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on be observed from the figure that one is forced to accept a total trip time on the *t order of 3 yr. o: In addition to the direct two-impulse transfers discussed thus far for ballistic ~ systems, optimum three-impulse trajectories were also investigated for the it following reasons: (1) a potential for lower total impulse, due to the 11° ... inclination of Eros' orbit to the ecliptic; (2) the possibility of improving the launch problem due to large DLA values; and (3) the inclusion of Earth a capture-orbit recovery, rather than direct reentry, as a more cautious mission profile in view of back-contamination uncertainty. Optimum three-impulse outbound and return (to Earth orbit) transfer points are included in figure 3. - The total outbound impulse Avo is indeed less than required by the minimum two-impulse transfer, but a DLA of −70°4 does not solve the launch problem. The three-impulse return transfer to Earth orbit requires a AvR of less than 4 km/s, which, although difficult, is not impossible to achieve with chemical propulsion. Table II summarizes the transfer characteristics for the two most promising ballistic mission profiles for the launch opportunities of 1974, 1977, and 1979. Both profiles utilize three-impulse outbound transfers to Eros rendezvous. The first profile uses a minimum single-impulse return trajectory to Earth reentry, whereas the second profile requires a three-impulse return transfer to Earth orbit. Note that, for the multi-impulse return, the arrival impulse provides a 12 hr Earth orbit that is more practical for subsequent recovery than the 24 hr orbit suggested in figure 3. Only the 12 hr recovery orbit is considered in the remainder of this paper. The results presented in table II are quite variant. The best (lowest total impulse) outbound transfer occurs in 1977. The best launch conditions occur in 1974 when DLA =–49°1. The best return transfers occur in 1979. In 1974, the best single-impulse return trajectory to Earth reentry is worse than the three-impulse transfer ending in Earth orbit. The stay times are variable, ranging from 88 to 378 days depending upon the opportunity and return transfers selected. The one parameter that does not vary much is the total trip time, which is always very nearly 3 yr. This was observed earlier and apparently is quite stable regardless of launch opportunity or mission profile. The launch vehicle used to inject the ballistic chemically propelled interplanetary vehicle into a trans-Eros trajectory is the Titan IIID(7)|Centaur. For the ballistic flight mode, all major impulsive velocity increments, including a 200 m/s guidance requirement, are provided by a space-storable chemicalpropulsion system that has an assumed specific impulse of 385 s. An interplanetary bus has been assumed for the chemical flight mode that has a mass of 250 kg and comprises the engineering subsystems. Upon return to Earth, both the electric- and chemical-propulsion flight modes assume a small solid rocket engine to provide the required velocity increment to place the return capsule (containing the sample) into orbit. Characteristics of the final orbit are: 500 km periapsis altitude, 40 000 km apoapsis altitude, and 12 hr period.

TABLE II.-Ballistic Transfer Characteristics for Eros Sample-Return Missions

1974 1977 1979
Parameter
3-impulse 1-impulse 3-impulse 3-impulse 1-impulse 3-impulse 3-impulse 1-impulse || 3-impulse
outbound return return outbound return return outbound return return

Stay time, days - 309.5 3.10.6 - 190.2 88.3 - 349.9 378.4
Launch date, Julian date 2435.2 3094.0 3095.1 3170.5 3843.0 377.1.1 3905.0 4688.0 4716.5

2440000
Launch impulse,” km/s 4.677 6.213 2.394 4.655 1.7.10 1.105 4.295 0.999 1.166
Launch DLA, deg –49.1 - - –70.4 - - –81.3 - -
Midcourse date, Julian date 2678.1 - 3298.3 3417.2 - 4029.9 4082.7 - -

2440000
Midcourse impulse, km/s 0.299 - 1.079 1.030 - 0.987 0.984 - -
Arrival date, Julian date 2784.5 3352.8 3532.6 3682.8 4260.2 4259.2 4338.1 4993.8 4991.7

2440000
Arrival impulse.” km/s 1.763 - 1.759 0.810 - 2.120 2.290 - 2.402
Reentry speed, km/s (ft/s) - 14.143 - - 13.348 - - 13.203 -

(46.370) (43 760) (43 320)

Total impulse, km/s 6.738 6.213 4.231 6.495 1.710 4.212 7.569 0.999 3.568
Transfer time, days 349.3 258.8 437.5 512.3 417.2 488.1 433.1 305.8 275.2
Total trip time, days - 917.6 1097.4 - 1089.7 1088.7 - 1088.8 1086.7

*Launch impulse at Earth from 185 km (100 m. mi.) circular parking orbit.
*Arrival impulse at Earth (when applicable) for capture into 12 hr orbit, Rp = 1.078Re, e = 0.7419. Rp is the radius of periapsis and Re is the radius

of Earth (6375 km).

