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MSC-04334
NATIQNAL AERONAUTICS AND SPACE ADMINISTRATION
MSC INTERNAL NOTE NO. 71-FM-197
June 8, 1971
.v.v.
ROUND TRIP LANDING MISSIONS TO
THE ASTEROID EROS, 1981 OPPORTUNITY
Advanced Mission Design Branch
MISSION PLANNING AND ANALYSIS DIVISION
MANNEC> SPACECRAFT CENTERHOUSTON/TEXAS
https://ntrs.nasa.gov/search.jsp?R=19720006191 2020-03-02T12:32:54+00:00Z
MSC-04334
MSC INTERNAL NOTE NO. 71-FM-197
ROUND TRIP LANDING MISSIONS TO THEASTEROID EROS, 1981 OPPORTUNITY
By Gregory A. ZamboAdvanced Mission Design Branch
JuneS, 1971
MISSION PLANNING AND ANALYSIS DIVISION
NATIONAL AERONAUTICS AND SPACE ADMINISTRATION
MANNED SPACECRAFT CENTER
HOUSTON, TEXAS
Approved:Funk, Chief
/Aavanced Mission Design Branch
Approved; y_^V J<iJ v^~^John P./Mayer, Chief "MissionyPlanning and Analysis Division
CONTENTS
Section Page
SUMMARY .i .. 1
INTRODUCTION . .... . . . ... .'.' . . . . . 2
SYMBOLS '-'•.'-. . . . . . . . . . . . . . 2
"PROCEDURE . .. . . . .. ... ... ... . ... . .... . 3
RESULTS ... . . . . . . 1*
CONCLUSIONS . . . . . . . . ... . , '. ......' , . . . . . . . 5
REFERENCES . . .•.....'. . ..'.". . . . . ''.. . ... ... . 20
iii
TABLES
Table • Page
I 1981-82 EARTH TO EROS ONE-WAY MINIMUM AV REQUIRE- •MENTS ' . . . . . . . . 6
I.I 1982 EROS TO EARTH ONE-WAY MINIMUM AV REQUIRE-MENTS •.' . 7
III 1981-82 EROS ROUND TRIP MISSIONS: LAUNCH DAYSAND FLIGHT TIMES
(a) Staytime at Eros >_ 0 days 8(b) Staytime at Eros >_ 5 days 9(c) Staytime at Eros >_ 10 days . . . . . . . . . . . . . 10(d) Staytime at Eros >_ 15 days 11(e) Staytime at Eros >_ 20 days 12(f) Staytime at Eros .25 days .13(g) Staytime at Eros >_ 30 days lU
IV VEHICLE CONFIGURATIONS AND COST COMPARISON(5000-LB PAYLOAD) 15
IV
FIGUEES
Figure Page
1 . Total mission AV versus total trip time for "fast"round trip landing missions to .Eros in the 1981opportunity 16
2 Characteristics and heliocentric sketch ofmission A (fast mission) IT
3 Characteristics and heliocentric sketch ofmission B (opposition class mission) 18
i| Characteristics and heliocentric sketch ofmission C (conjunction class mission) . . . . . . . 19
ROUND TRIP LANDING MISSIONS TO THE ASTEROID EROS,
1981 OPPORTUNITY
By Gregory A. Zambo
SUMMARY
The asteroids may provide a key link in understanding the origin ofthe solar system and to this end a study of round trip landing missionsto the asteroid Eros in the 1981 opportunity was conducted.
A comprehensive AV study of short staytime (0 to 30 days), shorttotal trip time (10 to l60 days) round trip landing missions (fastmissions) is presented. In addition, the characteristics of threeselected round trip landing missions are described. These three missionshave the following characteristics.
a. Mission A (fast mission): 120-day total trip time, 0-day stay-time, 73 000-fps total mission AV
b. Mission B (opposition class): 380-day total trip time, 0-daystaytime, 52 000-fps total mission AV
c. Mission C (conjunction class): 5 0-day total trip time, 175-daystaytime, 39 000-fps total mission AV
A study using three different propulsion stages, the large-tankAgena, the chemical propulsion stage (CPS), and a nuclear stage was con-ducted to determine which and how many stages could perform each of thethree missions. A payload of 5000 pounds was assumed. The propulsionrequirements for mission A were found to be two large-tank Agenas andten CPS's (or alternatively, two large-tank Agenas and five nuclearstages) while mission B required two large-tank .Agenas and two CPS's.Mission C, the conjunction class mission, can be performed with onelarge-tank Agena and one CPS.
