Lunar Dynamics And A Search For Objects
Near the Earth-Moon Lagrangian Points
Jill Eymann
Abstroct. For the Saint Mary's College Summer Research Project, I propose performing a CD imaging
search of the Earth-Moon Lagrangian positions, including the solar-synchronized positions in the stable
L4/15 libration orbits. Observations using the 0.5-m SC telescope at the SMC Norma Geissberger
Observatory will span 60" along the lunar orbital plane x 5' around Earth-Moon 15, 45" x 5' around 14.
Limiting magnitude for the detection of libration objects near 14, and L5 is assumed to be 17-l-9th
magnitude, the fainter limit depending on superior observing conditions. An automated search of
selected priority will be attempted using the Faint Object Classification and Analysis System (FOCAS)
software package from the National Optical Astronomy Observatories.
Background. ln astronomy, the adjective 'trojan' refers to a minor planet or natural satellite (moon) that
shares an orbit with a larger planet or moon, but does not collide with it because it orbits around one of
the two Lagrangian points of stability, L4 and 15, which lie 60' ahead of and behind the larger body. The
term originally referred to the Trojan asteroids orbiting Jupiter's Lagrangian points, as shown in the
figure below. Subsequently, objects have been found orbiting the Lagrangian points of Neptune as well
as Mars. ln addition, trojan moons are known to orbit the Lagrangian points of two of Saturn's mid-sized
moons. With this in mind, my project will explore the Lagrangian Points in the Earth-Moon system in an
attempt to discover natural satellites in those regions.
The Lagrangian points, are the five positions in an orbital configuration where a small object affected
only by gravity can theoretically be stationary relative to two larger objects (such as a satellite with
respect to the Earth and Moon). The Lagrange points mark positions where the combined gravitational
pull of the two large masses provides precisely the centripetal force required to rotate with them. They
are analogous to geostationary orbits in that they allow an object to be in a "fixed" position in space
rather than an orbit in which its relative position changes continuously.
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Moon
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A more precise but technical definition is that the Lagrangian points are the stationary solutions of the
circular restricted three-body problem in gravitational physics. For example, given two massive bodies
in circular orbits around their common center of mass, there are five positions in space where a third
body, of comparatively negligible mass, could be placed which would then maintain its position relative
to the two massive bodies. As seen in a rotating reference frame with the same period as the two coorbiting bodies, the gravitational fields of two massive bodies combined with the centrifugal force are in
balance at the Lagrangian points, allowing the third body to be stationary with respect to the first two
bodies.
Lagrangian satellite searches may be useful in detecting captured asteroidal bodies or impact ejecta
from the lunar surface; this unique and accessible material is important for astro-geological study and
could also help confirm theoretical predictions in the four-body problem in celestial mechanics. Also,
determining whether or not the stable libration orbits are clear of large obstacles is practical because of
the potential future use of these orbits for global telecommunication satellite systems and solar deepspace telemetry networks, space manufacturing facilities utilizing lunar or asteroidal raw materials, large
optical and radio telescope arrays, and/or as part of a comprehensive SETI (Search for Extraterrestrial
lntelligence) search for possible alien artifacts in the Solar System (Freitas, 1980).
The current observational status of the triangular libration orbits and L4/15 is sporadic with limits of L2-
14th magnitude (Freitas and Valdes, 1980); even after almost 20 years, the existence of material at
these points remains controversial. No searches for material at Earth-Moon L3 have been reported in
the literature. The lunar halo survey near Earth-M oon LL/L2 involves an investigation of the same
orbital space examined during previous searches for selenocentric satellites. The best modern effort
encompasslng
was byTombaugh et al. (1959), who achieved a limit of 11-12th magnitude in the region
No
environment.
the L1/12 halo orbits and 13-14th magnitude for most of the rest of the lunar satellite
have been reported in the
searches for discrete objects fainter than 14th magnitude near sun-Earth L2
literature. lt
is time
to revisit the problem and to renew a search with modern experimental facilities.
OBSERVING PROGRAM
objects in the
The observing program, with the major goal of obtaining maximum sensitivity to discrete
lunar orbital plane, will pursue five distinct objectives as follows.
