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The Role of the Cis-Lunar Libration Point in Lunar Operations View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Embry-Riddle Aeronautical University The Space Congress® Proceedings 1966 (3rd) The Challenge of Space Mar 7th, 8:00 AM The Role of the Cis-Lunar Libration Point in Lunar Operations W. Raithel General Electric Company Follow this and additional works at: https://commons.erau.edu/space-congress-proceedings Scholarly Commons Citation Raithel, W., "The Role of the Cis-Lunar Libration Point in Lunar Operations" (1966). The Space Congress® Proceedings. 4. https://commons.erau.edu/space-congress-proceedings/proceedings-1966-3rd/session-13/4 This Event is brought to you for free and open access by the Conferences at Scholarly Commons. It has been accepted for inclusion in The Space Congress® Proceedings by an authorized administrator of Scholarly Commons. For more information, please contact [email protected]. The Role of the Cis-Lunar Libration Point in Lunar Operations W. Raithel General Electric Company PhiladeIphia, Pennsylvania The purpose of this presentation is (4-body system) this balance is disturb­ to define the advantages which result ed. It appears that the two conditions from the use of the cis-lunar libration of constant celestial configuration and point LI as place of departure for des­ exact force balance are incompatible in cent to the Moon, as parking place for the Earth-Moon-Sun system. the Command Module and as place of ren­ dezvous after take-off of the Lunar In context with the initially stat­ Landing Vehicle (LLV) from the Moon in ed objective we can disregard this defi­ regard to simplifying operations in nition problem and address ourselves to lunar space and increasing the chances determining the magnitude of the force of success of lunar missions. imbalance at the 3-body libration points and to determining the motions of a The Earth-Moon System contains five spacecraft relative to these points, points where the initial forces are in Fig. 2 shows the radial accelerations exact balance with the gravitational due to 4-body conditions acting on a ve­ forces from Earth and Moon and which re­ hicle positioned at the 3-body libration main in fixed position relative to the points. The accelerations are plotted Earth-Moon configuration. These are the for LI and L4 in terms of standard ter­ so-called libration points. The unique­ restrial acceleration n g" as function of ness of these positions has made them time in terms of Moon-phases. It should the subject of a number of studies be­ be noted that this imbalance is very- ginning with those of La Grange in the small and can easily be counteracted by 18th century. a propulsion device. Weight addition, •required for station -keeping is a func­ For the restricted 3-body model, tion of spacecraft weight, time on sta- considering only Earth and Moon rotating tion, and propulsion method. In terms around their barycenter, the location of of velocity increment the station-keeping the libration points is shown in Fig. 1. effort amounts to an average of 10 ft/ The orbits of the triangular points L4 sec /day or 300 ft /sec for one month on and L5 are ellipses similar to that of station. An ion engine can do this sta­ the Moon's orbit, whose axes are tilted tion-keeping job with an additional 60° from that of the Moon. The orbits weight in the order of 1% of the total of the co-linear points L^, L£, and L3 vehicle weight for about one year. are ellipses concentric with that of the Moon. It should be noted that the tri­ If we do not use station-keeping, angular points are basically stable, the spacecraft drifts out of position whereas the co-linear points are basical­ even in the so-called stable cases. Typ­ ly unstable positions. The term "unsta­ ical trajectories are shown in Fig. 3 ble" means that any displacement of a and 4. From these diagrams and the above body from the exact location of the li­ discussion, we can conclude in unscien­ bration point will result in an ever- tific terms: increasing displacement away from the point. • The degree of stability of the triangular points L4 and L^ is The forces acting on a body at the not as great as expected. so-defined libration points are balanced only if the effect of the Sun is neglect­ • The degree of instability of ed (3-body system) . If the effect of the co-linear points Lj_, L2, the gravitational field of the Sun and and L3 is not as great as feared the motion of the Earth-Moon System and ample time is available for around the Sun is taken into account, corrective action in form of 605 propulsive forces. made in the following steps: The com­ bined spacecraft; namely, Command Module This latter conclusion is significant (CM) and Lunar Landing Vehicle (LLV), in evaluating the operational usefulness will be placed into the vicinity of L^ of the libration points. In this con­ with the additional expenditure of 1500- text we are interested not in the exact 2000 ft/sec over the lunar escape veloc­ points and their theoretical stability ity. After reaching L^ the LLV is de­ but rather in volumes of Earth-Moon Space tached and departs whenever ready for in which a spacecraft can be held in fix­ the desired place on the near side of ed position relative to the lunar surface the Moon with an additional propulsive with a minimum of propulsive energy, in effort of AV = 500-1000 ft/sec. During other words, play the role of a synchro­ the approach the landing area is always nous satellite of the Moon. In fact, a in full view of both LLV and CM. The more detailed analysis will show that duration of stay on the Moon is complete­ the point or rather flight path of mini­ ly at the discretion of the crew and mum station-keeping energy is not L^ but limited only by considerations of safety slightly off. and the consumption rate of expendables. After accomplishing its mission, the LLV For the case of Li we have plotted takes off and proceeds directly to the in Fig. 5 the velocity increment in ft/ waiting Command Module at L]_. During sec/day required to keep the spacecraft all this time, descent, stay on the Moon, in the vicinity of L-^, as a function of and ascent, there is always line-of- interval between corrective impulses, sight connection between LLV and CM. and in Fig. 6 some typical trajectories Rendezvous and docking in the vicinity in the vicinity of L^. Through suitable of LI are conducted in an environment optimization this energy can be further where the effect of gravitation and reduced. spacecraft motion are very small and practically uncoupled simplifying the Up to this point we have discussed job of the pilots during the maneuver. the properties of the libration points After completing rendezvous, the Command and approaches to cope with the peculiar­ Module disorbits for return to Earth ities of these points in space. We now with about 1500-2000 ft/sec and with would like to discuss the operational complete freedom of timing. advantages offered by the LI position. This location appears to be attractive The main advantages of this avenue for several reasons: of approach to lunar travel are: • Of the five libration points, • Unlimited window for the start L-JL is closest to the Moon at of LLV to the Moon. There is an average distance of 31,000 no need to have functional N.M. countdown coincide with a cer­ tain time and position in lunar • The spacecraft can be kept in orbit. the vicinity of L^ at the cost of less than Av = 10 ft/sec/ • Unlimited launch window for day in spite of the inherent return to LLV from the lunar instability of the position. surface. • The position is well-defined • Full-time communications as for practical purposes in spite well as optical and RF tracking of the mathematical difficul­ from L-^ to the near side of the ties and can be determined with Moon simplify greatly the nav­ sufficient accuracy with state- igation problem by permitting a of-the-art means. more active role of the pilot and a considerable reduction in • A spacecraft in L-^ is in fixed dependence on earth-based com­ position to the near side of puter and support operation. the Moon playing the role of a synchronous satellite. • Increased flexibility for be­ ginning return flight to Earth. In the proposed concept a t'rip made from the Earth to the Moon and back would be • Landings far off the lunar 606 equator can be made without in­ • Widening of launch window for creased propulsion requirements LLV both to and from the Moon. or without imposing operational restrictions, something which • Freeing the pilot from complete cannot be done with rendezvous dependence upon earth-based in low lunar orbit without computer by simplifying naviga­ changes in present LEM. tion and rendezvous control. Each of these advantages is at least • Full-time line-of-sight connec­ very desirable. Unfortunately, it is tion between the spacecraft and difficult to express the degree of im­ LLV. provement in simple numerical terms such as Ib, ft/sec, or similar units, without After acquiring more experience as to having to make use of subjective value man's capabilities and usefulness in judgments introducing individual opinions. space, we will be in a better position In sum total, however, it is hard to dis­ to provide answers to these questions.
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