The use of libration points as transfer nodes for an Earth-Mars transportation system is briefly described. It is assumed that a reusable Interplanetary Shuttle Vehicle (ISV) operates between the libration point and Mars orbit. Propellant for the round-trip journey to Mars and other supplies would be carried from low Earth orbit (LEO) to the ISV by additional shuttle vehicles. Different types of trajectories between LEO and libration points are presented, and approximate delta-V estimates for these transfers are given. The possible use of lunar gravity-assist maneuvers is also discussed

Dunham, David

Farquhar, Robert

English

NASA Technical Reports Server

LIBRATION-POINTSTAGINGCONCEPTS
FOREARTH-NARSTRANSPORTATION
N87- 17727 !
Robert Farquhar, Goddard Space Flight Center
and
David Dunham, Computer Sciences Corporation
ABSTRACT
The use of llbratton points as transfer nodes for an Earth-Nars
transporatlon system Is briefly described. It is assumed that a reusable
Interplanetary Shuttle Vehicle (ISV) operates between the llbratlon point
and Nars orbit. Propellant for the round-trip Journey to Mars and other
supplies would be carrled from low Earth orblt (LEO) to the ISV by
additional shuttle vehicles. Different types of trajectories between LEO
and libratlon points are presented, and approximate delta-V estimates for
these transfers are given. The possible use of lunar gravity-assist
maneuvers ls also discussed.
LIBRATION-POINT STAGING CONCEPTS FOR EARTH-NARS TRANSPORTATION
The existence of five positions of equilibrium in the gravita-
tional fleld of an isolated two-body system (e.g., Earth-Noon or Sun-
Jupiter) Is well known. As shown by the French mathematician, J. La-
grange in 1772, these "ltbratton points" have the interesting property
that if a third body were placed at one of them with the proper velocity,
the centripetal acceleration of the third body would be perfectly
balanced by the gravitational attractions of the two primary bodies.
Three points are sltuated on a line Jolnlng the two attracting bodies,
while the other two form equilateral triangles with these bodies.
Although the three colllnear polnts are inherently unstable and the two
triangular points are only quasi-stable, the statlonkeeplng cost to
maintain a spacecraft at or near one of these polnts for an extended
period of time is very small [1].
A total of seven ltbration polnts are located In the Earth's
neighborhood (see Figure 1). Five of them are members of the Earth-Noon
System and two belong to the Sun-Earth System. In the reference frame
shown in Flgure 1, the Sun-Earth line ls fixed and the Earth-Noon con-
figuration rotates around the Earth. From the standpoint of potential
applications to astronautics, the L1 and L2 points of both systems are
noteworthy. It is anticipated that some or all of these points will be
66
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utilized as transportation nodes in future manned expeditions to the Noon
and Mars [2].
Spacecraft trajectories from low Earth orbit (LEO) to collinear
libration points are difficult to analyze because these trajectories
spend considerable time in a region where the gravitational effects of
the two primary bodies are comparable. In this situation, standard
analytlc approximations such as the patched-conlc technique break down,
and numerical integration must be employed.
Figure 2 depicts fuel-optlmal examples of the two principal classes
of transfers between LEO and the Sun-Earth L1 point. Optimality has been
determined on the basis of the terminal maneuver at LI because the
injection delta-V at LEO is virtually identical for all cases. Although
the delta-V requirement is higher for the fast transfer, the flight time
is less than one-third of that needed by the slow transfer. Smaller
delta-V costs can be achieved by using transfers with much longer flight
times and/or by including a lunar gravlty-asslst maneuver. However, a
more effective way to reduce the delta-V cost is to simply target to an
orbit around the L1 point instead of the point Itself [3]. This method
was used to place the International Sun-Earth Explorer-3 (ISEE-3)
spacecraft into a large "halo orbit" around the L1 point [4] (see Figures
3 and 4). The retro delta-V for ISEE-3 was essentially the sum of delta-
V2 and delta-V3 (i.e., 36.3 m/sec).
Two types of trajectories between LEO and the Earth-Noon L2 point
are shown in Figure 5. In both cases the delta-V at LEO is roughly 3.15
km/sec. Notice that the two-lmpulse transfer is almost 5 days faster
than the three-impulse example. However, the retro delta-V for the
three-lmpulse transfer is smaller by about 900 m/sec. This comparison
demonstrates that the identification of an efficient trajectory to or
from the vicinity of a libration point can be a rather subtle exercise.
The use of a powered lunar swlngby to reduce the retro delta-V at L2 was
certainly not obvious.
The three-lmpulse trajectory of Figure 5 is a key element of a lunar
transporation concept that uses the Earth-Noon L2 point as a staging
location. In this concept, a large chemical orbit transfer vehicle (OTV)
carries payloads between LEO and L2 point. At the L2 point, the payload
is transferred to a smaller OTV that operates between L2 and low lunar
68
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FIGURE 5
TRAJECTORIES TO VICINITY OF EARTH-MOON L2 POINT
EARTH
MOON L2
