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A search for natural or artificial objects located at the Earth-Moon libration points
ICARUS 42, 442-447 (1980)
A Search for Natural or Artificial Objects Located at the Earth-Moon Libration Points R O B E R T A. F R E I T A S , JR. I00 Buckin~,,ham Drive. Santa Clara. ('alif~rnia 95051
AND
FRANCISCO VALDES l)epartment ~f A,~tronomy. ~ 'niverMty ,~t'tS'alil~rnia. Berkeley. ('alil~rnia q4720 Received October 29, 1979: revised April 4, 1980 Photographs in the vicinity of the Earth-Moon triangt,lar libration points L4 and L5, and of the solar-synchronized positions in the associated halo orbits (A. A. Kamel, 1969, Ph.D. dissertation. Stanford University). were made during A u g u s t - S e p t e m b e r 1979. using the 30-in Cassegrain telescope at l.euschner Observatory, Lafayette, California. An effective T' square field was covered at each I:x)sition. No discrete objects, either natural or artificial, were found. The detection limit was about 14th magnitude. The present work extends traditional SE'I'I observations to include the search for interstellar probes (R. A. Freitas, Jr., 1980, J. Brit. Interphmet. Soc. 33, 95-100).
If two bodies of appropriate masses orbit each other under their mutual gravitation, infinitesimal objects placed at certain points in the plane of revolution will also be in equilibrium. T w o points in particular, the Lagrangian or libration points L4 and L5, are stable. These correspond, respectively, to the leading and trailing apexes of equilateral triangles having as a c o m m o n edge a line connecting the two gravitating bodies. The Trojan asteroids are well-known examples of objects trapped in the stable libration points in the S u n - J u p i t e r system. The E a r t h - M o o n system also has triangular libration points. H o w e v e r , in the E a r t h - M o o n case the problem of stability is greatly complicated by the appreciable solar gravitational influence. Taking this properly into account, it can be shown theoretically and numerically that L4 and L5 are no longer stable. For instance, a detailed numerical integration of the motion o f objects initially at rest in the Lagrangian orbits was perlormed by Schutz and Tapley (1970). T h e y found large oscillations on the
order of the E a r t h - M o o n separation. For a object begun at L4 this led to a close lunar encounter with subsequent ejection from the system after 579 days. Though the Lagrangian points are not stable, large stable orbits around the libration points have been determined analytically by Schechter (1968) and Kamel (1969) and numerically by Kolenkiewicz and Carpenter (1968). Schechter found one stable orbit using a second-order perturbation procedure and assuming a circular lunar orbit. The stable orbit was synodic with the Sun. In addition he found that oscillations out of the lunar orbital plane were essentially decoupled from the in-plane motion. The numerical search by Kolenkiewicz and Carpenter. using restricted coplanar motion and eccentric lunar orbits, tbund two synodic stable orbits of similar size with a 180° phase difl'erence. The scale of the orbits found by Schechter and by Kolenkiewicz and C a r p e n t e r differed because of the loworder analytic technique. Kamel used a third- and fourth-order theory in the copla442
0019-1035/80/060442-06502.00/0 Copyright :,(=)19x0by Academi~; Press, Inc. All rights of reproduction in any form reserved
SEARCH FOR LIBRATION OBJECTS nar model, the third-order analysis including an eccentric lunar orbit, which agreed well with the numerical results. A schematic of these stable "halo orbits" is shown in Fig. 1. There have been occasional attempts to detect objects at the Earth-Moon libration points. Kordylewski (1961) and Simpson (1967a,b) reported visual sightings of dim clouds near L5, but subsequent groundbased observations failed convincingly to confirm these results (Roosen, 1968: Roosen and Wolff, 1969). Photographic observations from NASA's Convair-990 Jet Laboratory operating at an altitude of 12,000 m failed to find clouds at L5 (Wolff et al., 1967), but experiments conducted on Skylab using the Rutgers OSO-6 Zodical Light Analyzer produced new evidence for a libration cloud counterglow near both L4 and L5 (Munro et al., 1975; Roach, 1975). A search for discrete objects at L4 has been reported by Bruman (1969), using the 48-in Schmidt telescope at Palomar Observatory, with negative results down to 15-17th magnitude. To the best of our knowledge, no observations of the Earth-Moon halo orbits have yet been attempted, nor have searches specifically designed to detect discrete objects at L5 been reported in the literature. Investigation of these positions for trapped objects is important as a check on theoreti-
,
L ',
-
I
FoG. I. Schematic diagram of the E a r t h - M o o n triangular libration points L4 and 1+5, and their associated halo orbits, in the rotating coordinate system described by Kamel (1969). Coordinates x and y are in units of the mean E a r t h - M o o n separation.
