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an9er s611&n

elyyM

ui~itions and I ut Branch

FF 431 APR 70 431.1 .7004

i

UTEC ME 70-033

JUN 1970

SOLAR ELECTRIC GRAND TOUR MISSIONS

TO THE OUTER PLANETS

by

G. A. Flandro Associate Professor

to

National Aeronautics and Space Administration Washington, D.C. 20546

FINAL REPORT: NASA Grant No. NGR 45-003-050

University of Utah Department of Mechanical Engineering

Salt Lake City, Utah 84112

ACKNOWLEDGMENTS

The writer gratefully acknowledges the assistance offered by members of

the technical staff of the Jet Propulsion Laboratory, California Institute,

of Technology. Particular appreciation is due Thomas A. Barber for numerous

suggestions and to Carl G. Sauer for assistance in generating the low ttrust

trajectory data so essential to this research. Special thanks are due Alva

Joseph and Jeannyne Gunkel also of JPL for their aid in securing multiplanet

ballistic trajectories. Robert K. Wilson, a graduate assistant at the Univer­

sity of Utah during the course of this research, must also be mentioned in

this regard.

The author wishes to express his sincere appreciation to the National

Aeronautics and Space Administration for financial support in the form of

Grant No. NGR 45-003-050 which made this work possible.

ii

SOLAR ELECTRIC GRAND TOUR MISSIONS

TO THE OUTER PLANETS

G. A. Flandro University of Utah

SUMMARY

Practical unmanned exploration of the distant outer planets of the solar

systems requires application of advanced mission techniques. To achieve both

reasonable mission duration and payload mass, energy sources in addition to

that represented by the launch vehicle system itself must be employed. In

this study a combination of optimized solar electric low thrust propulsion

and gravitational boost from intermediate planet hyperbolic encounters was

applied to this purpose.

The period 1975-1980 abounds in multi-planet mission opportunities.

Earth-Jupiter-Saturn-Pluto and Earth-Jupiter-Uranus-Neptune "grand tour"

missions would enable a complete preliminary exploration of all of the outer

planets by a pair of spacecraft launched by booster vehicle systems already

in advanced stages of development. Optimum launch dates and performance

parameters for these missions were obtained for Titan/Centaur and Atlas/

Centaur launch systems with optimized solar-electric final propulsive stag­

ing. Payload is increased over purely ballistic trajectories by more than

three times. Use of the Titan 3X (1205)/Centaur permits two spacecraft of

over 1000 Kg (2200 lb) payload each to reach all planets of the outer solar

system within a seven-year period.

iii

TABLE OF CONTENTS

Acknowledgments --------------------------------------------------- ii

Summary ------------------------------------------------------ iii

Table of Contents ------------------------------------------------- iv

List of Figures ------------------------------------------------- v

INTRODUCTION ------------------------------------------------------ I

MISSION ANALYSIS PROCEDURES --------------------------------------- 4

Application of Energy Gained in Intermediate Planet Encounters ----------------------------------------- 4

Swingby Trajectory Optimization with Low Thrust Propulsion ------------------------------------------------ 10

EARTH-JUPITER-SATURN MISSIONS WITH SOLAR ELECTRIC PROPULSION ------------------------------------------------ 23

SOLAR ELECTRIC SWINGBY MISSIONS TO URANUS, NEPTUNE, AND PLUTO ------------------------------------------------- 38

SOLAR ELECTRIC GRAND TOUR MISSIONS -------------------------------- 49

Earth-Jupiter-Saturn-Pluto Grand Tour ------------------------- 49 Earth-Jupiter-Uranus-Neptune Grand Tour ----------------------- 51

CONCLUSIONS ------------------------------------------------------- 66

APPENDIX I -------------------------------------------------------- 71

LIST OF REFERENCES ---------------------------------------------- 83

iv

LIST OF FIGURES

Figure Title Page

1 Encounter Hyperbola 6

2 Cone of Allowable Outgoing Asymptotes 9

3 Maximum Speed

Energy Increment vs Hyperbolic Excess 11

4 Optimum Energy Change for a Given Approach Angle

12

5 Matching of Optimized Low Thrust Earth-Jupiter Trajectories with Ballistic Continuation Or­bits to Saturn

14

6 Gross Payload at Jupiter vs Launch Date for 1975 Synodic Period. Atlas SLV-3X/Centaur

17

7 Typical Optimum Earth-Jupiter Solar Electric Flight Path--indirect Mode

18

8 Hyperbolic Approach Speed at Jupiter vs Date for 1977 Synodic Period

Launch 19

9 Thrust Angle vs Time for Optimum 900-Day JupiterFlyby %Mission(Indirect Mode)

21

10 Typical indirect Mode Earth-Jupiter-Saturn Flight Path

24

11 Flight Duration vs Launch Date for 1976 Earth-Jupiter-Saturn Mission SLV-3X/Centaur indirect Mode

26

12 Flight Duration vs Launch Date for 1977 Earth-Jupiter-Saturn Mission SLV-3X/Centaur Indirect Mode

27

13 Fl ight Duration vs Launch Date for 1978 Earth-Jupiter-Saturn Mission SLV-3X/Centaur Indirect Mode

28

14 Flight Duration vs Launch Date for 1976 Earth-Jupiter-Saturn Mission. SLV-3X Centaur Direct Mode

29

V

Figure Title Page

15 Flight Duration vs Launch Date for 1977 Earth-Jipiter-Saturn Mission. SLV-3X/Centaur Direct Mode.

30

16 Flight Duration vs Launch Date for 1978 Earth-Jupiter-Saturn Mission. SLV-3X/Centau Direct Mode.

31

17 'Optimum Launch Date vs Payload Mass for 1976 Earth Jupiter-Saturn Mission. Direct Mode Titan 3X (1205)/Centaur Launch Vehicle

32

j8 Optimum Launch Date vs Payload for 1977 Earth-Jupiter-Saturn Mission. Direct Mode Titan 3X/ Centaur Booster.

33

19 Optimum Launch Date vs Payload for 1978 Earth-Jupiter-Saturn Mission. Direct Mode Titan 3X/ Centaur Booster.

34

20 Radius of Closest Approach to Jupiter vs Optimum Gross Payload for Earth-Jupiter-Saturn Mission. Titan 3X (1205)/Centaur Launch Vehicle, Direct Mode.

35

21 Flight Duration--Payload Jupiter-Saturn Mission. Direct Mode.

Tradeoff for Earth-Titan 3X/Centaur

36

22 Flioht Duration vs Launch Date for 1978 Earth-Jupiter-Uranus Mission. SLV-3X/Centaur Indirect Mode.

39

23 Flight Duration vs Launch Date for 1979 Earth-Jupiter-Uranus Mission. SLV-3X/Centaur Indirect Mode.

40

24 Flight Duration vs Launch Date for 1978 Earth-Jupiter-Uranus Mission. SLV-3X/Centaur Direct Mode.

di

25 Flight Duration vs Launch Date for 1979 Earth-Jupiter-Uranus Mission. SLV-3X/CentaUr Direct Mode.

42

26 Optimum Launch Date vs Payload Mass for 1978 Earth-Jupiter-Uranus Mission. Direct Mode Titan 3X (1205)/Centaur Launch Vehicle.

43

27 Optimum Launch Date vs Payload Mass for 1979 Earth-Jupiter-Uranus Mission. Direct Mode Titan 3X(1205)/Centaur Launch Vehicle.

A4

vi

Figure Title Page

28 Optimum Launch Date vs Payload Mass for 1980 Earth-Jupiter-Uranus Mission. Direct Mode Titan 3X(1205)/Centaur Launch Vehicle.

45

29 Radius of Closest Approach to Jupiter vs Opti-mum Gross Payload for Earth-Jupiter-Uranus Mission Titan 3X/Centaur Launch Vehicle, Direct Mode.

46

30 Flight Duration--Payload Tradeoff for Earth-Jupiter-Uranus Mission. Titan/Centaur Direct Mode.

47

31 Typical Direct Mode Earth-Jupiter-Saturn-Pluto "Grand Tour" Flight

Path 50

32 Radius of Closest Approach to Saturn for Earth-Jupiter-Saturn-Pluto "Grand Tour" Missions. Titan/Centaur Direct.

52

33 Payload--Trip Time Tradeoff for Earth-Jupiter- 53

Saturn-Pluto "Grand Tour" Miss-ion. Titan/Centaur Launch Vehicle. Direct Trajectory Mode.

34 Flight Duration vs Launch Date for 1976 Earth-Jupiter-Saturn-Pluto "Grand Tour" Mission. Atlas SLV-3X/Centaur Launch Vehicle. Direct Mode.

54

35 Flight Duration vs Launch Date for 1977 Earth-Jupiter-Saturn-Pluto "Grand Tour" Mission. Atlas SLV-3X/Centaur Launch Vehicle. Direct Mode.

