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NASA NTRS2004

Dynamics of Earth orbiting formations

In this paper the equations of motion of a formation consisting of n spacecraft in Earth orbit are derived via Lagrange's equations. The equations of motion of the formation are developed with respect to both (1) a bound Keplerian reference orbit, and (2) a specific spacecraft in the formation. The major orbital perturbations acting on a formation in low Earth orbit are also included in the analysis. In contrast to the traditional approach based on the balance of linear momentum, the use of Lagrange's equations leads to a high-level matrix derivation of the formation equations of motion. The matrix form of the nonlinear motion equations is then linearized about a bound Keplerian reference orbit. Next, it is demonstrated that under the assumption of a circular reference orbit, the linearized equations of motion reduce to the well-known Hill-Clohessy-Wiltshire equations. The resulting linear and nonlinear dynamic equations lead to maximal physical insight into the structure of formation dynamics, and are ideally suited for use in the design and validation of formation guidance and control laws.

formation flying↗

NASA NTRS2015

ARTEMIS Lunar Orbit Insertion and Science Orbit Design Through 2013

As of late-July 2011, the ARTEMIS mission is transferring two spacecraft from Lissajous orbits around Earth-Moon Lagrange Point #1 into highly-eccentric lunar science orbits. This paper presents the trajectory design for the transfer from Lissajous orbit to lunar orbit insertion, the period reduction maneuvers, and the science orbits through 2013. The design accommodates large perturbations from Earth's gravity and restrictive spacecraft capabilities to enable opportunities for a range of heliophysics and planetary science measurements. The process used to design the highly-eccentric ARTEMIS science orbits is outlined. The approach may inform the design of future planetary moon missions.

lunar orbiters↗

NASA NTRS2013

Trajectory Design for MoonRise: A Proposed Lunar South Pole-Aitken Basin Sample Return Mission

This paper presents the mission design for the proposed MoonRise New Frontiers mission: a lunar far side lander and return vehicle, with an accompanying communication satellite. Both vehicles are launched together, but fly separate low-energy transfers to the Moon. The communication satellite enters lunar orbit immediately upon arrival at the Moon, whereas the lander enters a staging orbit about the lunar Lagrange points. The lander descends and touches down on the surface 17 days after the communication satellite enters orbit. The lander remains on the surface for nearly two weeks before lifting off and returning to Earth via a low-energy return.

NASA's New Frontie↗

NASA NTRS1979

Influence of a weak gravitational wave on a bound system of two point-masses

The problem of a weak gravitational wave impinging upon a nonrelativistic bound system of two point masses is considered. The geodesic equation for each mass is expanded in terms of two small parameters, v/c and dimensionless wave amplitude, in a manner similar to the post-Newtonian expansion; the geodesic equations are resolved into orbital and center-of-mass equations of motion. The effect of the wave on the orbit is determined by using Lagrange's planetary equations to calculate the time evolution of the orbital elements. The gauge properties of the solutions and, in particular, the gauge invariance of the secular effects are discussed.

Turner, M. S.↗

NASA NTRS2004

Radioisotope Electric Propulsion Missions Utilizing a Common Spacecraft Design

A study was conducted that shows how a single Radioisotope Electric Propulsion (REP) spacecraft design could be used for various missions throughout the solar system. This spacecraft design is based on a REP feasibility design from a study performed by NASA Glenn Research Center and the Johns Hopkins University Applied Physics Laboratory. The study also identifies technologies that need development to enable these missions. The mission baseline for the REP feasibility design study is a Trojan asteroid orbiter. This mission sends an REP spacecraft to Jupiter s leading Lagrange point where it would orbit and examine several Trojan asteroids. The spacecraft design from the REP feasibility study would also be applicable to missions to the Centaurs, and through some change of payload configuration, could accommodate a comet sample-return mission. Missions to small bodies throughout the outer solar system are also within reach of this spacecraft design. This set of missions, utilizing the common REP spacecraft design, is examined and required design modifications for specific missions are outlined.