443
cal calculations, for the discovery of asteroidal material, and as a SETI (Search for Extraterristrial Intelligence) search for possible alien artifacts. The authors have attempted a preliminary photographic search with the 30-in. Cassegrain telescope at Leuschner Observatory in Lafayette, California. The SETI aspect of this observational search is based on the proposals that the Earth-Moon libration points might represent excellent parking orbits for SETI receiver antennae (Basler et al., 1977), for large space habitats (O'Neill, 1977), or for interstellar probes sent to the Solar System by advanced technical societies located elsewhere in the Galaxy (Lawton, 1974). The possibility of using messenger probes in the search for extraterrestrial intelligence was first suggested by Bracewell (1960), and the feasibility of this approach recently has been demonstrated by the British Interplanetary Society Starship Study (Martin, 1978). Much like the "preferred frequency" concept in SETI beacon theory, libration orbits might constitute the most universally convenient meeting places lbr alien spacecraft exploring arbitrary stellar systems. A viable long-term SETI program may be founded upon a search for these objects (Freitas, 1980a). We suggest (Freitas, 1980b), that halo orbits could be among the best places to begin a search for evidence of ancient spacecraft parked in the Earth-Moon system. Such orbits should be stable over geological time scales and are expected to be widely available in arbitrary solar systems that might be visited by exploratory spacecraft (Szebehely, 1967; Everhart, 1973: Weissman and Wetherill, 1974). In addition, libration/halo orbits may serve as well-defined loci for a network of interplanetary surveillance and communication relay stations (Strong, 1967; Farquhar, 1971). O B S E R V I N G PROGRAM
The aim of the observational program was to obtain maximum sensitivity to dis-
444
FREITAS AND VALDES
crete objects in the lunar orbital plane by and 0r. The angle 0~ between the Sun and guiding the telescope to follow the pre- the Moon was taken as the apparent angle dicted libration/halo orbits. Except for in the sky, since a trial projection of the Sun Bruman's work, all previous observations onto the lunar orbital plane produced only a have tracked at the sidereal rate or were negligible correction to the computed halo untracked. The combined effects of chang- orbits. The angle 0r between the Moon and ing horizontal parallax, rotation of the its point of perigee was determined by Earth, the mean orbital motion of the Moon linear interpolation of the preceding and and, for the halo orbits, the additional epi- succeeding ephemeris perigee positions to cyclic motion produce tracking rates of the date of observation. Calculations of from I s to 2.5 ~ per minute less than sidereal h a l o orbits about L5 were performed by and from 3" to 12" per minute in declination. reflecting the ( x - y ) coordinate system about Failure to correct for these variations the y-axis and reversing the time depenwould have reduced the photographic limits dence. This is indicated by the coordinate of the search by I-2 magnitudes, as deter- axis at L5 in Fig. I. mined by comparison of calibration expoThe mean motion of an object in an sures of stars in MI5. L 4 / L 5 halo orbit is synchronized with The equation for halo orbits about L4 in the synodic month (Kolenkiewicz and the (x, y) coordinate system defined in Fig. Carpenter, 1968; Schechter, 1968). Thus, it I is given by Kamel (third-order orbits e., is possible to determine a unique timeand ea with lunar orbital eccentricity e = variable position for trapped bodies or hypothetical ancient spacecraft. The sky 0.0549) as positions of the triangular libration points 8 and the four unique synodic halo points f = ~ {ai cos(i00 + b~ sin(i0s)} i=0 were computed using the American 5 Ephemeris and Nautical Almanac 1979 at + ~ {a~ cos((/ - 3)0~) + b~ sin((/ - 3)0~.)} every hour during the planned observing i=4 periods in A u g u s t - S e p t e m b e r 1979, and + a~ cos(2O~ - 0~,) + b6 sin(20~ - 0~.). (1) were interpolated to l-rain intervals to Kamel's halo orbits were calculated from permit close digital tracking. To obtain the best possible conditions, (I) by using i, a~, and b~ provided in Table 1 to generate the Lagrangicentric orbital co- the search was conducted close to maxiordinates ( f = x, f = y) as a function of 0~ mum reflection angle to ensure full brightTABLE
