Search NASA⌕ Search

SEARCH · Search NASA

Results for “Lagrange orbit”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 181 records · Page 10
All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

The Lunar L1 Gateway: Portal to the Stars and Beyond

Our Solar System is interconnected by a vast system of winding tunnels generated by the Lagrange Points of all the planets and their moons. These passageways are identified by portals around L1 and L2, the halo orbits. By passing through a halo orbit portal, one enters the ancient and colossal labyrinth of the Sun. This natural Interplanetary Supher highway System (IPS) provides ultra-low energy transport throughout the Earth's Neighborhood, the region between Earth's L1 and L2. This is enabled by an accident: the current energy levels of the Earth L1 and L2 Lagrange points differ from that of the Earth-Moon by only about 50 rn/s (as measured by AV). The significance of this happy coincidence to the development of space cannot be overstated. For example, this implies that Lunar L1 halo orbits are connected to halo orbits around Earth's L1 or L2 via low energy pathways...

lunar gateways↗
NASA NTRS2004

Spacecraft Formation Flying near Sun-Earth L2 Lagrange Point: Trajectory Generation and Adaptive Full-State Feedback Control

In this paper, we present a method for trajectory generation and adaptive full-state feedback control to facilitate spacecraft formation flying near the Sun-Earth L2 Lagrange point. Specifically, the dynamics of a spacecraft in the neighborhood of a Halo orbit reveals that there exist quasi-periodic orbits surrounding the Halo orbit. Thus, a spacecraft formation is created by placing a leader spacecraft on a desired Halo orbit and placing follower spacecraft on desired quasi-periodic orbits. To produce a formation maintenance controller, we first develop the nonlinear dynamics of a follower spacecraft relative to the leader spacecraft. We assume that the leader spacecraft is on a desired Halo orbit trajectory and the follower spacecraft is to track a desired quasi-periodic orbit surrounding the Halo orbit. Then, we design an adaptive, full-state feedback position tracking controller for the follower spacecraft providing an adaptive compensation for the unknown mass of the follower spacecraft. The proposed control law is simulated for the case of the leader and follower spacecraft pair and is shown to yield global, asymptotic convergence of the relative position tracking errors.

Wong, Hong↗
NASA NTRSDate not supplied

Lucy Orbit Determination Performance From Launch Through EGA-1

Lucy is a 12-year long NASA Discovery-class mission which launched on October 16, 2021 and is currently on its way to the Jupiter-Trojan asteroids at the L4 and L5 Lagrange points. On its journey to the Trojan asteroids, Lucy will also fly by two main belt asteroids, and perform 3 Earth fly bys. This paper summarizes primarily the Orbit Determination (OD) aspect of the first year of the mission from launch through the first Earth fly by (EGA-1). Some challenges were encountered for OD as part of the +Y solar array not fully deploying, but these were resolved within the first year of flight. The high quality radio-metric data from the Deep Space Network including 2- and 3-way Doppler, sequential 2-way ranging, complemented by delta differential one-way ranging (∆DOR) has enabled the OD team to characterize the Solar Radiation Pressure force, resolve desaturation maneuvers, generate both maneuver reconstructions and accurate long-term predicted trajectories. This paper discusses the filter setup and strategies implemented, as well as the OD performance from launch, through cruise, and including EGA-1.

Jeroen L. Geeraert↗
NASA NTRS2004

Orbit Determination Accuracy for Comets on Earth-Impacting Trajectories

The results presented show the level of orbit determination accuracy obtainable for long-period comets discovered approximately one year before collision with Earth. Preliminary orbits are determined from simulated observations using Gauss' method. Additional measurements are incorporated to improve the solution through the use of a Kalman filter, and include non-gravitational perturbations due to outgassing. Comparisons between observatories in several different circular heliocentric orbits show that observatories in orbits with radii less than 1 AU result in increased orbit determination accuracy for short tracking durations due to increased parallax per unit time. However, an observatory at 1 AU will perform similarly if the tracking duration is increased, and accuracy is significantly improved if additional observatories are positioned at the Sun-Earth Lagrange points L3, L4, or L5. A single observatory at 1 AU capable of both optical and range measurements yields the highest orbit determination accuracy in the shortest amount of time when compared to other systems of observatories.