55

36 Flight Duration vs Launch Date for 1978 Earth-Jupiter-Saturn-Pluto "Grand Tour" Mission. Atlas SLV-3X/Centaur Direct Mode.

56

37 Flight Duration vs Launch Date for 1976 Earth-Jupi-ter-Saturn-Pluto "Grand Tour" Mission, Atlas SLV­3X/Centaur Indirect Mode.

57

38 Flight Duration vs Launch Date for 1977 Earth-Jupiter-Saturn-Pluto "Grand Tour" Mission. Atlas SLV-3X/Centaur Indirect Mode.

58

39 Typical' Direct Mode Earth-Jupiter-Uranus-Neptune "Grand Tour" Flight Path.

59

40 Radius of Closest Approach to Uranus for Earth- Jupiter-Uranus-Neptune "Grand Tour" Missions Titan 3X/Centaur Launch Vehicle, Direct Mode.

60

vii

Figure Title Page

41 Payload--Trip Time Tradeoff for Earth-Jupiter- 61 Uranus-Neptune "Grand Tour" Mission. Titan 3X/ Centaur Launch Vehicle, Direct Mode.

42 Flight Duration vs Launch Date for 1978 Earth- 63 Jupiter-Uranus-Neptune "Grand Tour" Mission. Atlas SLV-3X/Centaur Launch Vehicle, Direct Mode.

43 Flight Duration vs Launch Date for 1979 Earth- 64 Jupiter-Uranus-Neptune "Grand Tour" Mission. Atlas SLV-3X/Centaur Direct Mode.

Ad Flight Duration vs Launch Date for 1978 Earth- 65 Jupiter-Uranus-Neptune "Grand Tour" Mission. Atlas SLV-3X/Centaur, Indirect Mode.

45 Gross Payload vs Time of Flight for Optimum 67 Earth-Jupiter-Saturn Solar Electric Missions

46 Gross Payload vs Time of Flight for Optimum 68 Earth-Jupiter-Uranus Solar Electric Missions

47 Gross Payload vs Time of Flight for Optimum 69

"Grand Tour" MissionsEarth-Jupi ter-Saturn-Pl uto Solar Electric

48 Gross Payload vs Time of Flight for Optimum 70 Earth-Jupiter-Uranus-Neptune Solar Electric "Grand Tour1' Missions

A.1 Gross Payload vs Time of Flight to Jupiter 72 Titan 3X(2205)/Centaur, Direct Mode

A.2 Hyperbolic Excess Speed at Jupiter vs Time of 73 Flight to Jupiter. Titan/Centaur, Direct Mode

A.3 Initial Spacecraft Mass vs Time of Flight to 74 Jupiter. Titan 3X/Centaur, Direct Mode

A.4 Total Propulsion Time vs Time of Flight to 75 Jupiter. Titan 3X(1205)/Centaur, Direct Mode

A.5 Optimum Thruster Input Power at Launch vs 76 Time of Flight to Jupiter. Titan/Centaur Direct Mode.

A.6 Propellant Mass vs Time of Flight to Jupiter 77 Titan 3X(1205)/Centaur, Direct Mode

A.7 Optimum Heliocentric Transfer Angle vs Time 78 of Flight to Jupiter. Titan/Centaur Direct Mode

viii

Figure Title Page

A.8 Optimum Departure Injection Energy vs Time 79 of Flight to Jupiter. Titan/Centaur, Direct Mode.

A.9 Sun-Planet-Probe Angle at Jupiter vs Time of 80 Flight to Jupiter. Titan 3X/Centaur, Direct Mode.

A.1O Optimum Exhaust Velocity vs Time of Flight 81 to Jupiter. Titan 3X/Centaur, Direct Mode.

ix

INTRODUCTION

The gain in heliocentric total energy available from close passage of

the massive planet Jupiter can greatly decrease required trip time to the

outer planets of the solar system (1,2,3). Although required launch energy

is also reduced somewhat, rather large launch vehicles are still required

to accommodate payloads of useful size. Other studies (4,5) have shown

that the application of low thrust electric propulsion in Jupiter flyby mis­

sions can significantly increase payload,and solar electric systems appear

to be developing at a rate which should make them available for flight in

the 1970 decade. It is thus natural to consider application of solar elec­

tric propulsion to make the Jupiter swingby missions possible without the

need for large launch vehicles. This approach was investigated by Flandro (6)

in a preliminary way for a single class of boost vehicles. This report ex­

tends that analysis to other vehicles and to a new set of "grand tour" mis­

sion profiles. Of particular interest are the Earth-Jupiter-Saturn-Pluto

and Earth-Jupiter-Uranus-Neptune missions which by use of optimum solar elec­

tric Earth-Jupiter trajectory legs open the entire outer solar system to auto­

matic unmanned scientific exploration utilizing launch vehicles already in

advanced stages of development.

The mission designs presentedhere offer advantages in performance and

simplicity over other proposed techniques such as staged space propulsion

systems (7). A possible disadvantage appears in the form of increased guid­

ance complexity,but preliminary studies (8)have indicated that standard

techniques are entirely sufficient for unmanned precursor probes of the type

2

considered here. The trajectory optimization method used in what follows is

based on maximization of payload delivered at the intermediate planet Jupiter

for a given time of flight. Continuation ballistic trajectories to the second­

ary target planets Saturn-Pluto and Neptune-Uranus are optimized by selection

of best possible Jupiter arrival date for a given low-thrust Earth-Jupiter

flight duration and thus arrival hyperbolic approach speed. This method

yields results representing very closely the optimum mission profiles. Com­

plete optimization computer programs are under development (9)but are not yet

in a form suitable for mission analysis. Because of the complexity introduced

into the mision analysis process by incorporation of low thrust propulsion

(5), only three potential launch vehicles were selected for detailed evaluation:

(1)Atlas SLV-3C/Centaur, (2) Atlas SLV-SX/Centaur, and (3)Titan 3X (1205)/

Centaur. This results mainly from the inseparability of the escape and inter­

planetary phases of powered flight in low thrust analyses. The spacecraft

itself must b- regarded as part of the launch vehicle and the propulsion sys­

tem most he optimized over the entire trajectory rather than only in the vicinity

of the earth. The performance results given in this report are based on cur­

rent electric propulsion state-of-the-art (powerplant specific mass of 30 kg/kw).

Earth-Jupiter-Saturn-Pl uto and earth-Jupiter-Uranus-Neptune missions were

chosen for detailed analysis in this study. A pair of such "Grand Tour" missions

would enable closeup study of all planets of the outer solar system; this scheme

avoids the Saturn ring constraint problem which arose in previous "Grand Tour"

profiles such as the earth-Jupiter-Saturn-Uranus-Neptune mission proposed in

References 3 and 6. For reasonable trip times, the previous mission designs

required passage of the spacecraft between Saturn's surface and its inner

3

ring structure. This is a doubtful approach since the guidance accuracy re­

quirements would be extreme and, in fact, material associated with the ring

system appears to extend much closer to the planet than formerly believed.

Optimum launch dates for each of the grand tour missions are established for

the three launch vehicle combinations. Performance is summarized in terms

of the tradeoff between payload and time of flight to the target planets.

MISSION ANALYSIS PROCEDURES

Developed in this section are the mission analysis procedures required

for combined use of the intermediate planet swingby technique and optimized

solar electric low thrust propulsion in the design of multiplanet trajec­

tories.

APPLICATION OF ENERGY GAINED IN INTERMEDIATE PLANET ENCOUNTERS

Modification of interplanetary trajectories by the gravitational pertur­

bation of an intermediate planet is not a new concept; Hohmann studied bal­

listic round trip trajectories to Mars and Venus in 1925 (10). More recent­

ly investigators (c.f. References 1 and 3) have realized that a significant

change in spacecraft heliocentric energy results from a midcourse planetary

encounter. Under favorable geometrical conditions this energy can be utili­

zed in reducing the required launch vehicle size required to fly a given pay­

load to the final target planet. In the case of missions to the outer solar

system, the most important application of the energy gained in a close pass­

age of the planet Jupiter is in reducing the total trip time to the final

target planets. For example, as compared to a direct ballistic flight,

travel time to the vicinity of Neptune can be reduced by a factor of four

by first passing Jupiter (1).

The mechanism by which the heliocentric energy of the space vehicle is

changed by the gravitational perturbation during passage of an intermediate

planet is readily demonstrated in terms of basic principles. To the space­

craft, the planet represents a force field moving relative to an inertial

heliocentric coordinate system. The work done by this moving force alters

5

the heliocentric kinetic energy.