1
COEFHCIENTS F O r EQUATIO.~ (1) I:OR H a t . o ORBITS WITH e = 0 . 0 5 4 9 (KAMEL, 1969) Inner halo
Outer halo
f=x
f-y
f-x
f-y
i
a~
b,
a,
b,
a~
b~
a,
0 1 2 3 4 5 6
-0.064577 -0.321277 0.016204 -0.001425 -0.011154 0.00007 0.002666
0 -0.132489 0.002959 0.001902 -0.116615 -0.000046 0.009637
0.018542 0.035567 0.003824 -0.002126 --0.05631 --0.00063 0.004462
0 0.23229 - 0.01069 0.00125 0.045241 -0.000003 -0.005623
-.0.068827 0.331245 - 0.016903 0.001541 -0.042675 0.00007 0.002666
0 0.139196 0.002706 -0.002065 -0.072047 -0.000046 0.009637
0.019775 -0.03396 0.00354 0.002317 -0.037866 -0.000063 0.004462
0 -0.2397 - 0.01156 0.001345 0.06184 -0.000003 -0.005623
SEARCH FOR LIBRATION OBJECTS ness from any objects that might be present. About half the photographs were taken in a moonless sky. The remainder were taken before moonset, as early (for L4) and as late (for L5) in the M o o n ' s phases as possible, consistent with the a b o v e reflection angle requirement. The e x p o s u r e s were made by manually guiding the telescope in declination and by adjusting the tracking oscillator continuously according to digital readouts. No visual target was available, so guiding was unavoidably imperfect. Conservatively, libration/halo objects m a y have trailed as much as i x in right ascension and 15" in declination during each exposure, thus decreasing the limiting magnitude. Seeing was generally 3-8" which further reduced the visual magnitude limit. It is likely that the true position of orbiting halo objects is very near the coplanar solution. The out-of-plane halo orbit motion studied by S c h e c h t e r (1968) was found not to be seriously excited by the Sun. Roosen et al. (1967) estimated an oscillation perpendicular to the E a r t h - M o o n plane with a period equal to the synodic period and an amplitude as seen from the Earth of about 0°.25, and concluded that the integrated effect of the Sun would be to s m e a r any material into bands lying in the plane of the lunar orbit. For particles initially at the triangular libration point L5 Schutz and Tapley (1970) found a progressive reduction in inclination from the mean lunar value of 5°. 15 down to a lower limiting value of about 2 ° after 5000 days, a trend which they were unable to explain. The search for objects at the Lagrangian points and in the halo orbits given by (I) allowed for excursions of up to 1° a w a y from the orbital plane and up to 8° along the plane of the orbit. The circular field of the L e u s c h n e r telescope is I°. Photographs were taken at points along the orbital plane and at positions offset by 0°.5 to survey a 2 ° square grid around each point. T h e s e observations covered only about 6 ° along the halo plane at intervals of about 2 °. A similar
445
sampling was made in the vicinity of the Lagrangian points L4 and L5. Given the limited sensitivity and narrow field of each photograph this search must be considered preliminary and is not complete. Each photograph consisted of a 10-min exposure, then a l-sec " j o g " obtained by briefly disengaging the telescope drive, followed by another 10-min e x p o s u r e on the same film. Any libration/haio objects thus would a p p e a r as doublets on each exposure, helping to eliminate most of the false alarms caused by defects in the photographic emulsion. O b s e r v a t i o n s took place during 1-4 August 1979, 14-17 August 1979, 29-31 August 1979, and 11-13 Sept e m b e r 1979. A total of 90 photographs was taken, including 41 at L4 and its associated halo orbit positions and 40 similarly near L5. A l l w e r e 4 × 5 i n . ( 1 0 0 × 1 3 0 m m ) , T r i X ASA 320 sheet film, firmly affixed to rigid glass plates during exposure and developed with manual agitation for 5 min in D-19. Nine calibration photographs were taken of M 15, a prominent and well-studied globular cluster, covering a variety of observing conditions. RESULTS AND CONCLUSIONS Each exposure was examined using a microfiche reader with two magnification levels available. The entire 1° photographic field was divided into 288 search squares of a p p r o x i m a t e angular dimensions 4' × 4', and each was visually scanned for the expected double image of a libration/halo object. The results were all negative. Each double-image candidate considered could be ruled out on the basis of size, doublet position angle or separation distance, tracking error, passage of aircraft or emulsion defect. To determine the limiting magnitude achieved, several calibration e x p o s u r e s of M 15 were taken tracked at the sidereal rate without a guide star to simulate the effects of imperfect guiding on libration/haio objects. C o m p a r i s o n o f these photographs, obtained under various conditions of seeing, with detailed photometric data on indi-