MISSION RESULTS Effect of Trip Time

With the assumptions made earlier, round-trip missions of various overall times were investigated for an Earth launch opportunity occurring during 1977. The sensitivity to trip time of capsule mass returned to Earth orbit is shown in figure 4 for the solar electric flight mode. There is a strong effect of overall time on the Eros round-trip mission with the maximum returned mass of 260 kg obtained for a time of 1100 days or approximately 3 yr. Capsule mass decreases very rapidly for trip times much shorter or longer than the optimum. The same characteristic has been found for the chemical flight mode.

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Stay time is defined as the total time spent in the vicinity of Eros. It includes the rendezvous and stationkeeping maneuvers, topographical survey, surface operations, and departure maneuvers. An investigation of the effect of stay time on returned mass is shown in figure 5 for the solar electric flight mode. Over a range of stay times, there does not appear to be any significant effect on the capsule mass. This allows the freedom to perform whatever operations in the vicinity of Eros are desired. Additionally, it was found that the optimum total trip time remains relatively constant at 3 yr as stay time is varied. That is, trip time is not appreciably shortened or lengthened as stay time is varied.

Effect of Launch Year Opportunity

In addition to the 1977 launch opportunity discussed thus far, other launch years were surveyed. Opportunities for round-trip missions to Eros occur about 2 yr apart, and their effect on returned mass is shown in figure 6. The open bars relate to the return capsule mass in Earth orbit and the shaded bars are merely an estimate of the soil sample size contained within the capsule. A scaling law used on a recent Mars sample-return study (Friedlander, 1970) relates the sample mass m, to the return capsule mass me by the relationship

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In figure 6(a) is shown the ballistic flight mode. For the years surveyed, the launch opportunity in 1977 results in the maximum sample returned. Similarly, for the solar electric flight mode shown in figure 6(b), the year 1977 is the most favorable opportunity for a sample return from Eros. Preceding and succeeding years have decreasing return mass. A preliminary estimate of the synodic cycle is 16 yr, at which time (1993) a most favorable opportunity should occur again.

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Figure 6.-Launch opportunity effect on returned mass. (a) Ballistic flight mode: Titan IIID(7)/Centaur/385; total trip time = 3 yr; stay time is variable (88 to 378 days); Earth return orbit = 500 x 40 000 km. (b) Solar electric flight mode; Titan IIID/Burner II; total trip time = 3 yr; stay time = 50 days.

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1977 TRAJECTORY GEOMETRY

Ecliptic projections of the outbound and return trajectories for the 1977 Eros round-trip mission are shown in figure 7(a) for the solar electric flight mode and in figure 7(b) for the ballistic flight mode. Both outbound and inbound trajectories for both modes have approximately 300° of travel angle. Launch dates from Earth are in early 1977. Arrival dates at Eros are at about mid-June 1978 at which time Earth is 2.2 AU from Eros, almost directly behind the Sun. After a stay time at Eros, departure takes place in latter September with Earth still about 2.2 AU away and very close to the sunline. Return dates back at Earth are approximately mid-January 1980, 3 yr after launch. In table III is given a flight plan that details the events, dates, and

Eros
Rendezvous
(15 Jun re)

EARTH as '

*ion;

-- *

EARTM at
RE not zvous

- - - - * - - - *

(o) EARTH to ERos. 475 Davs ERos to EARTH, 475 Days
stay time = too days

ERos
Rendezvous
t 23 Jun 78)

EARTH's
or 8 or
f

of PARTuRE
t is so P 78)
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EARt H. A.T
DEPARTuRE
w

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-- e EARTH At
RENOEzvous

N / Midcourse
N. z
toos. S Midcourse
orair ^. ... iMPulse ~ .*
> — — —-T Y----- T
(b) EARTH To Eros, 513 days EROS TO EARTH, 488 days

stay time = 88 days

Figure 7.-Transfer profiles for a 3 yr Eros sample-return mission. T indicates the vernal equinox. (a) Solar electric; stay time = 100 days. (b) Ballistic; stay time = 88 days.

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