Let the heliocentric position of the planet and the probe be designated

by p and R, respectively, and the position of the probe relative to the planet

by (see Figure 1). Thus

= p +r(1)

and the total work done on the spacecraft by the planetary gravitational force

is

U PFr' dP j PP (d; + d6 (2) o t

Limits i and o refer to incoming and outgoing points on the sphere of influence

of the planet. The perturbing force is

Fp GMr (3)3

Sr

where GM is the gravitational parameter of the planet and r is the planet-to­

spacecraft radial distance. The part of the work integral due to relative 0

motion, FP dr, is zero if it is assumed that there isno sensible influ­

ence on the planet's orbit due to passage of the probe. Introducing an angu­

lar position coordinate e as shown in Figure 1 and writing

dP (Hdt)dtdo = p de -de (4)d 1(

where a ismeasured from the axis of the encounter hyperbola and p isvelocity

vector of the planet

Vp = vp P(5)

P isa unit vector inthe direction of motion. Remembering that

do - [GMa(e-1)] (6) dt r2

for a hyperbolic trajectory where a is the semimajor axis and e the eccentricity,

IA 0IJTeCwMs ASYMV~TOTE

/ / PLANCT MOTION

WePERBOAWCOUNT4R

7

the angular rate can be written in terms of the hyperbolic excess speed vh since

.a = GM/v h2 Also, the eccentricity may be written in terms of the deflection

angle between the incoming asymptote I and the outgoing asymptote 06as e =

csc ip/2 . Finally

do = GM cot(*/2) (7)2(dt

where i = cos-(I 6)and I and 0 are unit vectors pointing along the incom­

ing and outgoing asymptotes as shown in Figure 1. Choosing a coordinate sys­

tem aligned with the axis of the encounter hyperbola, one may write the unit

vectors i and j defining a right-handed set in terms of I and 0 as follows

1t = I -0 3= 1+ 0,___ ___

V2 (1-cosui T 1(1+-cosp

In this system, the probe position is r = (r cos o)i + (rsin o)J and the work

integral becomes

U 2 vvtan/2] [ 1-co s dO

2 Integrating

U =vpvh P * (0 - 1) (8)

and if one neglects the change in 1rj during passage through the sphere of in­

fluence as compared to the change in ]pJ, the increment of vehicle heliocentric

total energy is equal to the work done by the moving gravitational perturbation.

Thus

AE = U = VpVh (^ (9)

which is the most useful form for swingby performance calculations.

It is convenient to define a characteristic energy

8

E* 2Vpvh (10)

which represents the largest theoretically possible energy increment; this cor­

responds to a point mass planet with vehicle passage at the center point and

* = 1800. All geometrical aspects of the encounter are encompassed in an ener­

gy change index f such that the actual energy increment is

AE = f E* (11)

f is a number between -1 and 1 given by

f p (0 - I) (12)

For a point mass approximation for the planet f = I if the probe approaches in

the direction of the planet, passes through the center, and executes a 180o

deflection. Of-course IfI<1 always due to the finite size of the planet so

E* can never be achieved in practice. The actual value of f depends on the

direction of the approach asymptote and the total deflection angle V' at the

planet. The latter depends on the gravitational parameter GM and on the dis­

tance of closest approach to the surface d: Vh2.-i 1 3

= 2 + (d + rp)]V 1 (13)

where rp = radius of planet at point of closest approach. The geometry repre­

sented in Equation 12 is illustrated in Figure 2. The vector I along the ap­

proach asymptote and P in the direction of the planet's heliocentric motion

are fixed by the incoming trajectory and the arrival date. A convenient refer­

ence angle between these two vectors is the approach angle defined by

= cosg (-p • ) (14)

For a given I and P, the value of f and the departure asymptote are set by 0.

The outgoing asymptote may be anywhere in a cone with semi-vertex angle equal

/tSz

FIG. 2 -CONE Of ALLOWABLE OUTGOING ASYMPTOTES

10

to the maximum deflection angle *max given by Equation 13 with d set equal to

a minimum allowable passage distance (see Figure 2). is determined for a

given target planet by the hyperbolic speed vh and the arrival date at the

intermediaLe Planet. Figure 3 shows maximum obtainable energy increments

for all planets of the solar system with known mass and radius. The incre­

ment may he oither a gain or an energy loss depending on whether the probe

passes in front of or behind the intermediate planet as shown in Figure 4.

Trajectory optimization for a given arrival hyperbolic speed is accomp­

lished by van'ing the arrival date at the intermediate planet. There will

in general be four possible continuation trajectories to the target planet

but of these only the type I, class I (c.f. Reference 3) are of interest in

outer planet missions. For ballistic vehicles, f and E* are set by the

launch date and launch energy. Trajectory optimization consists simply of

finding launch dates that minimize the flight duration for a given launch

energy. Optimization is more involved when low thrust propulsion is employ­

ed anywhere in the trajectory. This problem will be discussed in the

following section.

SWINGBY TRAJECTORY OPTIMIZATION WITH LOW THRUST PROPULSION

Equation 9 shows that to achieve a large energy gain with an accompany­

ing decrease in flight time to the target planet, the geometry of the midcourse

encounter must be optimized to produce the maximum possible energy gain index

f and vh must be as large as possible. For ballistic vehicles, f and E* are

set by the launch date and launch energy. Trajectory optimization then consists

simply of finding launch dates that minimize the flight duration for a given

launch energy. The optimization problem is much more complex when low-thrust

W POINT MASS APROX. (JUPITER)

aoo

emo 0300

0SAT U

F- EARTH

0 00 _ OP0 3.50 Vt) HYPERBOLIC .X(C-SS SPEED (I(M/SE )

FIG. 3 MAXIMUM ENERGY INCREMENT VS, HYPERBOLIC EXCESS SPEED

EN'RGY GAIN ENERGY LOSS

FIG. 4 -OPTIMUM ENERGY CHANGE FOR A GIVEN APPROACH ANGLE

13

propulsion is utilized, especially ifthe propulsion system operates beyond the

encounter with the intermediate planet. In addition to the complexities intro­

duced by the necessity to consider the spacecraft itself as part of the launch

vehicle, one must consider optimization of parameter f. Thus, constraints in

addition to the usual set encountered in low thrust flyby trajectory optimiza­

tion must be included in general. The low thrust steering program must be op­

timized to produce the best possible approach geometry. The problem reduces

to one of a tradeoff between payload delivered and travel time to the target

planet.

Inthe present case inwhich Jupiter is considered as the intermediate

planet and solar electric propulsion is used, several simplifications are pos­

sible. First, all optimum trajectory modes to Jupiter with solar electric

propulsive staging are characterized by shut-down of the propulsion system

long before Jupiter encounter. This eliminatesa complicated optimization

phase which would be required if the propulsion system functioned within

Jupiter's sphere of influence. Second, for the launch vehicles considered

inthis report, low thrust trajectories which optimize the payload delivered

at Jupiter can be found which also coincide very closely with optimum continu­

ation trajectories to the secondary target planets. This is possible because

the time of flight to the secondary planets changes quite slowly with varia­

tions in arrival date at Jupiter near the optimum encounter dates. This ef­

fect is illustrated in Figure 5 for earth-Jupiter-Saturn missions. Shown

are plots of time of flight from Jupiter to Saturn versus Jupiter arrival

date with hyperbolic excess speed as parameter. Superimposed are plots of

optimized solar electric trajectory data which match the hyperbolic excess

14

3400

C-1

Vh = 5 km/se

30 fro Curves of time of flight from Jupiter to Saturn for various arrival hyperbolicNexcess speed

2600 -- - Gurres of matching 7

arrival bVperbolic excess speed for optimum solar electric Earth-J pitert,.ajector Les

, 2200­

,100

1976 Launch

L,1400

o1977

E- 6001 7

200 L

0 200 400 600 800 1000 1200

JUPITER ARRIVAL DATE (days after J.D. 2A43500)

FIG. 5 -MATCHING OF OPTIMIZED LOW THRUST EARTH-JUPITER TRAJECTORIES WITH BALLISTIC CONTTNUATION OTBYTS TO SATURN

15

speeds onthe optimum first leg arrival dates. Note that vehicles launched in

1976 give nearly optimum continuation trajectories for vh z 5 km/sec. Similar­

ly 1977 launch dates are optimum for vh - 8 km/sec and 1978 gives optimum re­

sults for vh 15 km/sec. The low thrust data shown are for Titan/Centaur type I

(direct mode) solar electric trajectories. The data will be discussed in de­

tail later in the report. To summarize, combined low-thrust Jupiter swingby

trajectories can be found (which are very nearly optimum to within a few days

of flight duration) by systematically varying the launch year. On the basis of

these observations, the optimum trajectories for the purposes of this study

are those which deliver the largest payload to the intermediate planet for a

given hyperbolic excess speed at encounter.