INTRODUCTION
As in reference 1,
As long as the asteroids were regarded as fragmentsof a broken-up planet, interest in them was limited.There are now good reasons to believe that theasteroidal belt represents an intermediate stage inthe formation of planets. This links the presentconditions in the asteroidal region with the epochin which the earth and the other planets wereaccreting from interplanetary grains. Hence, inorder to understand how the solar system originatedit may be essential to explore the asteroids.
Round trip landing missions to the asteroid Eros (designatednumber U33) in the 1981 opportunity are considered using a 262- by262-n. mi. altitude orbit at Earth departure and a 200- by 38 529-n. mi.altitude (l-day period) orbit at Earth return. The "landing" at Erosis actually a rendezvous with Eros, because of the small gravitationalattraction of the asteroid. In fact, the concept has been discussed ofcapturing a small asteroid, bringing it back to Earth, and storing it inorbit about the Earth for later investigations (ref. l).. The threemissions presented herein (missions A, B, and C) are representative ofdirect missions to Eros in the 198l opportunity. Both two-impulse directand three-impulse (intermediate heliocentric impulse) direct one-way tra-jectories were considered in this study.
The author acknowledges Stanley R. Sudol and Gus R. Babb of theAdvanced Mission Design Branch for their assistance.
SYMBOLS
a semimajor axis
e eccentricity
I specific impulsesp
i inclination relative to the ecliptic plane
M mean anomaly
m mass of usable propellant
m burnout mass of stages
V^ magnitude of hyperbolic excess velocity vector
AV magnitude of impulsive velocity-change vector
ft longitude of ascending node, heliocentric ecliptic system
to argument of periapsis, heliocentric ecliptic system
Subscripts
AE arrive Earth
AR arrive Eros
DE depart Earth-
DR • depart Eros
I intermediate impulse
PROCEDURE
A computer program that minimizes one-way (Earth to Eros, or Erosto Earth) three-impulse AV was developed and used in this study. For agiven launch date from the departure planet and flight time to thearrival planet, the sum of the departure AV, the intermediate impulse AV,and the arrival AV is minimized as a function of four independent variables:the position vector (dimensioned three) of the intermediate impulse, andthe time from the departure planet to the intermediate impulse. A gradientmethod is used in the minimization process. The two-impulse one-way AV(Lambert's solution) is also calculated by the program.
This program uses an analytic Earth ephemeris based on reference 2and a two-body motion ephemeris for Eros (a = 1. 581 astronomical unit,e = 0.2228, i = 10.828°, n = 30 .012°, u = 1T8.08U0, and M = 238.913° onJanuary 6, 19 1). A 262- by 262-n. mi. altitude orbit at Earth departureand a 200- by 38 529-n. mi. altitude capture orbit at Earth return wereused in this study. The AV on arrival at Eros was assumed to be equal tothe V upon arrival at Eros and the AV on departure from Eros wasassumed to be equal to the V^ upon departure from Eros. A masslessplanet model (V^ vector defined as the heliocentric-transfer-conicvelocity vector minus the velocity vector of the planet) was assumedthroughout.. Impulsive (ideal) AV's and collinear burns at Earth departure,Eros arrival, Eros departure, and Earth arrival were also assumed throughout.Only one-way.trajectories with transfer angles of less than 360° were con-sidered.