Kay-Bunnell, Linda↗
DOE OSTI2025

An Open Benchmark of One Million High-Fidelity Cislunar Trajectories

Cislunar space spans from geosynchronous altitudes to beyond the Moon and will underpin future exploration, science, and security operations. We describe and release an open dataset of one million numerically propagated cislunar trajectories generated with the open-source Space Situational Awareness Python package (SSAPy). The model includes high-degree Earth/Moon gravity, solar gravity, and Earth/Sun radiation pressure; other planetary gravities are omitted by design for computational efficiency. Initial conditions uniformly sample commonly used osculating-element ranges, and each trajectory is propagated for up to six years under a single, fixed start epoch. The dataset is intended as a reusable benchmark for method development (e.g., space domain awareness, navigation, and machine-learning pipelines), a reference library for statistical studies of orbit families, and a starting point for community-driven extensions (e.g., alternative epochs). We report empirically observed stability trends (e.g., a band near ~5 GEO and persistence of some co-orbital classes including L4/L5 librators) as dataset descriptors rather than new dynamical results. The chief contribution is the scale, fidelity, organization (CSV/HDF5 with full state time series and metadata), and open availability, which together lower the barrier to comparative and data-driven studies in the cislunar regime.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS2018

Calibration of the DSCOVR EPIC Visible and NIR Channels using MODIS Terra and Aqua Data and EPIC Lunar Observations

The unique position of the Deep Space Climate Observatory (DSCOVR) Earth Polychromatic Imaging Camera (EPIC) at the Lagrange 1 point makes an important addition to the data from currently operating low Earth orbit observing instruments. EPIC instrument does not have an onboard calibration facility. One approach to its calibration is to compare EPIC observations to the measurements from polar-orbiting radiometers. Moderate Resolution Imaging Spectroradiometer (MODIS) is a natural choice for such comparison due to its well-established calibration record and wide use in remote sensing. We use MODIS Aqua and Terra L1B 1km reflectances to infer calibration coefficients for four EPIC visible and NIR channels: 443, 551, 680 and 780 nm. MODIS and EPIC measurements made between June 2015 and 2016 are employed for comparison. We first identify favorable MODIS pixels with scattering angle matching temporarily collocated EPIC observations. Each EPIC pixel is then spatially collocated to a subset of the favorable MODIS pixels within 25 km radius. Standard deviation of the selected MODIS pixels as well as of the adjacent EPIC pixels is used to find the most homogeneous scenes. These scenes are then used to determine calibration coefficients using a linear regression between EPIC counts/sec and reflectances in the close MODIS spectral channels. We present thus inferred EPIC calibration coefficients and discuss sources of uncertainties. The lunar EPIC observations are used to calibrate EPIC O2 absorbing channels (688 and 764 nm), assuming that there is a small difference between moon reflectances separated by approx.10 nm in wavelength provided the calibration factors of the red (680 nm) and near-IR (780 nm) are known from comparison between EPIC and MODIS.

Geogdzhayev, Igor V.↗
NASA NTRS2021

Calibration of the DSCOVR EPIC Visible and NIR Channels using Multiple LEO Radiometers

The first five years of operation of the Deep Space Climate Observatory (DSCOVR) Earth Polychromatic Imaging Camera (EPIC) at the Lagrange one point have produced results that uniquely complement the data from currently operating low orbit Earth-observing instruments. In this paper we describe an updated unified approach to EPIC calibration. In this approach, calibration coefficients and their trends were obtained by comparing EPIC observations to the measurements from polar orbiting radiometers. In this study L1B reflectances from Moderate Resolution Imaging Spectroradiometer (MODIS) onboard the Aqua and Terra satellites, Multi-angle Imaging Spectroradiometer (MISR) onboard Terra and Visible Infrared Imaging Radiometer (VIIRS) onboard the Suomi National Polar-orbiting Partnership (Suomi NPP) spacecraft were used to infer calibration coefficients for four EPIC visible and near-infrared channels: 443 nm, 551 nm, 680 nm, and 780 nm. EPIC Version three measurements made between June 2015 and August 2020 were used for comparison. The calibration procedure identifies the most homogeneous low Earth orbit radiometer scenes matching scattering angles that are temporarily and spatially collocated with EPIC observations. These scenes are used to determine reflectance to count (R/C) ratios in spectrally analogous channels. Seasonal average R/C ratios were analyzed to obtain EPIC calibration gains and trends. The trends for the full dataset period are not statistically significant except in the 443 nm channel. No significant changes in calibration were found after the instrument’s exit from safe hold in March 2020. The R/C ratios were also used to determine the differences in EPIC gains resulting from separate calibrations: against MODIS Aqua or Terra, as well as against forward or aftward MISR cameras. Statistical tests indicate that the differences between the two datasets are not significant except in the 780 nm channels where Aqua-derived coefficients may be around 2% lower compared to Terra. The dependence of EPIC calibration gains on the instrument scattering angle and on DSCOVR-Earth distance were investigated. Lastly, model Low Earth Orbit (LEO) reflectances calculated to match the EPIC viewing geometry were employed to study how EPIC calibration coefficients depend on EPIC-LEO viewing geometry differences. The effect of LEO and EPIC angular mismatch on calibration was shown to be small.