Techniques for generating optimized low thrust trajectory data are treat­

ed thoroughly in the literature (c.f. References 4 and 9) and will not be dis­

cussed here. A complete set of low thrust trajectory data for solar electric

earth-Jupiter flights is given in Reference 4 for the standard Atlas SLV-3C/

Centaur launch vehicle.* Appendix 1 summarizes the optimized solar electric

data for the Titan 3X (1205)/Centaur (referred to in what follows as Titan/

Centaur) launch vehicle. Shown in FiguresA-1 through A-1O are gross payload,

hyperbolic excess speed at Jupiter encounter, initial spacecraft mass, pro­

pulsion time, optimum thruster input power at launch, propellant mass, helio­

centric transfer angle, optimum injection energy, sun-planet-probe angle at

*The proposed SLV-3X/Centaur combination has very nearly the same basic trajec­

tory characteristics but about twice the payload capacity. Thus, SLV-3X per­

formance may be estimated conveniently by doubling SLV-3C payload data. SLV­

3X data presented in this report was secured in this manner.

16

Jupiter arrival, and optimum thruster exhaust velocity as functions of flight

time to Jupiter. Similar data are given in Reference 4 for the Atlas boost

vehicle. Figure 6 shows the variation of gross payload delivered to Jupiter

with launch date with earth-Jupiter trip time (Tf) as parameter. Data are

given for the entire earth-Jupiter synodic period of 1975. Later launch years

may be represented by adding appropriate multiples of the synodic period (about

398 days) to the dates shown. Note that solar electric Jupiter missions may

be flown at any time during the synodic period. However, two sub-regions ex­

hibit maxima in payload delivery and these are set off by dashed lines. Sub­

map 1 withthelargest payload for a given trip time involves use of the in­

direct trajectory mode (4,5) which requires an inward loop toward the sun to

make optimum use of the solar energy flux and a heliocentric transfer angle

of greater than 3600 degrees. Figure 7 illustrates a typical indirect mode

flight path. Submap 2 encompasses trajectories with lower performance in

terms of payload delivered. These trajectories will be referred to as "direct

mode" trajectories since they do not involve the solar loop. In addition to

the greater payload delivery, the trajectories of Submap 1 result in consid­

erably higher hyperbolic excess speed at Jupiter as shown in Figure 8. These

two characteristics couple to make the indirect trajectory performance for

swingby continuation to the secondary target planets significantly better

than that which can be achieved with the direct mode. However, this perform­

ance comes at the considerable expense of greatly increased spacecraft mechani­

cal complexity resulting from the following: (1)temperature control prob­

lems due to rather close passage of the sun (typically 0.6 a.u.) and (2)re­

quirement for wide variation in thrust vector pointing direction required for

17

0O0- SUBMAP REGION I

GRO0SS PAY LOAD,

kg0 -

.. ,

00 \\

co TOO

000 SUBMAP REGION 2

200­

1975

LAUNCH

197G

DATE

P7G. GQROSS PAYLOAD AT TiIP7I:TER VS,, LA.mu I:! DATE ?9.75 SYOW PERYX " ALAS SLN?/CENm

P0.'2, p..

y=M OTO OFF S(3 d5yV //1E ATS 'ALSARRIVUa

/ JUPITER AT ARROVA 03 J,,%UA,/R Y 978)

EA TH AT LAUNCH AUGUSTf U973-)__(2

\ 3 AU. 2

20JA2E LEO7,-7 PAL OT " EAflT!!-JU? 2 SO -TRICo,

TZ7".::? ?AT:l - riDZZ:,T t1OD3

Do.

270F YPE RD L 1

JUPIR 0 141 7,n:30 DAYS

OUDMA. % " gSrBMAP 2.-,.x...

0 12(Q100 Za9W, 9

-AUNCT',- DDA77 ,QIJLUA, D/M A7TIM 1?0911 244330)

TIG, 8 - t-UPIE-11OLT7 A??7ROAtC'4 SPEMD AT JUPITERl VS, IAUNCH IA.E V'2 ,1977SUMOD7C PERIOD.

20

generating the optimum indirect mode flight path. The latter effect is illus­

trated in Figure 9. Note that the spacecraft must provide for a swing of more

than 3600 in the thruster alignment relative to the spacecraft-sun line while

maintaining the solar panel array in normal attitude with respect to the sun.

Spacecraft designs which accomplish this have been proposed (11) but much of the

potential payload advantage resulting from the indirect mode approach is

lost in solving the mechanization problems. Additional problems relating

to spacecraft reliability and guidance considerations also arise; these are

difficult to assess quantitatively in terms of overall performance but the

present interpretation is that use of the direct mode is more desirable in

an overall sense. Both direct and indirect mode performance data will be dis­

cussed below for the Atlas/Centaur launch vehicles; Titan/Centaur payload

performance is given only for the direct mode on the basis of the above ob­

servations.

Methods for presentation of low thrust trajectory data are still evolv­

ing. Several forms of presentation are employed in what follows. A particu­

larly graphic representation of a given mission opportunity is provided in

plots of time of flight versus launch date.* In ballistic studies, the

launch energy or hyperbolic excess speed provides a convenient parameter for

these curves; payload for a given mission point is then determined for a

launch vehicle of interest by utilizing the launch energy versus payload curves

*This is preferable to the standard arrival date versus launch date plots in

outer planet studies since flight times are so long that data resolution is

lost if dates rather than time of flight are used.

21

120

S606Motor off

-0 -­

120 L­

-

00 00 300 400 500 600

TIME FROM TNJECTION (days)

FId0 9 - THRUST ANGLE VS TIME FOR OPTIMUM 900-DAY JUPITER FLYBY MISSION (INDIRECT MODE).

22

for that booster. As already pointed out, this simple procedure cannot be used

in low thrust studies since the spacecraft must be considered as part of the

launch vehicle system. Thus, separate performance curves are required for

each boost vehicle and a convenient form for data presentation is the use of

payload mass as parameter replacing the launch energy or hyperbolic excess

speed used in the corresponding ballistic plots. All trajectory data of im­

portance can be presented in this way--the mission designer can then tell

at a glance, by use of overlays of this data, where the best combination of

desired mission characteristics lies within the spectrum of launch dates.

Comparison of different launch vehicles and trajectory modes is most conveni­

ently made in terms of plots of payload versus mission duration for optimal

conditions. This method will be used later for assessing the capabilities of

the boost vehicles selected for the present study in low thrust swingby mis­

sions to the outer planets.

All low thrust earth-Jupiter trajectories utilized inwhat follows are

based on current state-of-the-art with powerplant specific mass of 30 kg/

kw. N-P solar cells are assumed and the solar constant is taken as 140 milli­

watts/cm2 . Solar power variation with radial distance is based on current

Jet Propulsion Laboratory N-P solar cell estimates. Ballistic continuation

trajectories were generated with a three-dimensional conic trajectory pro­

grams.*

*Space Research Conic Program Phase III, Jet Propulsion Laboratory Report 900­

130, April 1968.

EARTH-JUPITER-SATURN MISSIONS WITH SOLAR

ELECTRIC PROPULSION

The several possible launch years for flights to Saturn utilizing the

Jupiter encounter maneuver were established by superimposing plots of hyper­

bolic excess speed at Jupiter versus Jupiter arrival date for optimal low

thrust trajectories on plots of hyperbolic excess speed at Jupiter.required

for continuation to Saturn. These plots are related to those already dis­

cussed in Figure 5. Optimum launch year depends on the desired payload for

a given launch vehicle as will be shown. Acceptable launch dates for this

mission fall between the summer of 1976 and the winter of 1978. Constraints

which prohibit launch dates in earlier or later years will be discussed present­

ly. Three-year launch opportunities recur with a period of about twenty years;

thus, if the 1976-78 opportunity is missed, 1996 would represent the next

acceptable launch year.*

Figure 10 illustrates a typical Earth-Jupiter-Saturn flight path utiliz­

ing the indirect solar electric mode. The characteristic inward loop toward

the sun is evident. Motor operation time is quite long--typically 600 days

for the indirect mode. Direct mode trajectories are almost ballistic in ap­

pearance and motor operation time is much shorter--usually less than 400 days

for trajectories of interest (c.f. Figure A.4). This again represents a

reliability consideration in flight mode selection.

*These observations hold for ballistic as well as for solar-electric earth­

Jupiter-Saturn missions.

I-JTLY 091)

/ T

~I

EARTh ATLAUJ'C O TOMD R T977)

/

/

JUPITER ENCOUNTER

71G2 20 - 7"7CAL .DnT0TMD EAR72-JUP2T31-SATUIN FLIGHT PATH

25

Figures 11, 12, and 13 are plots of total flight time to Saturn versus launch

date with payload as parameter for the Atlas SLV-3X/Centaur booster for the

1976, 1977, and 1978 launch opportunities, respectively. These plots are are

for the indirect low-thrust mode. Launches in 1977 provide the best perform­

ance in terms of payload delivered for trip times less than four years; 1976

is the superior launch year for trip times greater than four years.

Figures 14, 15, and 16 show plots of flight duration versus launch date

for direct mode solar electric earth-Jupiter-Saturn missions utilizing the

Atlas SLV-3X/Centaur launch vehicle. Notice that for shorter flight times

(less than 3.5 years) and lower payloads (less than AOO kg), 1978 represents

the optimal launch year; for larger payloads (and flight time), 1977 is the

best launch year.

