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TABLE III.-Flight Plans for 1977 Eros Sample-Return Missions
Ballistic flight Solar electric flight
*LV - launch vehicle. *T - Titanic - centaur. *T - Titan; B - Burner.
masses for the 1977 Eros sample-return mission. A fixed sample size of 25 kg was assumed for each flight mode. Provisions were made in the launch vehicle capabilities to provide for a nominal DLA less than 36°.
SOLAR INTERFERENCE POTENTIAL
It is observed from the solar electric and ballistic transfer profile graphs (figs. 7(a) and 7(b), respectively) that Earth is nearly opposite Eros, on the opposite side of the Sun, during rendezvous, stationkeeping, and docking with the asteroid. The question of whether the Sun will interfere with the necessary spacecraft/Earth communications link during these critical maneuvers was investigated. Current Deep-Space Network (DSN) communications capability requires that the Earth/spacecraft line of sight be at least 2° off the Earth/Sun line (Douglas Aircraft Corp., 1965). In figure 8, the Earth/Eros line-of-sight trajectory during the 1978 Eros encounter is shown projected in a plane normal to the Earth/Sun line, positioned at the Sun. Dots are placed along this trajectory at 15 day intervals. The point of maximum solar interference (3° separation between Eros and the Sun as seen from Earth) occurs on Julian date 2443710 (July 20, 1978). The arrival and departure points for the ballistic and solar electric baseline mission profiles are also shown on the trajectory. In both cases, these points bracket the maximum solar interference date. Fortunately, this interference (3°) appears acceptable for reliable DSN communications. Further study of this problem is needed using more recent elements of Eros' orbit to accurately determine its line-of-sight trajectory. If further communication degradation were to result, it would be necessary to shift the entire stay time by 50 to 100 days. This, of course, would have an effect on the energy requirements and payload capability of the sample-return mission.
On the basis of the largest amount of sample material returned to Earth orbit, the 1977 launch opportunity appears to be the most favorable during a synodic cycle of approximately 16 yr. Mission times are invariant and are approximately 3 yr in length. Lengthy stay times do not decrease significantly the amount of sample returned. A sample size of 25 kg may be returned in this mission by either a Titan IIID/Burner II with a 10 kW solar electrically propelled vehicle or a Titan IIID(7)/Centaur/385 chemically propelled vehicle. Severe range safety problems exist (DLA = −70°) for the ballistic flight mode. This launch problem is diminished through the use of the solar-powered flight mode. Communications between Eros and Earth during the 1978 rendezvous may be somewhat impaired because of solar interference. Although this paper has considered round-trip sample-return missions to the asteroid Eros, many of the mission characteristics and results are applicable to other asteroids in the Mars-crossing group, such as Geographos, Apollo, Toro, and Amor. It was noted that launch opportunities to Eros occur in 1977, 1979, etc. Preliminary investigations indicate that launch opportunities to Geographos occur during the alternate years; i.e., 1976, 1978, etc. Missions to this asteroid also require 3 yr to complete a sample return.
Friedlander, Alan L. 1970, Solar Electric Propulsion Capabilities for Mars Surface Sample Return Missions. Internal Document, Illinois Inst. Technol. Res. Inst. Chicago.
Mascy, Alfred C., Dugan, Duane W., and Pitts, Samuel W. 1968, Applications of Combined Electric, High-Thrust Propulsion Systems. J. Spacecr. Rockets 5(7), 785-791.
Douglas Aircraft Corp. 1965, Study of Conjunction Class Manned Mars Trips—Part II. NASA CR 64119.
TRW, Inc. Study of a Common Solar-Electric Propulsion System for High-Energy Unmanned Missions. Contract NAS2-6040 for NASA Advanced Concepts and Missions Div., Moffett Field, Calif.