446
FREITAS AND VALDES
vidual stars in M15 provided by Sandage 11970) indicated a visual limit o f about 14th magnitude for this series o f observations. Our data therefore indicate that no ancient s p a c e c r a f t - - o r other object o f reflectivity greater than lunar a l b e d o - - h a v i n g the size o f Skylab or larger is parked at L4, L5, or in any o f the predicted halo orbits in the E a r t h - M o o n system. The authors would encourage others to perform more c o m p r e h e n s i v e observational investigations o f this type with the possibility in mind o f ancient artifacts in the Solar System. Our experience suggests such work could most profitably be accomplished using a wide field, wide aperture Schmidt telescope which would push the limiting magnitude to about +21. This corresponds roughly to an object at the distance of the M o o n having the size o f Pioneer 10 and an albedo like that of carbon black. ACKNOWLEDGMENTS It is a pleasure to acknowledge the generosity of the University of California, Berkeley A s t r o n o m y Department for making available the facilities at L e u s c h n e r Observatory, the helpful d i s c u s s i o n s with John V. Breakwell of Stanford University and A h m e d A. Kareel of the Ford Aerospace Corporation, and useful c o m m e n t s on the manuscript by Robert G. Roosen, Joseph A. Burns, and an u n n a m e d referree. REFERENCES B.~.SI.ER, R. P.. JOItNSON, G. L., AND V()NDRAK. R. R. 11977). A n t e n n a concepts for interstellar search s y s t e m s . Radio Sci. 12, 845-858. BRACFWEtt.. R. N. 11960). C o m m u n i c a t i o n s from superior galactic communities. Nature 186, 670671. BRL'XtAN. J. R. 11969). A lunar libration point experiment. Icarus 10, 197-200. E',ERHARr, E. 11973). H o r s e s h o e and trojan orbits associated with Jupiter and Saturn. Astron. J. 78, 316-328. FARQUHAR, R. W. 11970). The Control and U.~e o f Libration-Point Satellites. N A S A T R R-346. FRtqTAS, R. A.. JR. (1980a). Interstellar probes: A new approach to SETI. d. Brit. lnterphmet. Soc. 33, 95-100. FREIIAS. R. A., JR. (1980b). Possible locations of xenological artifacts in the solar s y s t e m . Submitted for publication. KAMIH , A. A. (1%9). t'erturbation Theory B a s e d on
Lie l'ran.s~f'orms attd Its Application to the Stability o f Motion N e a r Sun-Perturbed E a r t h - M o o n Triangular Libration Points. Ph.D. dissertation. Stanford University. KOLI-.NK]F-WlCZ, R., AND CARPENI ['.R, L. 11968). Stable periodic orbits about the Sun-perturbed E a r t h Moon triangular points. AIAA J. 6, 1301-1304. KORDYtFWSK~, K. 11961). Photographic investigations of the libration point L5 in the E a r t h - M o o n s y s t e m . Acta A.stron. II, 165-169. LAW ION, A. T. (1974). Interstellar communication: A n t e n n a or artifact? J. Brit. lnterplanet. Soe. 27, 286-294. MARTIN, A. R. (Ed.) (1978L Project D a e d a l u s - - T h e trinal Report on the BIS Starsho~ Study. Unwin Brothers, London. MUNRO, R. H.. GOSLING, J. T., HILDNF.R, E., MACQL~:I:N, R. M.. POLAND, A. I.. AnD ROSS, C. L. (1975). A search for forward scattering of sunlight from lunar libration clouds. Planet. Space Sci. 23, 1313-1321. O'NEIll.. G. K. (19771. The Iligh t"rontier: t l u m a n Colonies in Space. Morrow, N e w York. R o , c H , J. R. 11975). Counterglow from the E a r t h Moon libration points. Planet. S p a c e Sci. 23, 173181. ROOSEN, R. G. (1%8). A photographic investigation of the Gegenschein and the E a r t h - M o o n libration point L5. Icarus 9, 429-439. ROOSEN, R. G.. AND WOLf-F, C. L. (1969). Are the libration clouds real? Nature 224, 571. R o o s ~ y , R. G., HARRINGTO',I, R. S., JEI FRETS, W. H.. SIMPSON. J. W., AND MILLER, R. G. 11967). Doubt about libration clouds. Phys. Today 20, 5. 