Fiehler, Douglas↗

NASA NTRS2017

Low Thrust Cis-Lunar Transfers Using a 40 kW-Class Solar Electric Propulsion Spacecraft

This paper captures trajectory analysis of a representative low thrust, high power Solar Electric Propulsion (SEP) vehicle to move a mass around cis-lunar space in the range of 20 to 40 kW power to the Electric Propulsion (EP) system. These cis-lunar transfers depart from a selected Near Rectilinear Halo Orbit (NRHO) and target other cis-lunar orbits. The NRHO cannot be characterized in the classical two-body dynamics more familiar in the human spaceflight community, and the use of low thrust orbit transfers provides unique analysis challenges. Among the target orbit destinations documented in this paper are transfers between a Southern and Northern NRHO, transfers between the NRHO and a Distant Retrograde Orbit (DRO) and a transfer between the NRHO and two different Earth Moon Lagrange Point 2 (EML2) Halo orbits. Because many different NRHOs and EML2 halo orbits exist, simplifying assumptions rely on previous analysis of orbits that meet current abort and communication requirements for human mission planning. Investigation is done into the sensitivities of these low thrust transfers to EP system power. Additionally, the impact of the Thrust to Weight ratio of these low thrust SEP systems and the ability to transit between these unique orbits are investigated.

cislunar↗

NASA NTRS2017

Geotechnical Tests on Asteroid Simulant Orgueil

In the last 100 years, the global population has more than quadrupled to over seven billion people. At the same time, the demand for food and standard of living has been increasing which has amplified the global water use by nearly eight times from approximately 500 to 4000 cu km per yr from 1900 to 2010. With the increasing concern to sustain the growing population on Earth it is necessary to seek other approaches to ensure that our planet will have resources for generations to come. In recent years, the advancement of space travel and technology has allowed the idea of mining asteroids with resources closer to becoming a reality. During the duration of the internship at NASA Kennedy Space Center, several geotechnical tests were conducted on BP-1 lunar simulant and asteroid simulant Orgueil. The tests that were conducted on BP-1 was to practice utilizing the equipment that will be used on the asteroid simulant and the data from those tests will be omitted from report. Understanding the soil mechanics of asteroid simulant Orgueil will help provide basis for future technological advances and prepare scientists for the conditions they may encounter when mining asteroids becomes reality in the distant future. Distinct tests were conducted to determine grain size distribution, unconsolidated density, and maximum density. Once the basic properties are known, the asteroid simulant will be altered to different levels of compaction using a vibrator table to see how compaction affects the density. After different intervals of vibration compaction, a miniature vane shear test will be conducted. Laboratory vane shear testing is a reliable tool to investigate strength anisotropy in the vertical and horizontal directions of a very soft to stiff saturated fine-grained clayey soil. This test will provide us with a rapid determination of the shear strength on the undisturbed compacted regolith. The results of these tests will shed light on how much torque is necessary to drill through the surface of an asteroid. Most of the known asteroids are believed to be left over material during the formation of the solar system that never accreted to form planets. Asteroids can be found in several groups such as Trojan Asteroids, Near Earth Asteroids (NEAs) and the main asteroid belt. The Trojan Asteroids orbit the 4th and 5th Lagrange points of major planets in the Solar System while the NEA's have orbits that are close to and sometimes intersect with Earths orbit and the Main Asteroid Belt which is found between the orbit of Mars and Jupiter. Gravitational perturbations can alter the orbit of asteroids in the Main Asteroid Belt causing them to move closer to earth causing them to become in the NEA class.

resources↗

NASA NTRS1994

FRESIP: A Discovery Mission Concept To Find Earth-Sized Planets Around Solar Like Stars