The propulsion stages used herein were defined as follows:
a. Large-tank Agena: m = 1985 pounds; m = 35 000 pounds;S X
I = 292.5 secondssp .
b. CPS: m = 60 000 pounds; m = 5^0 000 pounds; I = k60 secondss , x sp
c. Nuclear stage: m = 88 000 pounds; m = 300 000 pounds;S , • I
I = 784 secondssp
RESULTS
Table I presents Earth to Eros one-way minimum two-impulse andthree-impulse AV requirements. In generating this table, only arrivalJulian dates at Eros of 2 4U4 960 through 2 HI* 5 020, in increments of5 days, and Earth to Eros flight times of 5 days through 100 days, inincrements of 5 days, were considered.
Table II presents Eros to Earth one-way minimum two-impulse andthree-impulse AV requirements. In generating this table, only departurefrom Eros Julian dates of 2 khk 980 through 2 hk5 QUO, in increments of5 days, and Eros to Earth flight times of 5 days through 100 days, inincrements of 5 days, were considered. In tables I and II, only one-waylegs with a minimum three-impulse AV of less than 900 000 fps are presented.
Table III presents the launch dates, the flight times, and the two-impulse and three-impulse minimum total mission AV's for round tripmissions. On each subtable of table III, the staytime at Eros is heldfixed and the total trip time is varied. Each mission of table III wasgenerated by choosing from all possible combinations of one-way trajec-tories from tables I and II, the round trip mission having, for the givenminimum staytime and the given total trip time, the minimum total missionAV. Staytimes of 0 through 30 days, in increments of 5 days, and totaltrip times of 10 through 160 days, in increments of 5 days, are presentedin table III.
Figure 1 graphically presents the table III results. Minimum totalmission AV is plotted against total trip time, with the contour linesbeing lines of fixed minimum staytime at Eros. No difference betweentwo-impulse and three-impulse total mission AV was found, thereforefigure 1 represents identically both two-impulse and three-impulse roundtrip missions.
Three missions representative of the 1981 opportunity were selectedand their characteristics are presented in figures 2, 3, and k. Mission A,a "fast mission" to Eros, is represented in figure 2. This mission has a
0-day staytime at Eros and is seen to be the 120-day total trip timemission of table Ill(a). Mission B, an "opposition class" mission toEros, is characterized in figure 3 while mission C, a "conjunctionclass" mission to Eros,, is shown in figure h.
Table IV presents the vehicle configurations capable of performingeach of three aforementioned missions. A gross cost comparison isalso presented.
CONCLUSIONS
The "fast mission" to Eros (120-day total trip time) required73 000-fps total mission AV and is too costly to be considered seriously.The "opposition class" mission (380-day total trip time) requires52 000-fps total mission AV and can be performed with two large-tankAgenas and two CPS's. The "conjunction class" mission (5 0-day totaltrip time) requires 39 000-fps total mission AV and, although l60 dayslonger in total trip time than the "opposition class" mission, it requiresonly one large-tank Agena and one GPS. Furthermore, it has a staytimeat Eros of 175 days as compared to the 0-day staytime of the "oppositionclass" mission.
For an unmanned (5000-lb payload) mission to Eros in the 198lopportunity, a cost consideration dictates the "conjunction class" missionas the obvious choice.