1015. SANDAGI~. A. 11970). Main-sequence photometry, color-magnitude diagrams, and ages for the globular clusters M3. MI3. MI5. and M92. Astrophys. J. 162, 841-870. SC')I~-CHtI.R.H.B. 11968). Three-dimensional nonlinear stability analysis o f Sun-perturbed E a r t h - M o o n equilateral points. AIAA J. 6, 1223-1228. S c H u r / , B. E.. a Y o TAPI.EY, B. D. (1970). Numerical studies of solar influenced particle motion near the triangular E a r t h - M o o n libration points. In Periodic Orbits. Stability a n d R e s o n a n c e s (G. E. O. Giacaglia, Ed.), pp. 128-142. Reidel, Dordrecht, Holland. S,Mf, s o ~ , J. W. (1967a). Dust cloud m o o n s of the Earth. Phys. 7~day 20, 2. 39-46. Stxlpsoy, J. W. (1967b). L u n a r vibration cloud photography. In The Zodiacal LO,,ht and the lnterplanetar)" Medium (J. 1~. Weinberg, Ed.). pp. 97-107. N A S A SP- 150. S'rRON~, J. ~1967). Trojan r e l a y s - - a m e t h o d for radio c o m m u n i c a t i o n across the solar s y s t e m . Wireless World 73, 3. 119-121. SZLBEHI-t.Y, V. 11967). Theory ~t" Orbits: 77ze Restricted Problem o.1 17tree Bodies. Academic Press, New York.
SEARCH FOR LIBRATION OBJECTS WEISSMAN, P. R., AND WETHERILL, G. W. (1974). Periodic Trojan-type orbits in the Earth-Sun systern. Astron. J. 79, 404-412.
447
WOLFF, C., DL!NKEI_MAN, L., aND HAU(;tlNEY, L. C. (1967). Photography of the Earth's cloud satellites from an aircraft. Science 157, 427-429.
A Search for Natural or Artificial Objects Located at the Earth-Moon Libration Points R O B E R T A. F R E I T A S , JR. I00 Buckin~,,ham Drive. Santa Clara. ('alif~rnia 95051
AND
FRANCISCO VALDES l)epartment ~f A,~tronomy. ~ 'niverMty ,~t'tS'alil~rnia. Berkeley. ('alil~rnia q4720 Received October 29, 1979: revised April 4, 1980 Photographs in the vicinity of the Earth-Moon triangt,lar libration points L4 and L5, and of the solar-synchronized positions in the associated halo orbits (A. A. Kamel, 1969, Ph.D. dissertation. Stanford University). were made during A u g u s t - S e p t e m b e r 1979. using the 30-in Cassegrain telescope at l.euschner Observatory, Lafayette, California. An effective T' square field was covered at each I:x)sition. No discrete objects, either natural or artificial, were found. The detection limit was about 14th magnitude. The present work extends traditional SE'I'I observations to include the search for interstellar probes (R. A. Freitas, Jr., 1980, J. Brit. Interphmet. Soc. 33, 95-100).
If two bodies of appropriate masses orbit each other under their mutual gravitation, infinitesimal objects placed at certain points in the plane of revolution will also be in equilibrium. T w o points in particular, the Lagrangian or libration points L4 and L5, are stable. These correspond, respectively, to the leading and trailing apexes of equilateral triangles having as a c o m m o n edge a line connecting the two gravitating bodies. The Trojan asteroids are well-known examples of objects trapped in the stable libration points in the S u n - J u p i t e r system. The E a r t h - M o o n system also has triangular libration points. H o w e v e r , in the E a r t h - M o o n case the problem of stability is greatly complicated by the appreciable solar gravitational influence. Taking this properly into account, it can be shown theoretically and numerically that L4 and L5 are no longer stable. For instance, a detailed numerical integration of the motion o f objects initially at rest in the Lagrangian orbits was perlormed by Schutz and Tapley (1970). T h e y found large oscillations on the
order of the E a r t h - M o o n separation. For a object begun at L4 this led to a close lunar encounter with subsequent ejection from the system after 579 days. Though the Lagrangian points are not stable, large stable orbits around the libration points have been determined analytically by Schechter (1968) and Kamel (1969) and numerically by Kolenkiewicz and Carpenter (1968). Schechter found one stable orbit using a second-order perturbation procedure and assuming a circular lunar orbit. The stable orbit was synodic with the Sun. In addition he found that oscillations out of the lunar orbital plane were essentially decoupled from the in-plane motion. The numerical search by Kolenkiewicz and Carpenter. using restricted coplanar motion and eccentric lunar orbits, tbund two synodic stable orbits of similar size with a 180° phase difl'erence. The scale of the orbits found by Schechter and by Kolenkiewicz and C a r p e n t e r differed because of the loworder analytic technique. Kamel used a third- and fourth-order theory in the copla442
