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NASA NTRS1990

Sun-earth libration point trajectories that avoid the solar exclusion zone

Three-dimensional orbits in the restricted three-body problem have been the subject of a number of recent studies. One type of three-dimensional, quasi-periodic orbit that emanates from the general vicinity of the collinear libration points is known as a 'Lissajous' trajectory. Future mission plans include trajectories near the interior libration point. (L1) in the sun-earth system and may consider Lissajous orbits as part of the trajectory design. Such orbits may be constrained, however, to remain beyond the region of the solar disk as viewed from earth. This effort involves the numerical determination of Lissajous trajectories of arbitrary, but predetermined, length that never violate such a constraint as a result of maneuvers directed, in general, perpendicular to the ecliptic plane.

Howell, K. C.↗
NASA NTRS1983

Accelerometer-enhanced orbit control near the sun-earth L1 libration point

Because the halo-orbit about the sun-earth L(1) libration point in which the satellite ISEE-3 was maintained for nearly four years is unstable, a loose control scheme about a precomputed nominal path was implemented which required orbit maneuvers approximately every three months. Execution errors were minimized by processing on-board accelerometer telemetry data in real time, and adjusting the maneuvers. Because spacecraft vibrations caused oscillations in the accelerometer data, smoothing techniques were applied to provide accurate estimates of the performance of pulse mode thrusters employed in the spin stabilization of the spacecraft. It has been found that the processed accelerometer data has an average error of only + or - 1.3 per cent.

Muhonen, D. P.↗
NASA NTRS1990

Use of libration-point orbits for space observatories

The sun-earth libration points, L1 and L2, are located 1.5 million kilometers from the earth toward and away from the sun. Halo orbits about these points have significant advantages for space observatories in terms of viewing geometry, thermal and radiation environment, and delta-V expediture.

Farquhar, Robert W.↗
NASA NTRS1979

The first libration-point satellite - Mission overview and flight history

On August 12, 1978, a scientific spacecraft called International Sun-Earth Explorer-3 (ISEE-3) was launched towards the interior sun-earth libration point, L1. The spacecraft was placed into a 'halo orbit' around the L1 point on November 20, 1978, thus becoming the first libration-point satellite. During its 100-day transfer trajectory, ISEE-3 lingered in a region where the gravitational effects of the sun and the earth are comparable, leading to some interesting tradeoffs concerning the maneuver strategy for halo-orbit insertion. Following orbit insertion, stationkeeping maneuvers were required to maintain the delicate equilibrium in the halo orbit. Details are presented for all of the velocity change maneuvers that were executed prior to the completion of the first halo orbit on May 14, 1979. Orbit selection, trajectory design, and the scientific objectives of the ISEE-3 mission are also discussed.

Farquhar, R. W.↗
NASA NTRS1984

Trajectories and orbital maneuvers for the ISEE-3/ICE comet mission

The ISEE-3/ICE spacecraft, (launched in 1978), and expected to obtain the first measurements of comet Giacobinni-Zinner in September 1985, has undertaken a combination of propulsive maneuvers, lunar swing-bys, and solar perturbations to produce its present trajectory profile. ISEE-3 is a drum-shaped, spin-stabilized spacecraft equipped with a redundant pair of high-resolution sun sensors, a medium-gain S-band antenna, a hydrazine propulsion system and a science experiment payload. After being placed into a sun-earth libration halo orbit in late 1978, ISEE-3 was retargeted to the geomagnetotail in mid-1982 and became the first spacecraft to explore the geomagnetic tail between 80 and 237 earth radii in 1983. These types of maneuvers may prove important for future scientific missions planned as follow-ons to ISEE-3/ICE, such as a joint NASA/ISAS project spacecraft scheduled for Shuttle launch in 1991, and a possible encounter with two comets in 1996 anad 1998.

Farquhar, R.↗
NASA NTRS1991

International Cometary Explorer (ICE)

The primary mission objectives of the International Cometary Explorer (ICE) Comet Mission are to determine the composition and physical state of the Giacobini-Zinner Comet's nucleus; to determine the processes that governs the composition and distribution of neutral and ionized species in the cometary atmosphere; and to investigate the interaction between the solar wind and the cometary atmosphere. The spacecraft was in a halo orbit around the Sun-Earth libration point until it was moved 10 Jun. 1982 to the Earth's Geomagnetic Tail (GT). The spacecraft reached the GT in Jan. 1983 and remained there until Dec. 1983, at which time a lunar swing-by placed the spacecraft in a trajectory heliocentric orbit which encountered the comet Giacobini-Zinner in Sep. 1985. The spacecraft provided observations of solar wind upstream of Halley's Comet in 1986. Information is presented in tabular form and includes the following areas: Deep Space Network support, frequency assignments, telemetry, command, and tracking support responsibilities.