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TABLEIU.- 1981-82 EROS ROUND TRIP MISSIONS: LAUNCH DATES AND FLIGHT TIMES
(a) Staytitne at Eros £ 0 days
TTT= Total trip time, daysDV2 = Total mission AV, two-impulseDV3 = Total mission AV, three-impulseJDDE = Julian date of Earth departure - 2 440 000
Tl = Earth to Eros flight time, daysS = Staytime at Eros, daysT2 = Eros to Earth flight time, daysJDDR = Julian date of Eros departure - 2 440 000
T H R E E - I M P U L S E
TT.T . DY2.. 0V..1. — Li..V
__L2 J.O-OK _4Oa£ Ll -S-_
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V0676H7224B4403
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.'1.113-70744
6 V y S 4
68462...6.7985
6398984722683Q48332516551 988081738811 493801 3548412206311349310&4 1599/629459490676B7224644036202479925
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i>0 5000....•?J1 50 OQ.i5 500060 500060 50006'i 500065 50007o iinan75 50007 Cj l^Qllf|
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TABLE HI.- 1981-82 EROS ROUND TRIP MISSIONS: LAUNCH DATES AND FLIGHT TIMES - Continued
(b) Staytime at Eros 2.5 days
TTT
IS202530351015505560657075808590950005101520253035101515015S160
DV2
826389SAB5131U08833171012639262228181*83171 /115215921511579^1353921273111 198151 H262U9091101777KJ132S97886950789269990350883168660781926833918202680792795827815977129
DV3
826389S685131008833171012639262228181983171 71152159215115791135392127311I 19815I 1126210909110177710132597886950789269990350883168660781926833918202680792795827815977129
JDUE
199Q1985
1(
51010 -
198Q 1519UQ 1519B51980
I9601975197519701970197Q19651965I960I960I96019551955195519!>S1950195019501950191519151915
1520202n252530303035351010IflISIS1515SO
5050555555
^
S M
5 SS 55 105 105 IS5 205 20S 2S5 305 305 3b5 355 10S 155 155 So5 S>05 55S 60S 6Q5 655 70S 7S5 755 8g5 855 9Q5 90JL ..1S_5 100
JDDR
5000500050005000500O5Q05snos500550055005SOOS50055005500550055005
500550055005SOOSSOOS5005SOOS
50055005SOOS
_S_0_O5_..5005
f
19901985198519801980198*1900
1980197&19751970197019701965
I96ui96019&5195519&5195519SO
19&01950191519151915
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10
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50005000 - - . . . ...SOOS
SOOS
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SOOS5005 _5005
50055DOS ....SOOS
10
TABLE EL- 1981-82 EROS ROUND TRIP MISSIONS: LAUNCH DATES AND FLIGHT TIMES - Continued
Cc) Staytime at Eros £10 days
-IHKEE..-11FULSE
T T T D V 2 D V 3\ f
JO U £ ..... T i _______ § __TJJ ___ JJHL B _______ J B fl-t_ _ LI ________ 3.__L2 _____ I QOfL
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b 5000in m-inc.
15 5005 .15 50452U 5005
25 500525 5005
•*0 b00530 SOUS
35 5005.-.JL5 5..QJ1540 500540 500S45 500545 snniibO 5005bfi . _5n.r)555 500575 SOln
75 501080 bnlQ85 50109U E-niO90 50109i 5Q1 n
100 501010.0- . 50 in
Q gn
4980
llll4980497549/51970 _
497C
4965
4960
4955M9 SO
4950
49H&49654940
4960
49S?49b&i?&.0_
10in1015152.CU202525
30-IS-354040
MS5050
40
40
45
4560
101 0101010
101010
10-J-0-10
i n101 Q
101 010in10101010101 D1010
51 015)b20
252530
35„ ..AS--
404045MbbO'•O557575
85909095
100.- 1 on
500060 0">5005500-5 . .5005
5005
6005
50055005.. -.5005
&OfTi5005SJDOS5005
500550 1 05010501 050105-Q-l_n.5010sn i oSDIO501.0. -
11
TABLEIU.- 1981-82 EROS ROUND TRIP MISSIONS: LAUNCH DATES AND FLIGHT TIMES - Continued
(d) Staytime at Eros £15 days
25 99999930 92470635 66893540 52541015 411631
0V 3
999999921705668935525110111631
50 371074 371074
55 329601 .32.9601 _60 28921165 2621/670 23900375 22012280 20543085 19156190 18Q96395 170847100 16201H105 1S3966110 116475115 H0013120 134374125 129206
130 124214135 119847140 1 15935115 i 12414150 1UB992155 105875
28921 1262176239Q032201222051301915611 80963170847162044153966116475140013
1343741292061242441 1 98471 159351 12444108992105875
1r£o-
J.DUE TJ_
1890 100199549854985498Q19BQ198Q19/519/5197049/049654965496549754975197Q
197019/0197019651965196519651965
I960I960
5101015IS152G20252530303025253030303035353535351010
•IMPULSE^
$-__7_2_.