Figures 17, 18, and 19 are plots of the optimum launch dates versus pay­

load mass for 1976, 1977, and 1978 for direct mode trajectories utilizing the

Titan/Centaur boost vehicle. Figure 20 shows the corresponding passage dis­

tances at Jupiter required to enter the Jt'piter-to-Saturn continuation orbits.

Notice that short flight-time trajectories in 1976 are limited by the deflec­

tion angle constraint; to achieve continuation with total flioht time less than

3.2 years would require a propulsive maneuver near Jupiter. It must be pointed

out that in addition to the payload-flight duration tradeoff already discussed,

the mission planner must take account of intermediate planet passage distance

in terms of desired scientific data return. The instrumentation requirements

play a part in launch year selection; 1976 trajectories yield very close pass­

age distance while 1978 launches pass far from Jupiter's surface since the re­

quired continuation bend angle is much smaller. Payload performance for the

three available launch years is summarized in Figure 21 for the Titan/Centaur

26 1700 /

//

1500 800

0

<=1

),00 600

T)l 500 ks

1200

15 30 15 3o 35 30 15 30 JlJLV AUGUST SEPTEMBER OCTOBER,

LAUNC!U DATE 3976

FIG. 33 - FLIGF71 DURATION VS LAUNCH DATEI FOR 1976 FAaTi'l JUP!TR STU&! ,iSTO)ISLVY32,!Centaur ,N')iP*f.T MOPS

27

1700! / /

Ei 16009 /

800

121300

700

1200

600

I0500 13

FTG. 12

310 R5 30 .5 3 SEPTEMBER OCTOBER

LAUNCH DATE ?977

FLI.GHT DUPATTON VS LAUNCH DATE FOR ,977 SATUPI IMTSSXOU SLV--'GENTAUP. TND-E'tCT

25 -0 NOVEMITER

EAP5Th-JUPITER-MODT,

28 2200

0

/ / 2100

2000

1900

c1

CJ'o1700121800

- 1500 _ _ _ _ _ _ _ _

1400

"60 01300 1 1

gitP 500 kg

1200t15 30 _ 15 ?a0 15 10 35 2

SEPTEMBER OCTOBER NOVEMBER DECEMBER

LAUNCH DATE 1978

FIG. 13 - FLIGHT DURATION VS LAUNCH DATE FOR 1978 EARTH-JUPITER-SATUP! MISSION SLV-3r/CENTAUR INDWIECT MODE

29

1900

f-i

550)

C5'0

Z1700

1600

r-, 1500b

(-1

.350 kg

1300 -- - -I 10 20 30 30 20

LY JUN&

Launch Date 1976

FIG. IA - FLIGHT DURNTION VS LAUNCH DATE FOR 1976 EART-!UJUPITER-SATURN MISSTON SLV-Y/CENTAUP. DYRECT MODE.

30

1900

1800

.1700 Ml = 550 kg

cq1

R- 1600

CIO

1500 500 -

0

1500

1200

30 10 20 30 10 20 JUNE JULY

LAUNCH DATE 1977

F1G. 15 FLIGHT DURATION VS LAUNCH DATE FOR :1977 EARTH-JUPITER­-

SATURN M.SS70N. Sy,V -32/CENTAUPR DIRECT MODE°

31

1900

1800

1700

'c 1600

cie

U) A50

Cs

-,400

400 1300

13000

12.00 __ __ __ "----

10 20 30 10 20 30 JTULY AUGUST

LAUNCH DATE 1978

FIG. 6 - FLIGHT DURATION VS LAUNCH DATE FOR 1978 EARTH-JUPITER-SATURN MISSION. SLV-3XK/CENTAUR DIRECT MODE..

32

2200

2000 i

v 1 V r

1800­

-

:,71600

.1200 _ -

H

o 1000 Jupiter SurfaceConstraint

600 i LL __ wIL_ J , 20 25 30 5 10

JUNE 1976 JULY 1976

OPTIMUM LAUNCH DATE 1976

FIG. 17 - OPTIMUM LAUNCH DATE VS PAYLOAD MASS FOR 1976 EARTH JUPXTER-SATURN MISSION. DTRECT MODE TITAN 3X(1205)/CNTAUR LAUNCH VEHICLE. -

IJL. 15

33

2200 ­ 1 -T f-FI I - -T I~I 1

2000 -­__-_

1800

cn _ _ _ _o 1600

00 co

C 1200

1000

800

600 WS 5 10 15 20 25 30

AUGUST 1977

OPTIMU LAUNCH DATE 1977

FIG. 18 - OPTIMUM LAUNCH DATE-VS PAYLOAD FOR'1977 EARTH-JUPITER-SATURN MISSION. DIRECT MODE TITAN 3X/CENTAUR BOOSTER.

34

I

2000

220l I III I

< 1600

rs

ion

SETME 19784

6 0 0-LLWJJW=LJ~U WLIL 5 '.0 15 20 25 30

SEPTEMBER 1978

OPTI UM LAUNCH DATE 1978

FIG. 19 - OPTIMUM LAUNCH DATE VS PAYLOAD FOR 1978 EARTI-JUPITER-SATUR MISSION. DIRECT MODE TITAN 3K/CENTAUR BOOSTER.

35 20 /

Q16 f

C)IA 41

Optimum Launch in 1978

_____

rtl

R V'

P o 10 E-I

Optimum Launch in 1977

Ii

o)

a r-,

~Opt imum-Launch in19767

Planet

700 900 1100 1300 1500 1700 7900 2100

OPTIMUM GROSS PAYLOAD KLASS (kg)

FIG. 20 -RADIUS OF CLOSEST APPROACH TO JUPITER VS OPTiMI14 GROSS PAYLOAD FOP, EAPT11-JUP!TEPR-SATURNq MISSIONoTITAN 3X( ]205)/GENTAUR, LAUNCHI VEHICLE . DIRECT MODS.o

__ _ _ _ _ _ _ _

36

2200 I

Optimum Launch

in 19772000 2000 _._ ,

1800 OptimumWXly- Launch /

c 1600

Optimum Launch in 1976

1400

0

Jupiter Surface

000 L /Constraint

800 /// 1oo 1 800 / /___ _____ _____

600! /2.0 2.5 3.0 3.5 4.0 4.5 5.0

TOTAL FLIGHT TIME TO SATURN (years)

FIG. 21 FLIGHT DUrATTON - PAYLOAD TRADEOFF FOR EARTLIJUPITER-SATU N MISSION. TITAN 3X/CENTAUR DIRECT MODE.

37

booster. Mote that 1978 produces the best trajectories for flight times less

than 3.2 years, 1977 is best for flights between 3.2 and 4.8 years duration,

and 1976 is best for mission times greater than 4.8 years.

SOLAR ELECTRIC SWINGBY MISSIONS TO

URANUS, NEPTUNE, AND PLUTO

The techniques discussed previously were used to investigate Jupiter

swingby missions to Uranus, Neptune, and Pluto with optimum low thrust pro­

pulsion. Since Neptune and Pluto may be reached by continuation trajector­

ies from Uranus and Saturn, respectively, to be discussed in the next sec­

tion, detailed data is not given here for those mission possibilities.

Reference 6 gives some results for earth-Jupiter-Neptune and earth-Jupiter-

Pluto missions.

Figures 22 and 23 are plots of flight duration to Uranus versus launch

date for Atlas SLV-3X/Centaur indirect mode optimum solar electric trajec­

tories; Figures 24 and 25 give the same results for direct mode trajectories

utilizing the Atlas/Centaur and laUnches in 1978 and 1979. Indirect mode

trajectories are best launched in 1978; direct mode flights of less than

6.5 years duration should be initiated in 1979. Direct mode flights of

duration longer than 6.5 years are best launched in 1978.

Figures 26, 27, and 28 show optimum launch dates in the years 1978, 1979,

and 1980, respectively, for direct mode earth-Jupiter-Uranus flights utilizing

the Titan/Centaur boost vehicle. Figure 29 illustrates the closest approach

distance corresponding to the above trajectories. The Uranus surface con­

straint called out in Figure 29 refers to continuation trajectories to Nep­

tune to be discussed later. Figure 30 summarizes the Titan/Centaur data in

terms of a trip time-payload tradeoff for the three potential launch years.

1980 is an acceptable launch year only for very high energy (low payload)

39

0

2800

2700

2600

2500

En

2400 800

2300

2200 -00 /---

2100 ­

2000 ­ = 00 kgi

1900 15 AUGUST

30 15 SEPTEMBER

30 15 OCTOBER

30 15 NOVEMBER

30

LAUNCH DATE 1978

FIG. 22 - FLIGHT DURATION VS LAUNCH DATE FOR 1978 EARTH-JUPITER-URANUS MISSION. SLV-3X/CENTAUR INDIRECT MODE,

40 3900

3700 :===

3500 /,

3300

3100

800S2900

2700

500

2 3 0 0 60 0

2100 ____ _____ _ _ _2= 500 kg

1900 15 30 15 30 15 30 15 30

SEPTEMBER OCTOBER NOVEMBER DECEMBER Launch Date 1979

FIG. 23 - FLIGHT DURATION VS LAUNCH DATE FOR 1979 EARTIIJUPITER-UPTkuS MISSION. SLW-3[x/CENTAUR INDIRECT MODE.