deep space climate observatory/earth polychromatic↗
NASA NTRS1972

The topology of the regularized integral surfaces of the 3-body problem.

A method is described by which the integral surface can be modified in such a way that Newton's equations of motion actually give a flow. The process of regularization of vector fields by surgery, as described by the author (1971) is reviewed. The planar 3-body problem and its regularization, and the topology of the integral surfaces are considered. The Lagrange-Jacobi identity is used to show that there exists an isolating block such that any orbit which ends in a triple collision must enter and remain in this block.

Easton, R.↗
NASA NTRSDate not supplied

The Space Weather Follow On – Lagrange 1 Mission

The Space Weather Follow On – Lagrange 1 (SWFO-L1) Observatory will be situated in a Sun-Earth L1 Lissajous orbit with the goal of providing continuous measurements of the space environment and observations of the Sun’s outer atmosphere, and contributing to accurate forecasts of space weather disturbances. Unique to the SWFO-L1 mission are challenges of a rideshare launch, immoderate momentum management delta-V residuals, and spacecraft maneuver design considerations, resulting in specialized operational approach, management, and support.

cislunar↗
NASA NTRSDate not supplied

The Space Weather Follow On – Lagrange 1 Mission

The Space Weather Follow On – Lagrange 1 (SWFO-L1) Observatory will be situated in a Sun-Earth L1 Lissajous orbit with the goal of providing continuous measurements of the space environment and observations of the Sun’s outer atmosphere, and contributing to accurate forecasts of space weather disturbances. Unique to the SWFO-L1 mission are challenges of a rideshare launch, immoderate momentum management delta-V residuals, and spacecraft maneuver design considerations, resulting in specialized operational approach, management, and support.

Dynamical Systems↗
NASA NTRS2003

Active and Passive Sensing from Geosynchronous and Libration Orbits

The development of the LEO (EOS) missions has led the way to new technologies and new science discoveries. However, LEO measurements alone cannot cost effectively produce high time resolution measurements needed to move the science to the next level. Both GEO and the Lagrange points, L1 and L2, provide vantage points that will allow higher time resolution measurements. GEO is currently being exploited by weather satellites, but the sensors currently operating at GEO do not provide the spatial or spectral resolution needed for atmospheric trace gas, ocean or land surface measurements. It is also may be possible to place active sensors in geostationary orbit. It seems clear, that the next era in earth observation and discovery will be opened by sensor systems operating beyond near earth orbit.

Schoeberl, Mark↗
NASA NTRS2002

Searching for life with the Terrestrial Planet Finder: Lagrange point options for a formation flying interferometer

In this paper, we describe the mission design for TPF assuming a distributed spacecraft concept using formation flight around both a halo orbit around L2 as well as a heliocentric orbit. Although the mission architecture is still under study, the next two years will include study of four design cncepts and a downselect to two concepts around 2005.

TPF Terrestrial Planet Finder extrasolar system li↗
NASA NTRS1977

Analytic theory of orbit contraction

The motion of a satellite in orbit, subject to atmospheric force and the motion of a reentry vehicle are governed by gravitational and aerodynamic forces. This suggests the derivation of a uniform set of equations applicable to both cases. For the case of satellite motion, by a proper transformation and by the method of averaging, a technique appropriate for long duration flight, the classical nonlinear differential equation describing the contraction of the major axis is derived. A rigorous analytic solution is used to integrate this equation with a high degree of accuracy, using Poincare's method of small parameters and Lagrange's expansion to explicitly express the major axis as a function of the eccentricity. The solution is uniformly valid for moderate and small eccentricities. For highly eccentric orbits, the asymptotic equation is derived directly from the general equation. Numerical solutions were generated to display the accuracy of the analytic theory.