30 1001515ISISISL5_
151515ISIS1515ISISISISISIS15.1515ISIS15 1
1010151520252530303S3510155560
606570
757580859095
95UO
"\
5n20501550105010£01050105010501050105Q1050105010501Q.501050155015
50J.55015501550155015S01S50155015501550155015
THKEE-r__J00.E.
1890199549854985198Q4990
4975197519701970
496549754975
49704970497049454945
__i?_6_54945
i960i960
IMPULSE_S ~
inn 305 1510 1510
1515..2020
15|515
15|5
25 IS25 J530 1530 15302525
30303035
353535351010
151515ISIS
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...L2 10 OR
1.0 P 5020 ...10 501510 SD1015
~2~0
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657075
808590
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5010. . 50.10... ...
5010S0.10 -5010501050105.0.1 D5010
... 5010501050155015
.-..5.01.5 .5015
.. _5.0 1 5.501550155015
_50_155015
....5015sots
I6C 103496 103496 4955 45 15 100 5015 49|5 45 15 100 5015
12
TABLE IH.- 1981-82 EROS ROUND TRIP MISSIONS: LAUNCH DATES AND FLIGHT TIMES - Continued
(e) Staytime at Eros £20 days
TWO-iMF'U
TTT
30.354045bOb56065707580859095
IOC105
1 52U._2530
135MO145ISC155160
DV2
9V 9 9.9 9..9999998!0_438_^477715424224622/84U1981357920320642292745268244246526229087214727201 3061892421 /8945170C4516_196.7.15419947371413413 6 0 U 430836
26(141219551 18503
DV3 JDUE
s*~
1 I S
9.99.?.9_9_ HJB_V_0 _.1.11D 3o_._999999 489Q (QJ 3o840438 498Q 10 20647771542422462278401 98135792032064229274b268244246526229067214727201 306189242L? 8 9 4 b170046
54 1994737 14134130Q043083626| 1421 95b
1 18503
4985
4990498Q498o49854985498549604980
49BO4975497549/54975
497049704970
4965
49054960
10 20LQ. 2Q_.15 2015 2015 20IS 2015 2020 2020 2020 2o
20 2025 2025 2025 2Q_25 2010 12 D_..30 2030 203G 2030 2035 2035 2n
LS£_
'2
IHSEL-
JDUR
100 502QliiC 602010 5nlnIS 501520. S_02B._20 501525 5015303b4Q
45
bb
bb
606B70
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35 20 1UO40 20 100
502050205020
5020SQ_2U50205020
f
489049qD498&
4980498b498S
j'ao4980
49SO4973
5020 497S-50.20- _49.7_5_5020 497S
__b.Q20 49706020 4970b020 49705020
b020_ 5£L20_b020&Q2Q
49/0H 9 JLtt_
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1001010
lblb15lblb2020202026252525
_J.O_303030_3Q.35
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30?n20
2020202020
20202020202020
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15 5015-.20 &Q2020 501S25 5015303540
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Sb 5020bb 5020606570
-7.0-758085
90
1001.00
502050205020-6020 - -..5020
502050205020.5O205020
13,
TABLEEL- 1981-82 EROS ROUND TRIP MISSIONS:.LAUNCH DATES AND FLIGHT TIMES - Continued
(0 Stay.time.at Eros £25 days
TWO-IMPULSE
TTT
351015SO5560.657075808590951001051 101 1512012513013511011515015516C
OV2
999999VV99999618137/118863355053S6'93'I706b911781237139133619530921228171 1262713•211512229213•21582220275119115118161117298916191 II!>73121*0705111925139757131805
0 V'3
99999999999996181:377118863355053S69317065911781237139133619530921228171 1262713;211b12'229213215822202/5119115118161117298916191 1157312150705111925139757131805
rJOWE
1890189Q
- -1995• •' 19854 199Q: 19VQ'l99Q19B519851985'1985! 1980
? 19bQ' 198Q
19/51975197519751975197019701970197019651965
' rr100Toor. ,5 .:
io10iu151515152020202025
25252530
- 3030303535
S
3030252525252525252525252525252525252525252525252525
" T2
1UO•10015
• 15202530 '30
HO1515 'bO556060657075808085909595
1UO
JOUR
50205020b0255020502550255025502550255025502550255025502550255025502550255025b02S50 2 S50255025502550255025
THKEE-r"Joof.