0019-1035/80/060442-06502.00/0 Copyright :,(=)19x0by Academi~; Press, Inc. All rights of reproduction in any form reserved
SEARCH FOR LIBRATION OBJECTS nar model, the third-order analysis including an eccentric lunar orbit, which agreed well with the numerical results. A schematic of these stable "halo orbits" is shown in Fig. 1. There have been occasional attempts to detect objects at the Earth-Moon libration points. Kordylewski (1961) and Simpson (1967a,b) reported visual sightings of dim clouds near L5, but subsequent groundbased observations failed convincingly to confirm these results (Roosen, 1968: Roosen and Wolff, 1969). Photographic observations from NASA's Convair-990 Jet Laboratory operating at an altitude of 12,000 m failed to find clouds at L5 (Wolff et al., 1967), but experiments conducted on Skylab using the Rutgers OSO-6 Zodical Light Analyzer produced new evidence for a libration cloud counterglow near both L4 and L5 (Munro et al., 1975; Roach, 1975). A search for discrete objects at L4 has been reported by Bruman (1969), using the 48-in Schmidt telescope at Palomar Observatory, with negative results down to 15-17th magnitude. To the best of our knowledge, no observations of the Earth-Moon halo orbits have yet been attempted, nor have searches specifically designed to detect discrete objects at L5 been reported in the literature. Investigation of these positions for trapped objects is important as a check on theoreti-
,
L ',
-
I
FoG. I. Schematic diagram of the E a r t h - M o o n triangular libration points L4 and 1+5, and their associated halo orbits, in the rotating coordinate system described by Kamel (1969). Coordinates x and y are in units of the mean E a r t h - M o o n separation.
443
cal calculations, for the discovery of asteroidal material, and as a SETI (Search for Extraterristrial Intelligence) search for possible alien artifacts. The authors have attempted a preliminary photographic search with the 30-in. Cassegrain telescope at Leuschner Observatory in Lafayette, California. The SETI aspect of this observational search is based on the proposals that the Earth-Moon libration points might represent excellent parking orbits for SETI receiver antennae (Basler et al., 1977), for large space habitats (O'Neill, 1977), or for interstellar probes sent to the Solar System by advanced technical societies located elsewhere in the Galaxy (Lawton, 1974). The possibility of using messenger probes in the search for extraterrestrial intelligence was first suggested by Bracewell (1960), and the feasibility of this approach recently has been demonstrated by the British Interplanetary Society Starship Study (Martin, 1978). Much like the "preferred frequency" concept in SETI beacon theory, libration orbits might constitute the most universally convenient meeting places lbr alien spacecraft exploring arbitrary stellar systems. A viable long-term SETI program may be founded upon a search for these objects (Freitas, 1980a). We suggest (Freitas, 1980b), that halo orbits could be among the best places to begin a search for evidence of ancient spacecraft parked in the Earth-Moon system. Such orbits should be stable over geological time scales and are expected to be widely available in arbitrary solar systems that might be visited by exploratory spacecraft (Szebehely, 1967; Everhart, 1973: Weissman and Wetherill, 1974). In addition, libration/halo orbits may serve as well-defined loci for a network of interplanetary surveillance and communication relay stations (Strong, 1967; Farquhar, 1971). O B S E R V I N G PROGRAM
The aim of the observational program was to obtain maximum sensitivity to dis-
444
FREITAS AND VALDES
crete objects in the lunar orbital plane by and 0r. The angle 0~ between the Sun and guiding the telescope to follow the pre- the Moon was taken as the apparent angle dicted libration/halo orbits. Except for in the sky, since a trial projection of the Sun Bruman's work, all previous observations onto the lunar orbital plane produced only a have tracked at the sidereal rate or were negligible correction to the computed halo untracked. The combined effects of chang- orbits. The angle 0r between the Moon and ing horizontal parallax, rotation of the its point of perigee was determined by Earth, the mean orbital motion of the Moon linear interpolation of the preceding and and, for the halo orbits, the additional epi- succeeding ephemeris perigee positions to cyclic motion produce