TWO-IMPULSE TRANSFER 4 DAYS
/ FAT MOON: 184 m{sec-I
EAR(/TH/ ,// L AT L2: 148 m/sec _J
THREE-IMPULSE TRANSFER
MOON L2
5.83 DAYS 8.83
DAYS
72
orbit (LLO). Comparison of this scheme with the more conventional
techniques of using a single OTV between LEO and LLO showed that a
significant performance advantage could be gained by using L2 staging
[51.
Llbration point staging may also be advantageous for Earth-Mars
transportation. In this case, there are six potential locations for
transfer nodes. They are the L1 and L2 points of the Sun-Earth, Earth-
Moon, and Sun-Mars Systems. One or all of these points could be used.
The L1 and L2 points of the Sun-Mars system average about 1.08 million
kilometers from Mars, but their distance varies by more than 10_ due to
the eccentricity of Mars' orbit.
For instance, consider a reusable stage that is stationed in the
vicinity of the Sun-Earth L1 point. This vehicle would operate between
the L1 point and Mars orbit (or possibly a Sun-Mars libration point).
The transfer would be initiated by applying a small impulse at L1 to
bring the interplanetary shuttle vehicle (ISV) close to the Earth. Near
perigee, a larger delta-V maneuver would be used to place the ISV into
the proper trans-Mars trajectory. The ISV would also be used to achieve
Mars orbit (either by aerocapture or propulsive maneuver). A reverse
procedure would be used to return the ISV to the Sun-Earth LI point.
Resupply of the ISV would be accomplished by OTV's that travel between
the L1 point and LEO. In all likelihood, these would be the same OTV's
that would be used for lunar transportation.
Prellmlnary delta-V estimates for transfers that begin or end in a
halo orbit around the Oun-Earth and Earth-Moon llbratlon points (L1 and
L2) are given in Figure 6. T!_e second delta-V for the escape case is
applied near the Earth, at the perigee of a highly eccentric transfer
orbit whose initial apogee is at the departure halo orbit. These data
can be used to obtain a coarse measure of the performance of the
llbration-polnt staging concept. However, as noted earlier, delta-V
costs for transfers to llbratlon-polnt orbits are sensitive to variations
in flight time and the type of trajectory that Is employed. It is hoped
that a more accurate and complete summary of these delta-V costs will be
available in the near future.
Lunar gravity-asslst maneuvers can be used to improve performance,
reduce flight times, and ease launch-wlndow restrictions [6, 7, 8].
73
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74
These maneuvers are expected to play an important role In shaping the ISV
and OTV flight profiles. An example of how lunar swingby maneuvers can
be used to augment orbital energy is shown in Figure 9. Notice that the
two lunar maneuvers have increased the C3 value from -0.5 to +4.5
km2/sec2. It may be possible to add a third swingby maneuver to attain
sufficient energy to reach Venus and then on to Mars. The flight times
for this scenario might be too long for crew transfers, but should be
satisfactory for cargo missions.
The main idea of the transportation concept outlined here is to use
the ltbration point region as a stepping stone to get to Mars. By
starting the Mars Journey from a location at the rim of the "energy well"
instead of LEO, the delta-V requirement for the ISV is cun°JdeL'ably
lower. However, performance is not the only relevant factor. Tradeoffs
involving flight time, launch-window flexibility, rendezvous operations,
abort modes, propulsion options, etc. should be included in comparison
studies of alternative mission modes for Earth-Mars transportation. A
thorough system study of the competing concepts is needed to identify a
baseline plan.
95
FIGURE 7
HYPERBOLIC DOUBLE LUNAR SWlNGBY TRAJECTORY TO
COMET GIACOBINI-ZlNNER
L 1 ToSun
÷----I
S
So
Geomagnetic Tail
Orbit
1 Day
EVENT 1984 DATE G.M.T. DISTANCE SHADOW C 3 (km/sec) 2
P0 Sept. 5 9.4 Re
A 0 Oct. 24 307 R e
S0 Dec. 17 16h 23 m 2283 km 46 m -0.46
P1 Dec. 19 10 23 1.8 Re 29 +1.20
S 1 Dec. 21 4 20 1800 km 29 +4.49
76
RE_RENCES
[1] Farquhar, R. W., "The Control and Use of Libratlon-
Point Satellltes", NASA TR R-346, September 1970.
(Originally published as Stanford Unlverslty Report
SUDAn-350, July 1968).
[2] Farquhar, R. W., "Future Misslons for Libratlon-Polnt
Satellites," Astronautics and Aeronautics, Vol. 7, No.
5, May 1969.
[3] Farquhar, R. W., Muhonen, D. P., and Richardson, D. L.,
"Mlsslon Design for a Halo Orbiter of the Earth".
Journal of Spacecraft and Rockets, Vol. 14, No. 3,
March 1977.
[4] Farquhar, R. W., Muhonen, D. P., Newman, C. R., and
Heuberger, H. S., "Trajectories and Orbital Manuevers
for the First Llbratlon-Polnt Satellite", Journal of
G_Idance and Control, Vol. 3, No. 6, November-December
1980.
[5] Farquhar, R. W., "The Utlllzatlon of Halo Orbits in
Advanced Lunar Operatlons",NASA TN D-6365, July 1971.
[6] Farquhar, R. W., and Dunham, D. W., "A New Trajectory
Concept for Exploring the Earth's Geomagnetic Tall",
Journal of Guidance and Control, Vol. 4, No. 2, March-
April 198i.
[7] Special IsG_e on ISEE-3/ICE Mission, Journal of the
Astronautical Scl_nces, Vol. 33, No. 3, July-September
1985.
[8] Ross, D. J., "Materlal Capture by Double Lunar Gravlty
Aislst", AIAA Paper 80-1673, August 1980.
V7


Libration-point staging concepts for Earth-Mars transportation

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