Wales, R.↗
NASA NTRS1990

Halo-orbit and lunar-swingby missions of the 1990's

A significant number of spacecraft are planning to use halo orbits and lunar-swingby trajectories in the next decade. Four spacecraft will be placed into halo orbits around the earth's sunward libration point, while two others will be stationed near the sun-earth L2 libration point in the distant geomagnetic tail. Six spacecraft, including two of the aforementioned halo orbiters, will make use of lunar-swingby maneuvers to fulfill their mission objectives. Thus, a total of ten spacecraft, five from the Soviet Union, two from Japan, two from the United States, and one from the European Space Agency, will employ halo orbits and/or lunar-swingby trajectories in the 1990's. Pertinent facts are presented for each of these missions.

Farquhar, Robert W.↗
NASA NTRS1976

Mission design for a halo orbiter of the earth

The International Sun-Earth Explorer (ISEE) scientific satellite to be stationed in 1978 in the vicinity of the sun-earth interior libration point to continuously monitor the space between the sun and the earth, including the distant geomagnetic tail is described. Orbit selection considerations for the ISEE-C are discussed along with stationkeeping requirements and fuel-optimal trajectories. Due to the alignment of the interior libration point with the sun as viewed from the earth, it will be necessary to place the satellite into a 'halo orbit' around the libration point, in order to eliminate solar interference with down-link telemetry. Parametric data for transfer trajectories between an earth parking orbit (altitude about 185 km) and a libration-point orbit are presented. It is shown that the insertion magnitude required for placing a satellite into an acceptable halo orbit is rather modest.

Farquhar, R. W.↗
NASA NTRS1992

Double lunar swingby and Lissajous trajectory design for the WIND mission

Two alternative mission profiles are presented for the WIND mission whose baseline design includes two years in a double lunar swingby (DLS) orbit followed by one year in a Lissajous orbit about the sun-earth L1 libration point. The first alternative uses a half-month high-inclination transfer orbit between two lunar gravity assists to change the initial sunward DLS orbit to a DLS orbit in the geomagnetic tail region. The second alternative uses a direct insertion from launch into a large-amplitude Lissajous orbit followed by a sunward DLS orbit.

Sharer, P. J.↗
NASA NTRS1993

Atlas IIAS ascent trajectory design for the SOHO mission

In 1995, an Atlas IIAS launch vehicle will loft the Solar and Heliospheric Observatory (SOHO) as part of the International Solar and Terrestrial Physics program. The operational phase of the SOHO mission will be conducted from a `halo orbit' about the Sun-Earth interior libration point. Depending on the time of the year of launch, the optimal transfer requires a parking orbit of variable duration to satisfy widely varying inertial targets. A simulation capability has been developed that optimizes the launch vehicle ascent and spacecraft transfer phases of flight together, subject to both launch vehicle and spacecraft constraints. It will be shown that this `ground-up' simulation removes the need for an intermediate target vector at Centaur upper stage/spacecraft separation. Although providing only a modest gain in deliverable satellite mass, this capability substantially improves the mission integration process by removing the strict reliance on near-Earth target vectors. Trajectory data from several cases are presented and future applications of this capability are also discussed.

Willen, Robert E.↗
NASA NTRS1990

A station-keeping method for libration point trajectories

Three-dimensional orbits in the vicinity of the interior libration point of the sun-earth/moon barycenter system are currently being considered for use with a number of missions planned for the 1990s. Since such libration-point trajectories are generally unstable, spacecraft moving on these paths must use some form of trajectory control to remain close to their nominal orbit. The primary goal of this effort is the development of a stationkeeping strategy applicable to such trajectories. A method is presented that uses maneuvers executed impulsively at discrete time intervals. The analysis includes some investigation of a number of the problem parameters that affect the overall maneuver costs. Simulations are designed to provide representative stationkeeping costs for a spacecraft moving in a libration-point trajectory, and preliminary results are summarized.

Howell, K. C.↗
NASA NTRS1972

Gegenschein-Moulton region photography from lunar orbit

Apollo 16 photography during lunar orbit of the Gegenschein-Moulton region was used to determine the libration points of the Sun-Earth system. Triangulation for the system is discussed, along with background experimental information.