tracking rates of the date of observation. Calculations of from I s to 2.5 ~ per minute less than sidereal h a l o orbits about L5 were performed by and from 3" to 12" per minute in declination. reflecting the ( x - y ) coordinate system about Failure to correct for these variations the y-axis and reversing the time depenwould have reduced the photographic limits dence. This is indicated by the coordinate of the search by I-2 magnitudes, as deter- axis at L5 in Fig. I. mined by comparison of calibration expoThe mean motion of an object in an sures of stars in MI5. L 4 / L 5 halo orbit is synchronized with The equation for halo orbits about L4 in the synodic month (Kolenkiewicz and the (x, y) coordinate system defined in Fig. Carpenter, 1968; Schechter, 1968). Thus, it I is given by Kamel (third-order orbits e., is possible to determine a unique timeand ea with lunar orbital eccentricity e = variable position for trapped bodies or hypothetical ancient spacecraft. The sky 0.0549) as positions of the triangular libration points 8 and the four unique synodic halo points f = ~ {ai cos(i00 + b~ sin(i0s)} i=0 were computed using the American 5 Ephemeris and Nautical Almanac 1979 at + ~ {a~ cos((/ - 3)0~) + b~ sin((/ - 3)0~.)} every hour during the planned observing i=4 periods in A u g u s t - S e p t e m b e r 1979, and + a~ cos(2O~ - 0~,) + b6 sin(20~ - 0~.). (1) were interpolated to l-rain intervals to Kamel's halo orbits were calculated from permit close digital tracking. To obtain the best possible conditions, (I) by using i, a~, and b~ provided in Table 1 to generate the Lagrangicentric orbital co- the search was conducted close to maxiordinates ( f = x, f = y) as a function of 0~ mum reflection angle to ensure full brightTABLE
1
COEFHCIENTS F O r EQUATIO.~ (1) I:OR H a t . o ORBITS WITH e = 0 . 0 5 4 9 (KAMEL, 1969) Inner halo
Outer halo
f=x
f-y
f-x
f-y
i
a~
b,
a,
b,
a~
b~
a,
0 1 2 3 4 5 6
-0.064577 -0.321277 0.016204 -0.001425 -0.011154 0.00007 0.002666
0 -0.132489 0.002959 0.001902 -0.116615 -0.000046 0.009637
0.018542 0.035567 0.003824 -0.002126 --0.05631 --0.00063 0.004462
0 0.23229 - 0.01069 0.00125 0.045241 -0.000003 -0.005623
-.0.068827 0.331245 - 0.016903 0.001541 -0.042675 0.00007 0.002666
0 0.139196 0.002706 -0.002065 -0.072047 -0.000046 0.009637
0.019775 -0.03396 0.00354 0.002317 -0.037866 -0.000063 0.004462
0 -0.2397 - 0.01156 0.001345 0.06184 -0.000003 -0.005623
SEARCH FOR LIBRATION OBJECTS ness from any objects that might be present. About half the photographs were taken in a moonless sky. The remainder were taken before moonset, as early (for L4) and as late (for L5) in the M o o n ' s phases as possible, consistent with the a b o v e reflection angle requirement. The e x p o s u r e s were made by manually guiding the telescope in declination and by adjusting the tracking oscillator continuously according to digital readouts. No visual target was available, so guiding was unavoidably imperfect. Conservatively, libration/halo objects m a y have trailed as much as i x in right ascension and 15" in declination during each exposure, thus decreasing the limiting magnitude. Seeing was generally 3-8" which further reduced the visual magnitude limit. It is likely that the true position of orbiting halo objects is very near the coplanar solution. The out-of-plane halo orbit motion studied by S c h e c h t e r (1968) was found not to be seriously excited by the Sun. Roosen et al. (1967) estimated an oscillation perpendicular to the E a r t h - M o o n plane with a period equal to the synodic period and an amplitude as seen from the Earth of about 0°.25, and concluded that the integrated effect of the Sun would be to s m e a r any material into bands lying in the plane of the lunar orbit. For particles initially at the triangular libration point L5 Schutz and Tapley (1970) found a progressive reduction in inclination from the mean lunar value of 5°. 15 down to a lower limiting value of about 2 ° after 5000 days, a trend which they were unable to explain. The search for objects at the Lagrangian points and in the halo orbits given by (I) allowed for excursions of up to 1° a w a y from the orbital plane and up to 8° along the plane of the orbit. The circular field of the L e u s c h n e r telescope is I°. Photographs were taken at points along the orbital plane and at positions offset by 0°.5 to survey a 2 ° square grid around each point. T h e s e observations covered only about 6 ° along the halo plane at intervals of about 2 °. A similar