189018901995,19851990.19901990
"; I98bI98b.I98b"198b1980
' 1980i9ao19751975I97b1975197519701970
! 19701970I96b1965
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100|005101Q_1010.lb
.lblb20 .2020202525252525303030303535
IMPULSE
S
30302s
252525
2525252.52b
2*25
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T2 JODR
1.00 t;020.100 502015 5025
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25 502530 c,n?*
30 502535 5025HO .502515 5025H5 5025SO 5Q2555 50256p f.O7f>60 502565 S02570 502575 502580 502580 502515 502590 502595 502595 5025100 5025
TABLEBI.- 1981-82 EROS ROUND TRIP MISSIONS: LAUNCH DATES AND FLIGHT TIMES - Concluded
fg) Staytime at Eros £30 days
TWO-
TTT
45
65606570758C85
"" 951001051 101 15
t2£12513013514C
150155
DV2
V999999V99999V99998B94937220586059945286H347325542040B3/B6373458Bq3194052949042/3004254557238S07225.21421 1807
..2001125.1897/61 808821 '280416516S1S8772
OV3
99999999999999999988949372205860599452864347325642040837863734588031940529490H27300H25M55723R807
21 I 807
1897761808821728041.6 5 1 6 5.158772
'JDUE
4B9n
Tl
1 nil1*8<'o loo•*B9Q ,nn49954990499Q4990499049854905498549854980498Q498Q498049SQ:H97549754975497549704970
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16
300
280
Staytimeat|Eros, day
262- by 262-n. mi. altitudetat Earth departure
200- by 38 529-n. mi.altitude at Earth return
20 60 80Total trip time,
140 160
Figure 1.- Total mission AV versus total trip time for "fast" round trip landing missionsto Eros in the 1981 opportunity.
210°
220°
230°
240°
250°
260°
270°
280°
290°
300°
310°
320°
200° 190°
IT
180° 170° 160° 150°
120 day total trip time0 day staytime at ErosTotal AV = 73 161 fps
262- by 262-n. mi. altitude at Earth departure200- by 38 529-n. mi. altitude at Earth return
' HffTito vernal equinox)
140°
130°
120°
110°
100°
go-
70°
60°
50°
40°
330° 340° 350° 0 10'
Figure 2.- Characteristics and heliocentric sketch of mission A (fast mission).
18
210° 200° 190° 180° 170° 160° 150°
220°
230°
240°
250°
260°
270°
280°
290°
300°
310"
320°
July 19, 1982
380 day total trip time0 day staytime at ErosTotal AV = 52 069 fps
--- Spacecraft trajectory
tffttttH2b2- by 262-n. mi. altitude at Earth departure200- by 38 529-n. mi. altitude at Earth return
T (to vernal equinox)
60°
50°
40°
330° 340° , 350° 0 10° 20° 30°
Figure 3.- Characteristics and heliocentric sketch of mission B (opposition class mission).
210° 200° 190° 180° 170° 160° 150°
220°
230°
240°
250°
260°
270°
280"
290°
300°
310°
320°
545 day tots' trip time175 day staytime at ErosTotal AV = 39 395 fps
Spacecraft trajectory-
262- by 262-n. mi. altitude at Earth departure- by 38 529-n. mi. altitude at Earth return
"J w .1'. . . _ . . , „ , .^ v ^. v* \ X V\X \
T (to vernal equinox)
140°
130°
120°
110°
100°
90°
80°
70°
60°
50°
40°
330° 340°, 350° 0 10° 20° .30°
Figure 4.- Characteristics and heliocentric sketch of mission C (conjunction class mission).
20
REFERENCE
1. Alfven, H.; and Arrhenius, G.: Mission to an Asteroid. Science,Vol. 167, Jan. 9, 1970, pp. 139-1 1.
NASA MSC