Dunkelman, L.↗
NASA NTRS1973

Four-body trajectory optimization

A collection of typical three-body trajectories from the L1 libration point on the sun-earth line to the earth is presented. These trajectories in the sun-earth system are grouped into four distinct families which differ in transfer time and delta V requirements. Curves showing the variations of delta V with respect to transfer time, and typical two and three-impulse primer vector histories, are included. The development of a four-body trajectory optimization program to compute fuel optimal trajectories between the earth and a point in the sun-earth-moon system are also discussed. Methods for generating fuel optimal two-impulse trajectories which originate at the earth or a point in space, and fuel optimal three-impulse trajectories between two points in space, are presented. A brief qualitative comparison of these methods is given. An example of a four-body two-impulse transfer from the Li libration point to the earth is included.

Pu, C. L.↗
NASA NTRS1983

Stochastic analysis of the control of the movement of the spacecraft in the vicinity of the colinear libration point by means of the forces of luminous pressure

This paper is dedicated to the possible investigation of the utilization of the solar radiation pressure for the spacecraft motion control in the vicinity of collinear libration point of planar restricted ring problem of three bodies. The control is realized by changing the solar sail area at its permanent orientation. In this problem the influence of the trajectory errors and the errors of the execution control is accounted. It is worked out, the estimation method of the solar sail sizes, which are necessary for spacecraft keeping in the vicinity of collinear libration point during the certain time with given probability. The main control parameters were calculated for some examples in case of libration points of the Sun-Earth and Earth-Moon systems.

Lukyanov, S. S.↗
NASA NTRS1993

Transfer trajectories for distant retrograde orbiters of the Earth

A new mission concept is introduced for future astrophysical observatories. This concept is to use a solar orbit that remains bounded to the Earth at a large distance on the order of several million kilometers. These orbits are termed here distant Retrograde Orbits (DRO's). This type of orbit is ideal for a space telescope that needs to be separated from the Earth by a large distance to avoid the near-Earth environmental effects, yet needs to remain bounded within some pre-defined distance for communication purposes. Another application is for a solar storm warning system that can provide warning times greater than those available from a similar system at the interior libration point of the Sun-Earth/Moon system. Several classes of DRO's in the Sun-Earth/Moon system are presented. The associated launch and insertion energies for impulsive and continuous thrust transfers from a low Earth parking orbit are investigated.

Ocampo, Cesar A.↗
NASA NTRS1993

Transfer trajectories for distant retrograde orbiters of the Earth

A new mission concept is introduced for future astrophysical observatories. This concept is to use a solar orbit that remains bounded to the Earth at a large distance on the order of several million kilometers. These orbits are termed here Distant Retrograde Orbits (DRO's). This type of orbit is ideal for a space telescope that needs to be separated from the Earth by large distance to avoid the near Earth environmental effects, yet needs to remain bounded within some predefined distance for communication purposes. Another application is for a solar storm warning system that can provide warning times greater than those available from a similar system at the interior libration point of the Sun-Earth/Moon system. Several classes of DRO's in the Sun-Earth/Moon system are presented. The associated launch and insertion energies for impulsive and continuous thrust transfers from a low Earth parking orbit are investigated.

Ocampo, Cesar A.↗
NASA NTRS1993

Orbit determination error analysis and comparison of station-keeping costs for Lissajous and halo-type libration point orbits and sensitivity analysis using experimental design techniques

Spacecraft in orbit near libration point L1 in the Sun-Earth system are excellent platforms for research concerning solar effects on the terrestrial environment. One spacecraft mission launched in 1978 used an L1 orbit for nearly 4 years, and future L1 orbital missions are also being planned. Orbit determination and station-keeping are, however, required for these orbits. In particular, orbit determination error analysis may be used to compute the state uncertainty after a predetermined tracking period; the predicted state uncertainty levels then will impact the control costs computed in station-keeping simulations. Error sources, such as solar radiation pressure and planetary mass uncertainties, are also incorporated. For future missions, there may be some flexibility in the type and size of the spacecraft's nominal trajectory, but different orbits may produce varying error analysis and station-keeping results. The nominal path, for instance, can be (nearly) periodic or distinctly quasi-periodic. A periodic 'halo' orbit may be constructed to be significantly larger than a quasi-periodic 'Lissajous' path; both may meet mission requirements, but perhaps the required control costs for these orbits are probably different. Also for this spacecraft tracking and control simulation problem, experimental design methods can be used to determine the most significant uncertainties. That is, these methods can determine the error sources in the tracking and control problem that most impact the control cost (output); it also produces an equation that gives the approximate functional relationship between the error inputs and the output.

Gordon, Steven C.↗