41

3000

2900 50o~

cc

2800

z 2700

0

2600 F-4

2500 40

2400

2300 30 10

JULY 20 30

LAUNCH DATE 1978

10 AUGUST

20 30

FIG. 2A - FLIGHT DURATION VS LAUNCH DATE FOR 1978 EARTH-JUPITER-URANUS MISSION. SLV-3X/CENTAUR DIRECT MODE.

42 3900 / 42

3700

3500

3300

o 3100 /

05

I-,10 2900

2700

400 2500

2300 Ml = 350 kg

10 20 30 10 20 30 AUGUST SEPTEMBER

LAUNCH DATE 1979

FIG. 25 - FLIGHT DURATION VS LAUNCH DATE FOR 1979 EARTH-JUPITER-URANUS MISSION. SLV-3X/CENTAUR DIRECT MODE.

43

2200 I IIIF IIII 1 I Wv F 7­

2000

_18001

cn 16001 CI

1400

En 0 1200

[.4 Jupiter Surface__1l0001

Constraint

800

600 25201505

SEPTEMBER 1978

OPTIMUM LAUNCH DATE 1978

LAUNCH DATE VS PAYLOAD MASS FOR 1978 FIG. 26 -OPTIMUM MODEMISSION. DIRECTEARTH-JUPITER-URANUS

LAUNCH VEHICLE.TITAN 3X(12OS)/CENTAUR

__

44

2200

2000

1800

1600

1400

1200 ­

1000L6001 1_

o Uranus Surface

Constraint

800

5 10 15 20 25 30

OCTOBER 1979

OPTIMUM LAUNCH DATE 1979

FIG. 27 - OPTIMUM LAUNCH DATE VS PAYLOAD MASS FOR 1979 EARTH-JUPITER-URANUS MISSION. DIRECT MODE TITAN 3X(1205)/CENTAUR LAUNCH VEHICLE.

45

22 0 0 w 77Th 77Th 1 -WV7ThV

2000

1800

En

m 1600

1400

0

o 1200

P4 o 1000 \

800

10 15 20 25 30 5

NOVEMBER 1980 DECEMBER 1980

OPTIMUM LAUNCH DATE 1980

FIG. 28 - OPTIMUM LAUNCH DATE VS PAYLOAD MASS FOR 1980 EARTH-JUPITER-URANUS MISSION. DIRECT MODE TITAN 3X(1205)/CENTAUR LAUNCH VEHICLE.

46

20 ­

18

16 Optimum Launch in 1980

414

Optimum Launch

0 12 __in /12 1979

'-4

o

C,,E-, 10

P4N 8

o 6

~Uranus Uau Optimum Launch o - Surfac in 1978 -

Constraint i

2 , / Planet

Surface

0 700 900 1100 1300 1500 1700 !900 2100

OPTIMUM GROSS PAYLOAD MASS (kg)

FIG. 29 - RADIUS OF CLOSEST APPROACH TO JUPITER VS OPTIMUM GROSS PAYLOAD FOR EARTH-JUPITER-URANUS MISSION TITAN 3X/CENTAUR LAUNCH VEHICLE, DIRECT MODE.

47

2200 I I

Optimum Launch in 1978

2000 _ _ _______ _

1800

o --Optimum Launch in 1979

In 1600 ­

fit /Optimum Launch rn in 1980 C)

c,1200

- Jupiter Surface Constraint P4 IWO

80 Uranus Surface Constraint800 ____

//

600(- _ _ _

4 5 6 7 8 9 10 11 TOTAL FLIGHT TIME TO URANUS (years)

FIG. 30 - FLIGHT DURATION - PAYLOAD TRADEOFF FOR EARTH­JUPITER-URANUS MISSION, TITAN/CENTAUR DIRECT MODE.

48

trajectories of less than 4.6 years duration. 1979 is the best launch year for

flights between 4.6 and 6.5 years in length; 1978 yields best payload for flight

duration of greater than 5.5 years. Uranus opportunities via Jupiter are avail­

able about every 14 years.

SOLAR ELECTRIC GRAND TOUR MISSIONS

Itwas shown by Flandro (1,6) that earth-Jupiter-Saturn trajectories

launched in the 1977-1978 opportunity may be continued after Saturn encounter

to Uranus and finally to Neptune. This mission opportunity is repeated every

175 years. An unfortunate feature of the "grand tour" as this four-planet

mission is often called results from the interaction of Saturn's ring system

with the Saturn-Uranus trajectory leg. Trajectories which pass outside of

the ring system require too long to reach Uranus and Neptune; those passing

between the surface of Saturn and the rings might require unattainable guid­

ance accuracy. In the latter regard, recent data seems to indicate that ring

material may extend much closer to the planet than previously believed, thus

making passage beneath the rings somewhat risky. It has thus been proposed

that instead of a single "grand tour" mission that two be considered: (1)Earth­

Jupiter-Saturn-Pluto and (2)Earth-Jupiter-Uranus-Neptune. By bypassing Saturn

in the Uranus-Neptune mission the ring constraint obviously vanishes. Ring

geometry is not so severe an effect in the earth-Jupiter-Saturn continuation

to Pluto. Thus, with a pair of spacecraft launched in the 1977-1979 period,

the entire center solar system can be explored utilizing launch vehicles al­

ready in advanced stages of development. Application of solar electric pro­

pulsion to the earth-Jupiter leg of the trajectory allows delivery of more

than three times the gross payload which could be accommodated on a ballis­

tic flight with the same basic launch vehicle.

EARTH-JUPITER-SATURN-PLUTO GRAND TOUR

Figure 31 shows the projection of a typical direct mode Pluto grand tour

50

Pluto at Arrival June 3, 1984

40.20 Saturn at Arrival March 10, 1980

/

/ \/ \\ / 54,

Earth at Launch - C August 23, 1977 ,/

/ Jupiter at N - - Arrival

Nov. 18, 1978

1470 Motor of f 278 days

FIG. 31 - TYPICAL DIRECT MODE EARTH-JUPITER-SATURN-PLUTO "GRAND TOUR" FLIGHT PATH

51

in the ecliptic plane. As Figure 32 indicates, the required passage distances

at Saturn for the trajectories of interest are sufficiently great to preclude

problems due to the Saturn ring system. Details for the earth-Jupiter-Saturn

portion of the mission profile were given in a previous section of the report.

Optimum launch dates are the same as for the earth-Jupiter-Saturn missions.

Figure 33 shows the payload-flight duration tradeoff for Titan 3X/Centaur

booster. Note that launches in either 1977 or 1978 make possible delivery

of payloads greater than 1000 Kg (2200 lb) in less than seven years with

this launch vehicle. 1977 is the best launch year for flights of less than

9.3 years duration; 1976 launch gives higher payload for missions of greater

than 9.3 years duration.

Figures 34 to 36 show curves of time of flight to Pluto versus launch

date with payload as parameter for the 1976, 1977, and 1978 launch dates.

These curves are for the Atlas SLV-3X/Centaur launches with direct flight

mode. Indirect mode trajectories are represented in Figures 37-and 38 for

the same boost vehicle system. Notice again the payload advantage exhibited

by indirect mode trajectories as already discussed.

EARTH-JUPITER-URANUS-NEPTUNE GRAND TOUR

Figure 39 shows the flight path for a representative direct mode Neptune

grand tour. Detailed data and optimum launch dates for the mission are dis­

cussed in the earth-Jupiter-Uranus section of the report. Figure 40 shows the

required passage distance at Uranus for ballistic continuation to Neptune for

the three possible launch years 1978, 1979, and 1980. All trajectories are

type I, class I orbits representing minimum time of flight continuations.

Figure 41 summarizes trajectory results for direct mode Neptune grand tours

52

20

18

Optimum Launch in 1978

16

14

(n4-34

~12

H Optimum

CLaunch

Sin 1977

01

[-,

0- 6, L _ _ _ _ _

Optimum Launchin 1976

~~2

L Planet

Surface

700 900 1100 1300 1500 1700 1900 2100

OPTIMUM GROSS PAYLOAD MASS (kg)

FIG. 32 - RADIUS OF CLOSEST APPROACH TO SATURN FOR EARTH-JUPITER­SATURN-PLUTO "GRAND TOUR" MISSIONS. TITAN/CENTAUP DIRECT.