Vinh, N. X.↗
NASA NTRSDate not supplied

Flight Dynamics Planning and Operations Support for the JWST Mission

The James Webb Space Telescope (JWST) was launched from Kourou Spaceport on December 25, 2021, at 12:20 UTC on an Ariane 5 launch vehicle. The launch vehicle inserted JWST into a 30-day transfer trajectory to the Sun-Earth-Moon (SEM) Lagrange point L2 region. JWST executed three mid-course correction maneuvers (MCCs) to insert the spacecraft into a quasi-halo orbit about SEM L2; JWST will maintain its trajectory about L2 for at least 5.5 years, with a goal of at least 10.5 years. This paper summarizes the flight dynamics support for JWST, including the prelaunch nominal trajectory design, the launch window analysis, contingency planning for trajectory-related anomalies, mission operations support for the first 6 months, and a comparison of the planned and achieved actual JWST trajectory results. The orbit determination strategy, both planned and executed, will be summarized, and the method of addressing the anomalies as they occurred will be included.

Space Operations↗
NASA NTRSDate not supplied

Flight Dynamics Planning and Operations Support for the JWST Mission

The James Webb Space Telescope (JWST) was launched from Kourou Spaceport on December 25, 2021, at 12:20 UTC on an Ariane 5 launch vehicle. The launch vehicle inserted JWST into a 30-day transfer trajectory to the Sun-Earth-Moon (SEM) Lagrange point L2 region. JWST executed three mid-course correction maneuvers (MCCs) to insert the spacecraft into a quasi-halo orbit about SEM L2; JWST will maintain its trajectory about L2 for at least 5.5 years, with a goal of at least 10.5 years. This paper summarizes the flight dynamics support for JWST, including the prelaunch nominal trajectory design, the launch window analysis, contingency planning for trajectory-related anomalies, mission operations support for the first 6 months, and a comparison of the planned and achieved actual JWST trajectory results. The orbit determination strategy, both planned and executed, will be summarized, and the method of addressing the anomalies as they occurred will be included.

Karen Richon↗
NASA NTRS2014

Cryogenic Propellant Storage and Transfer Technology Demonstration: Advancing Technologies for Future Mission Architectures Beyond Low Earth Orbit

As part of U.S. National Space Policy, NASA is seeking an innovative path for human space exploration, which strengthens the capability to extend human and robotic presence throughout the solar system. NASA is laying the groundwork to enable humans to safely reach multiple potential destinations, including the Moon, asteroids, Lagrange points, and Mars and its environs. In support of this, NASA is embarking on the Technology Demonstration Mission Cryogenic Propellant Storage and Transfer (TDM CPST) Project to test and validate key cryogenic capabilities and technologies required for future exploration elements, opening up the architecture for large cryogenic propulsion stages and propellant depots. The TDM CPST will provide an on-orbit demonstration of the capability to store, transfer, and measure cryogenic propellants for a duration that enables long term human space exploration missions beyond low Earth orbit. This paper will present a summary of the cryogenic fluid management technology maturation effort, infusion of those technologies into flight hardware development, and a summary of the CPST preliminary design.

Chojnacki, Kent T.↗
NASA NTRS2020

Direct Exploration of the L2 Isolated Invariant Set Using Isolating Neighborhoods

Previous studies have used isolating blocks to explore the isolated invariant set around the L2 Lagrange point in the circular restricted three-body problem by computing trajectories on the asymptotic set and using them to track particular orbits. Once an initial map of the location of the orbits within the isolated invariant set projected into configuration space has been found, it is possible to further explore these orbits more directly by starting from appropriately chosen points within the mapped space. Here, we develop a method that uses these points to explore the periodic and quasiperiodic orbits within the isolated invariant set.

Lo, Martin W.↗
NASA NTRS1973

Mars gravity derived from the long-period motion of Mariner 9

The spherical harmonic coefficients in the Mars gravity field are determined using a two-stage filtering process. In the first stage, a weighted least-squares orbit determination processor is applied to Mariner 9 radio data to estimate the mean Kepler elements of each orbit. A finite difference method is then used to generate orbital element rates. In the second stage, the gravity coefficients are determined using another weighted least-squares processor which fits the long period Lagrange perturbation equations to the estimated rates. The resulting gravity potential and associated equipotential surface is presented and error sources discussed. Gravity field results are applied to various physical properties of Mars, such as moments of inertia.-

Ferrari, A. J.↗