(tracked
Eorth-Moon L4/15 Libration orbit objects. My highest priority will be to obtain pairs of images
The telescope
and sidereal) at the unique solar-synchronized stable phases in the L4/15 libration orbits.
methods
drive will be adjusted to track the predicted stable libration orbital positions computed by the
erred
described in Freitas and Valdes (1980). Previous observers (e.g., Bruman, 1969) have sometimes
the lunar
drastically by using a simple 1-/6 Moon phase formula and then neglecting to take into account
orbital eccentricity and the fact that each lunar ephemeris tabulated in the Nautical Almanac
in
incorporates the heliocentric motion of the observer, all of which can cause pointing inaccuracies
predicted to be dynamically
excess of 10.. Though the Lagrangian points L4 and L5 are themselves
Each CCD
unstable, a third CCD image pair will be taken at both L4 and L5 tracked at the lunar rate.
image will be a sky-limited exposure determined by nightly conditions.
Eorth-Moon L4/15 Libration Orbit Survey. The degree of stability and the mechanics of trapping objects
in precisely the theoretical libration orbit and phase are unknown. Oscillations around the ideal stable
locations (in the Earth-Moon plane) are likely for natural objects injected into such orbits with arbitrary
initial conditions; in which case possible trapped bodies may deviate significantly from the solarless
synchronized positions. Also, the extent of out-of-plane motion is thought to be a few degrees or
(Roosen eI al., !967;Schechter, 1968; Schutz and Tapley ,1970), but is, at present, undetermined by
reliable theoretical computations. Consequently, a series of CCD images spanning more than the entire
45. libration orbit regions with 0.5" overlap will be tracked at the lunar rate. Survey images on
successive nights will be overlapped to compensate for possible diurnal object movement.
The choice of observing time is dictated by a number of factors that serve
to maximize the probability of
detection of faint libration objects with known or anticipated orbital characteristics. To obtain the
maximum reflected brightness from bodies trapped near L4 and 15, the following conditions need to be
satisfied: (1) end of astronomical twilight; (2) end of lunar twilight; (3) maximum lunar declination for a
(5)
minimum zenith angle for L4 or L5; (4) maximum elongation angle of solar-synchronized objects;
minimum reflection angle ensuring "full" phase of possible targets; (6) maximum distance from the
(15)
Milky Way background for L4 and L5; and (7) maximum post-moonset (14) or pre-moonrise
(5) and (7)
observing time. For libration orbit objects the best compromise between requirements
places the Moon no more than 95' (7.4 days lunar phase) from the Sun. Hence a four-night observation
schedule is best completed over the lunar-phase Days 5-8 for L4 and Days21'-24 for 15.
t
REFERENCES
BREAKWELL, J. V. AND J. V. BROWN (1979). The 'halo' family of 3-dimensional periodic orbits in the
Earth-Moon restricted 3-body problem. Celest. Mech. 20,389-404.
BRUMAN, J. R. (1969). A lunar libration point experiment. lcarus 10,197-200.
FARQUHAR, R. W. (1970). The Moon's influence on
the location of the Sun-Earth exterior libration point.
Celest. Mech. 2, 13I-133.
FRE1TAS, R.
A., JR. (1980). lnterstellar probes:A new approach to SETI.
i. Brit. lnterplanet. Soc.33,95-
100.
FRE;TAS, R. A., JR., AND F. VALDES (1980). A search
for natural or artificial objects located at the Earth-
Moon libration points. lcarus 42,442-447.
JARV|S, J. F., AND J. A. TYSON
(1930). FOCAS: Faint Object Classification and Analysis System. Astron.
J.
86,476-495.
ROOSEN, R. G., R. S. HARRTNGTON, W. H. JEFFREYS, J. W. SIMPSON, AND R. G. MILLER (1967]'. Doubt
about liberation clouds. Phys. Today 20(5), 10-15.
SCHECHTER, H. B. (1968).
Three-dimensional nonlinear stability analysis of Sun-perturbed Earth-Moon
equilateral points. AIAA J. 6,1223-1228.
SCHUTZ, B. E., AND B. D. TAPLEY (1970). Numerical studies of solar influenced particle
motion near the
triangular Earth-Moon libration points. ln Periodic Orbits, Stability and Resonances (G.
Ed.), pp. !28-1,42. Reidel, Dordrecht.
E. 0.
Giacaglia,
VALDES, F. (1932). Faint Object Classification and Analysis System. Kitt Peak National Observatory,
Computer Support Group, Tucson, Arizona.
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