53

p-timum Launch in 1976

Optimum Launch in 1977

Optimum Launch in 1978

1800 ____

b 1600

z __________ ___toS1400

0 /-4

1200 U)

o Jupiter

1 / --- Surface 1000/ ­/Constraint

/

///i 800 aoo ,/ ____

60 0 ... . .. _i 5 6 7 8 9 10 11 12

TOTAL FLIGHT TIME TO PLUTO (years)

FIG. 33 - PAYLOAD - TRIP TIME TRADEOFF FOR EARTH-JUPITER­SATUPN-PLUTO "GRAND TOUR" MISSION. TITAN/CENTAUR LAUNCH VEHICLE. DIRECT TRAJECTORY MODE.

54 6000

5500 _ _ _ _ _ _ _ _ _ __ _ _ _ _

5000

4

1E,4500 =

H ~500 0

'"' ' '---- " '-' '-- j .450

400

3500­

3000 Mp! = 350 kg

30 00 20 30 10 20

APRIL MAY JUNE

LAUNCH DATE 1976

FIG. 34 - FLIGHT DURATION VS LAUNCH DATE FOR 1976 EARTH-JUPITER­SATURN-PLUTO "GRAND TOUR" MISSION. Atlas SLV3X/ Centaur LAUNCH VEHICLE. DIRECT MODE.

55

6000

5500

5000 -1 500 CD 0P4

S4500

'4

4000 450

400

3500 _

3000

30 10 20 30 i0 20 JUNE JULY

LAUNCH DATE 1977

FIG. 35 -FLIGHT DURATION VS LAUNCH DATE FOR 1977 EARTH-JUPITER­SATURN-PLUTO "GRtAND TOUR" MISSION. ATLAS SLV3X/ CENTAUP LAUNCH VEHICLE° DIRECT MODE.

56

10,000

9000 450

-..8000

H

00

0 6000

400

5000

4000

30 10 JULY

20 30

LAUNCH DATE 1978

10 AUGUST

20

FIG. 36 - FLIGHT DURATION VS LAUNCH DATE FOR 1978 EARTH-JUPITER-SATURN-PLUTO "GRAND TOUR" MISSION. ATLAS SLV-3X/CENTAUR DIRECT MODE.

57

4300

4100

3900 _

3700 900 /

0800

P370000 oo

bt00 50-R

15 30 15 30 25 30 15 30 JUME JULY AUGUST" SEPTEMBER

UUNCH DATE 1976

FIG. 37 - FLIGHT DURAT!ON4 VS LAUNCH DATE FOR 1976 BAPTH­JUPITER-SATUM.-PLUTO "GRA ND TOUR" MISSIOW, ATUAS SLV-3X/CE:NTAUR 'NDI)IRCT MODE.

58

4500

01

IL300

4100

cd3900

800

50023700

H 3500

fr-I

or 700

3300

3100

2900

27001ii 30 15 30 15 30 15 30 15

AUGUST SEPTEMBER OCTOBER NOV

LAUNCH DATE 1977

FIG. 38 - FLIGHT DURATION VS LAUNCH DATE FOR 1977 EARTH-JUPITER-SATURN-PLUTO "GRAND TOUR" MISSION. ATLAS SLV-3X/CENTAUR TNDIRECT MODE,

59 Neptune at Arrival Dec. 6, 1986

Uranus at Arrival May 15, 1984

//

22.20

// " 70.8'

Earth at Launch /Oct. 17, 1979 Jupiter at

arrival _____________ N~.Jan 12, 1981

Motor OffK 278 days

1470

FIG. 39 - TYPICAL DIRECT MODE EARTH-JUPITER-UPANUS-NEPTUNE "GRAND TOUR" FLIGHT PATH.

_ _

60

20

18

16-

14

n12

Optimum Launcho 0 in .1980

0

88

0

o

opmum

in 1978Planet -Surface

0 700 900 1100 1300 1500 1700 1900 2100

OPTIMUM GROSS PAYLOAD MASS (kg)

FIG. 40 - RADIUS OF CLOSEST APPROACH TO URANUS FOR EARTH-JUPITER-URANUS-NEPTUNE "GRAND TOUR" MISSIONS TITAN 3/CENTAUR LAUNCH VEHICLE, DIRECT MODE.

61

2200

Optimum Launch in 1978

2000 Optimum Launch in 1979

Optimum Launch in 1980

1800 _

bo g 1600 V3

1400

cn 1200 ,___ 0

/ ; " Jupiter" 1000 I -" \ Surface .

,./Constraint

800 ;

Uranus

Surface Constraint

600 1 1 6 7 8 9 10 11 12 13

TOTAL FLIGHT TIME TO NEPTUNE (years)

FIG. 41 -PAYLOAD - TRIP TIME TRADEOFF FOR EARTH-JUPITER-URANUS-NEPTUNE "1G&AND TOUR" MISSION. TITAN'3X/CENTAUR LAUNCH VEHICLE, DIRECT MODE.

62

utilizing the Titan/Centaur launch vehicle. For total flight duration of less

than 9.3 years, the best launch year is 1979. However, there exists an Uranus

surface constraint due to required deflection angle at Uranus for continuation

to Neptune for the 1979 launches which precludes flights launched in that year

of less than seven years duration. It is possible to launch in 1978 with

flight time as low as 6.7 years at which point the Uranus surface constraint

is interposed. For flight duration of greater than 9.3 years, the optimum

launch year is 1978.

Plotted in Figures 42 and 43 are flight time versus launch date at earth

for 1978 and 1979 Neptune grand tour missions utilizing the Atlas/Centaur

launchers and direct solar electric trajectory mode. Figure 44 gives simi­

lar data for the 1978 indirect mode which year represents the best launch op­

portunity involving that mission mode.

The kinetic energy of the spacecraft at any time after Jupiter encounter

in any of the trajectories discussed in the previous sections of the report

exceeds that required for solar system escape; outer planet missions could

well be continued after the final planetary encounters with Pluto or Neptune

as galactic probes.

63

4900

4700

"o4500 500

4300

z 0

H 4100

'450

0

'- 3900

400

3700­

~MI= 350 kg

3500 30 10 20 30 10 20 30

JULY AUGUST

LAUNCH DATE 1978

FIG. 42 - FLIGHT DURATION VS LAUNCH DATE FOR 1978 EARTH-JUPITER URANUS-NEPTUNE "GRAND TOUR" MISSION. ATLAS SLV-3X/ CENTAUR LAUNCH VEHICLE, DIRECT MODE.

64

6000

5500

V

5000z4

0

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _

4500

-4000 _____ __ 400___ ___._.________

350

3500 _ M p1 350 kg

10 AUGUST

20 30 10 20 SEPTEMBER

LAUNCH DATE 1979

30

FIG. 43 - FLIGHT DURATION VS LAUNCH DATE FOR 1979 EARTH-JUPITER-URANUS-NEPTUNE "GRAND TOUR" MISSION. ATLAS SLV-3X/CENTAUR DIRECT MODE.

65 4600 / 65

4400

4200 __

cd 4000

r900

Ttl 3800 z 0

S3600 t00 __ __

E-4

2800 000

3200 _ _ _ _ _ _ _ __ _ _ _

3000 1________

28001M15

AUGUST

30

50k

15 30 15

SEPTEMBER OCTOBER

LAUNCH DATE 1978

30 "15 --­3'0

NOVEMBER

FIG. 44 - FLIGHT DURATION VS LAUNCH DATE FOR 1978 EARTH­JUPITER-URANUS-NEPTUNE "GRAND TOUR" MISSION. ATLAS SLV-3X/CENTAUR,, INDIRECT MODE.

CONCLUSIONS

It has been shown that significant performance advantage results from

application of optimized solar electric low thrust propulsion to the initial

leg of Jupiter swingby missions to the outer planets. The indirect mode of

solar electric flight with its initial close passage of the sun yields best

payload performance at the expense of spacecraft design complications. Gross

payload is typically tripled at the target by incorporation of electric pro­

pulsion.

Performance data for the mission designs considered herein are summarized

in Figures 45 through 48. Optimum launch years, time of flight, and payload

for each mission are represented for earth-Jupiter-Saturn, earth-Jupiter-

Uranus, earth-Jupiter-Saturn-Pluto and earth-Jupiter-Uranus-Neptune flights.

Notice again that the entire outer solar system is opened to unmanned explora­

tion by the combined use of solar-electric propulsion and the intermediate

planet swingby technique. Two spacecraft of more than 1000 Kg (2200 lb) pay­

load launched in the 1977-1979 period could reach Saturn within 2.4 years,

Uranus within 4.6 years, and Neptune and Pluto within seven years. Only

launch vehidle systems which are already "off-the-shelf" items are required

for this exploration.

The ultimate feasibility of complex space missions of the type described

herein will depend on advances in guidance of low thrust vehicles, improved

reliability of electric propulsion systems, and solution of spacecraft de­

sign problems posed by application of continuous propulsion. Solution of

these problems will make possible the unmanned exploration of the entire

solar system with launch vehicles of moderate size.