MULTIPLE ASTEROID FLYBY MISSIONS
DAVID R. BROOKS AND WILL/AM F. HAMPSHIRE //
The use of spacecraft for studying the physical properties of the asteroid belt can be approached in several ways. Certainly the simplest approach is to send a spacecraft into the asteroid belt and measure the effects of the environment encountered; this has the advantage of not requiring a vehicle to be targeted to any particular destination. With such an approach, properties may be obtained for those classes of objects that are populous enough to provide a significant number of encounters within the measurement range of the spacecraft. Unfortunately, the large asteroids do not constitute such a class of objects; the probability of an undirected spacecraft passing within measurement range of an asteroid having a diameter of 1 or more km is negligible.
For studying the properties of the large asteroids as a class, as opposed to studying one particular asteroid, it is clear that a way must be found to sample the population of large asteroids by studying more than one, preferably with the same equipment on the same mission. This task requires the assumptions that the position of likely targets can be predetermined with sufficient accuracy and that the spacecraft has onboard guidance and propulsion for maneuvering to preselected positions in space and time. It is assumed that the permanently numbered asteroids (presently 1748 in Ephemeris, 1971) is the group of objects from which minor planet targets will be chosen, because the assignment of a permanent number to an asteroid usually denotes a reasonably well-known ephemeris based on numerical integration of osculating orbital elements.
It is the purpose of this paper to define various types of multiple asteroid flyby missions involving the 1748 numbered asteroids, to determine the magnitude of impulsive Av demands for performing typical missions, and to relate these requirements to spacecraft capabilities planned or envisioned for other applications. A particular goal of the study is to identify possible multiple flyby missions whose in-flight propulsive requirements are attainable with reasonably sized chemical systems, rather than being so large as to make advanced propulsion schemes necessary or highly desirable for effective spacecraft performance. The idea of searching for close asteroid encounters that can be obtained with small Av maneuvers is not new. Bender (1967) has conducted a similar study in a search for cis-Martian asteroid encounter opportunities; and the desirability of multiple flyby missions has been mentioned recently by several authors involved in solar electric mission analysis (Archer, 1970; Brooks, 1970; Wrobel and Driver, 1969).
RANDOM ENCOUNTERS WITH LARGE ASTEROIDS
It was stated in the introduction that the probability of a spacecraft encountering large asteroids by chance was negligible. Deferring for a moment the definition of “encounter,” this statement can be justified easily. Actual count of the 1748 numbered asteroids shows that at any given time an average of about 431 are contained in a washer-shaped volume having an inside radius of 1.8 AU, an outside radius of 3.7AU, and a thickness of 0.2 AU, centered about the ecliptic plane. If these asteroids are assumed to be uniformly distributed in the volume, T(3.7% -1.8%)0.2 AU3, and to have, on the average, velocities equal to the circular velocity, the number of encounters to be expected by a spacecraft in this volume for a time t3-ti is
where vsc and ve are the spacecraft and circular velocity vectors and mRE” is the constant cross-sectional area of a spherically symmetric encounter volume of radius RE about the spacecraft.
The question of what RE must be to result in a useful encounter cannot and need not be answered exactly. Bender (1967) assumed that the closest distance of approach should be less than 2 X 104 km for telescopic observation. For asteroid mass determinations based on perturbations of a spacecraft's velocity, passage distances are required that range from 10° km for smaller numbered asteroids to as much as 10° km for Ceres (Meissinger, 1971, personal communication). For the purposes of obtaining a number from equation (1), assume that the largest radius at which useful data can be obtained is RE = 107* AU (1.5 X 10° km). For this radius, a spacecraft in a 1 by 3 AU orbit in the ecliptic will encounter an average of only 6 × 10−9 asteroids per orbit.
Accounting for all those asteroids that could be observed from Earth and cataloged along with the present 1748 numbered asteroids will improve, of course, the chances of a random encounter. However, even if the total number of large asteroids is as high as 10°, the sample trajectory given above will still yield only 3 × 107* encounters per orbit—an increase of about 50 times above the previous result. An encounter radius as large as 0.1 AU, on the other hand, should result in about six encounters with the numbered asteroids per orbit for the same trajectory.