445
sampling was made in the vicinity of the Lagrangian points L4 and L5. Given the limited sensitivity and narrow field of each photograph this search must be considered preliminary and is not complete. Each photograph consisted of a 10-min exposure, then a l-sec " j o g " obtained by briefly disengaging the telescope drive, followed by another 10-min e x p o s u r e on the same film. Any libration/haio objects thus would a p p e a r as doublets on each exposure, helping to eliminate most of the false alarms caused by defects in the photographic emulsion. O b s e r v a t i o n s took place during 1-4 August 1979, 14-17 August 1979, 29-31 August 1979, and 11-13 Sept e m b e r 1979. A total of 90 photographs was taken, including 41 at L4 and its associated halo orbit positions and 40 similarly near L5. A l l w e r e 4 × 5 i n . ( 1 0 0 × 1 3 0 m m ) , T r i X ASA 320 sheet film, firmly affixed to rigid glass plates during exposure and developed with manual agitation for 5 min in D-19. Nine calibration photographs were taken of M 15, a prominent and well-studied globular cluster, covering a variety of observing conditions. RESULTS AND CONCLUSIONS Each exposure was examined using a microfiche reader with two magnification levels available. The entire 1° photographic field was divided into 288 search squares of a p p r o x i m a t e angular dimensions 4' × 4', and each was visually scanned for the expected double image of a libration/halo object. The results were all negative. Each double-image candidate considered could be ruled out on the basis of size, doublet position angle or separation distance, tracking error, passage of aircraft or emulsion defect. To determine the limiting magnitude achieved, several calibration e x p o s u r e s of M 15 were taken tracked at the sidereal rate without a guide star to simulate the effects of imperfect guiding on libration/haio objects. C o m p a r i s o n o f these photographs, obtained under various conditions of seeing, with detailed photometric data on indi-
446
FREITAS AND VALDES
vidual stars in M15 provided by Sandage 11970) indicated a visual limit o f about 14th magnitude for this series o f observations. Our data therefore indicate that no ancient s p a c e c r a f t - - o r other object o f reflectivity greater than lunar a l b e d o - - h a v i n g the size o f Skylab or larger is parked at L4, L5, or in any o f the predicted halo orbits in the E a r t h - M o o n system. The authors would encourage others to perform more c o m p r e h e n s i v e observational investigations o f this type with the possibility in mind o f ancient artifacts in the Solar System. Our experience suggests such work could most profitably be accomplished using a wide field, wide aperture Schmidt telescope which would push the limiting magnitude to about +21. This corresponds roughly to an object at the distance of the M o o n having the size o f Pioneer 10 and an albedo like that of carbon black. ACKNOWLEDGMENTS It is a pleasure to acknowledge the generosity of the University of California, Berkeley A s t r o n o m y Department for making available the facilities at L e u s c h n e r Observatory, the helpful d i s c u s s i o n s with John V. Breakwell of Stanford University and A h m e d A. Kareel of the Ford Aerospace Corporation, and useful c o m m e n t s on the manuscript by Robert G. Roosen, Joseph A. Burns, and an u n n a m e d referree. REFERENCES B.~.SI.ER, R. P.. JOItNSON, G. L., AND V()NDRAK. R. R. 11977). A n t e n n a concepts for interstellar search s y s t e m s . Radio Sci. 12, 845-858. BRACFWEtt.. R. N. 11960). C o m m u n i c a t i o n s from superior galactic communities. Nature 186, 670671. BRL'XtAN. J. R. 11969). A lunar libration point experiment. Icarus 10, 197-200. E',ERHARr, E. 11973). H o r s e s h o e and trojan orbits associated with Jupiter and Saturn. Astron. J. 78, 316-328. FARQUHAR, R. W. 11970). The Control and U.~e o f Libration-Point Satellites. N A S A T R R-346. FRtqTAS, R. A.. JR. (1980a). Interstellar probes: A new approach to SETI. d. Brit. lnterphmet. Soc. 33, 95-100. FREIIAS. R. A., JR. (1980b). Possible locations of xenological artifacts in the solar s y s t e m . Submitted for publication. KAMIH , A. A. (1%9). t'erturbation Theory B a s e d on
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