67

2000 I TITAN/CENTAUR/S OLAR ELECTRIC lo (direct mode)

1800 ­

1600 /

1400 /

ATLAS SLV-3X/CENTAUR/SOLAR ELECTRIC (indirect mode)'1200 .

o 1000

0 S800

y SLV-3X/CENTAUR/,ATLAS / SOLAR ELECTRIC

600 (direct mode)

400 / )

ATLAS SLV-3X/CENTAUR/ BURER Ii (ballistic)

200 ___

0 2.0 2°5 1.0 3.5 4.0 4.5 5.0

TIME OF FLIGHT TO SATURN (years)

FIG. 45 - GROSS PAYLOAD VS TIME OF FLIGHT FOR OPTIMUM EARTH-JUPITER-SATURN SOLAR ELECTRIC MISSIONS

68

2200

TITAN/CENTAUR/SOLAR ELECTRIC

2000

1800

1600 /

1979 0~1400 ___ ___ ___

(1o /

1200 I ATLAS SLV-3X/CENTAUR/SOLAR ELECTRIC

/ / --(idirect mode)

1000

800 //1980 ATLAS SLV-3X/CENTAUR/

SOLAR ELECTRIC 600 (direct mode)

400

200 .... ­

4 5 6 7 8 9 10 11

TIME OF FLIGHT TO URANUS (years)

FIG. 46 - GROSS PAYLOAD VS TIME OF FLIGHT FOR OPTIMUM EARTH-JUPITER-URANUS SOLAR ELECTRIC MISSIONS

__

69 2oooII I TITANI/CENTAUR/SOLAq R ELECTRIC

1800 (direct m ),,a.

1600

.00o

J4o120n

~f1OO __ __e) - __ [ J ATLAS SS---3X/CEN TAR/

000 SOLAR E SLECTRICA__ET _ I

find (rct mode )

-I84/ 3/CENTAUR/

200

Ii

0 &... .... ......... ... . .. . .. .r ...

5 6 7 8 910 11

TIME OF FLIGHT TO PLUTO (years)

T11 G .7 G-gOSS PY7V.QAD VS TIME OF FLIGHT FOR OPTIMUM EARTI-.1UP ZTER-SATURN -PLUTO SOLAR ELECTRIC

tGCAIND TOUR" MISSIONS.

12

70

2200

TITAN/CENTAUR/SOLAR ELECTRIC 2000 (direct mode) i,

1800

1600

- 1400 z

1979

1200

ATLAS SLV-3X/CENTAUR/SOLAR ELECTRIC (indirect mode)

000 0

800 - _ _ _ _ _ _ _ _ _

1980 / ATLAS SLV-3X/CENTAUR/

SOLAR ELECTRIC600___ 600 (irect mode)-

200 __ 6 7 8 9 10 11 12 13

TIME OF FLIGHT TO NEPTUNE (years)

-GROSSFIG. 48 PAYLOAD VS TIME OF FLIGHT FOR OPTIMUM EARTH-JUPITER-URANUS-NEPTUNE SOLAR ELECTRIC "1GRAND TOUR" MISSIONS.

APPENDIX 1

Basic Low Thrust Trajectory Data for Optimum Solar

Electric Flight to Jupiter Utilizing Titan/Centaur

Launch Vehicle

72

2200

2000 __

1800

1600

1400

1200

100 1000

600,

400 600 800 1000 1200 1400

TIME OF FLIGHT TO JUPITER (days)

Fig. A.1 - GROSS PAYLOAD VS. TIME OF FLIGHT TO JUPITER TITAN 3X(1205)/CENTAUR, DIRECT MODE.

73

18

16

1214

14

I-4

cn

FI

S10

rilr

M>4

4 I-I 800 000 1200 1400400 600

TIME OF FLIGHT TO JUPITER (days)

EXCESS SPEED AT JUPITER VS TIME OFFIG. A.2 -HtYPERBOLIC FLIGHT TO JUPITER. TITAN/CENTAUR, DIRECT MODE

74

4000

1-4

4500

3500 /

3000

2500

2000

400 600 800 1000 1200 1400 TIME OF FLIGHT TO JUPITER (days)

FIG. A.3 - INITIAL SPACECRAFT MASS VS TIME OF FLIGHT TO JUPITER. TITkN 3X/CENTAUR, DIRECT MODE.

1500

75

500

C'p

400

H/P"4 00

0a4

300

400 600 800 1000 1200 1400 TIME OF FLIGHT TO JUPITER (days)

FIG. A.4 - TOTAL PROPULSION TIME VS TINdE OF FLIGHT TO JUPITER. TITAN 3X(1205)/CENTAUR, DIRECT MODE.

76

45

40

35

-30

25

0 *20

400

FIG. A.5

600 800 1000 1200 1400

TIME OF FLIGHT TO JUPITER (days)

- OPTIMUM THRUSTER INPUT POWER AT LAUNCH VS TIME OF FLIGHT TO JUPITER. TITAN/CENTAUR, DIRECT MODE.

77

900

800

o700

600

: 500

400

300 400 600 800 1000 1200 1400

TIME OF FLIGHT TO JUPITER (days)

FIG. A.6 - PROPELLANT MASS VS TIME OF FLIGHT TO JUPITER TITAN 3X(1205)/CENTAUR, DIRECT MODE.

78

260

240

- 220

ir 200

[,-a

H180

S160

140

120 400 600 800 1,0 1200 1400

,TIME OF FLIGHT TO JUPITER (days,.)

FIG. A.7 -OPTIMUMHELIOCENTRIC TRANSFER ANGLE VS TIME OF FLIGHT TO JUPITER. T,ITAN/CENTAUR DIRECT MODE.°

79

80

70

60 ta

F4pID

z ~6- 30

10

400 600 800 1000 1200 1400

TIME OF FLIGHT TO JUPITER (days)

FIG. A.8 -OPTIMUM DEPARTURE INJECTION ENERGY VS TIME-OFFLIGHT TO JUPITER. TITAN/CENTAUR, DIRECT MODE.

80

350 , . , . .: . , ,

• 310 ,___"_q,,

A44

290 r4

S290 - * 4

P44.

E-4

<270 _____

O

.4­

230

210

400 600 Soo 1000 1200 14Z 00

1 TIME OF FLIGHT TO JUPITER (days)

FIG. A.9 -SUM-PLANET-PROBE ANGLE AT JUPITER VS TIME OF FLIGHT TO JUPITER. TITAN 3X/CENTAUR, DIRECT MODE.

81

31

0 o

29

H

. 28

S27

.

0

26

25 400 600 800 1000 1200 1400

TIME OF FLIGHT TO JUPITER (days)

FIG. A.10 - OPTIMUM EXHAUST VELOCITY VS. TIME OF FLIGHT TO JUPITER. TITAN 3X/CENTAUR, DIRECT MODE.

LIST OF REFERENCES

1. Flandro, G. A., "Fast Reconnaissance Missions to the Outer Solar System Utilizing Energy Gained from the Gravitational Field of Jupiter." Astronautica Acta. 12:4, 329-337. 1966.

2. Flandro, G. A., "The Mechanics and Applications of the Planetary Swingby Technique for Optimization of Interplanetary Trajectories." Paper 68-4-1, American Astronautical Society. 1968.

3. Minovitch, M. A., "Determination and Characteristics of Ballistic Inter­planetary Trajectories under the Influence of Multiple Planetary Attractions." Technical Report No. 32-464, Jet Propulsion Labora­tory. 1963.

4. Sauer, C. G., "Trajectory Analysis and Optimization of a Low-Thrust Solar Electric Jupiter Flyby Mission." Paper 67-710, AIAA. 1967.

5. Flandro, G. A. and Barber, T. A., "Mission Analysis for Interplanetary Vehicles with Solar Electric Propulsion." Paper 67-708, AIAA. 1967.

6. Flandro, G. A., 'Solar Electric Low-Thrust Missions to Jupiter with Swingby Continuation to the Outer Planets." Journal of Spacecraft and Rockets. 12:4, 329-337. 1966.

7. Dugan, D. W., "The Role of Staged Space Propulsion Systems in Interplanetary Missions." NASA Technical Note D-5593. 1969.

8. Friedlander, Alan, "Guidance Analysis of the Multiple Outer Planet (Grand Tour) Mission." Paper 68-109, American Astronautical Society. 1968.

9. Horsewood, J. L., "A Patched-Conic Low-Thrust Swingby Trajectory Optimiza­tion Program." Report No. 69-23, Analytical Mechanics Associates, Inc. November 1969.

10. Hohmann, W., DieErreichbarkeit der Himmelskoerper. Munich: Oldenburg Publishing Corporation. 1925.

11. Barber, T. A., et al, "1975 Jupiter Flyby Mission Using a Solar Electric Spacecraft." Report ASD 760-18, Jet Propulsion Laboratory. March 1968.