar Plants for Advanced interplanetary
EP-Missions?‘,
missions
Papers of the 3rd Russian-German conference on electric propulsion and their technical applications, Stuttgart, 1994, pp.ws-P14. Efunov G.B., Konstantinov M. S., Petukhov V. G., Fedotov G.G. “investigation of Pluto Hyby Possibility by means of Solar Powered Electric Propulsion”, preprint, Inst. Appl.
Mathem., Russia Academy of Sciences, 1994, N25.