The current nebular theory postulates that planets are. a consequence of the formation of stars from viscous accretion disks. Condensation from the accretion disk favors the formation of small rocky planets in the hot inner region, and the formation of gas giants in the cool outer region. Consequently, terrestrial-type planet in inner orbits should be commonplace. From geometrical considerations , Borucki and Summers have shown that 1% of planetary systems resembling our solar system should show transits for Earth-sized (or larger) planets. Thus a photometric satellite that uses a wide field of view telescope and a large detector array to simultaneously monitor 5000 target stars should detect 50 planetary systems. To differentiate regularly recurring transits from statistical fluctuations of the stellar flux, one must observe over several orbital periods so that the false positive rate can be reduced to one event or less. A one-meter aperture telescope placed in a halo orbit about either the L1 or L2 Lagrange points and viewing perpendicular to both the orbital and ecliptic planes can view continuously for the required period because neither the Sun, Earth, or Moon would enter the field of view. Model calculations show that the observations should provide statistically significant estimates of the distributions of planetary size, orbital radius, coplanarity, and the frequency of planetary systems that have Earth-sized planets in inner orbits. Because approximately one half of the star systems observed will be binary systems, the frequency of planetary systems orbiting either one or both of the stars can also be determined.

Borucki, William↗

NASA NTRSDate not supplied

Launching and Deploying the James Webb Space Telescope

On December 25, 2021, at 12:20 UTC, the James Webb Space Telescope lifted off and onward to its destination in orbit at the second Lagrange point. With more than two decades in development, and an international collaboration between NASA, CSA, and ESA, Webb is one of the most anticipated science missions ever launched. After a dramatic and flawless launch, Webb's toughest and riskiest days lie ahead. Unprecedented in its complexity and ambition, over the next two weeks Webb would undergo the most complex on-orbit deployment sequence ever attempted, with any single deployment anomaly carrying the risk of full mission failure. An exquisite design, years of ground testing, a exhaustively trained and rehearsed operations and engineering team, and an unprecedented level of contingency planning, all resulted in a fully and successfully deployed Webb observatory, on its way to L2, and nominally cooling to its cryogenic temperatures. Although Webb still had many more months of commissioning left, there was a collective sigh of relief heard round the world. This incredible achievement was not by chance but was years in the making. We go behind the scenes of Webb's first month on orbit, starting with the unique and challenging launch itself, the time criticality of its mid-course corrections, and a summary of nearly 14 days to undergo nearly 50 major deployments. We discuss what went better than planned and how years of robust and detailed contingency planning were prepared for unanticipated events and on-orbit spacecraft behavior. And finally, we provide a brief overview of the entire commissioning process which successfully completed on July 10th, 2022.

Keith A Parrish↗

NASA NTRS2011

NASA Technology Area 07: Human Exploration Destination Systems Roadmap

This paper gives an overview of the National Aeronautics and Space Administration (NASA) Office of Chief Technologist (OCT) led Space Technology Roadmap definition efforts. This paper will given an executive summary of the technology area 07 (TA07) Human Exploration Destination Systems (HEDS). These are draft roadmaps being reviewed and updated by the National Research Council. Deep-space human exploration missions will require many game changing technologies to enable safe missions, become more independent, and enable intelligent autonomous operations and take advantage of the local resources to become self-sufficient thereby meeting the goal of sustained human presence in space. Taking advantage of in-situ resources enhances and enables revolutionary robotic and human missions beyond the traditional mission architectures and launch vehicle capabilities. Mobility systems will include in-space flying, surface roving, and Extra-vehicular Activity/Extravehicular Robotics (EVA/EVR) mobility. These push missions will take advantage of sustainability and supportability technologies that will allow mission independence to conduct human mission operations either on or near the Earth, in deep space, in the vicinity of Mars, or on the Martian surface while opening up commercialization opportunities in low Earth orbit (LEO) for research, industrial development, academia, and entertainment space industries. The Human Exploration Destination Systems (HEDS) Technology Area (TA) 7 Team has been chartered by the Office of the Chief Technologist (OCT) to strategically roadmap technology investments that will enable sustained human exploration and support NASA s missions and goals for at least the next 25 years. HEDS technologies will enable a sustained human presence for exploring destinations such as remote sites on Earth and beyond including, but not limited to, LaGrange points, low Earth orbit (LEO), high Earth orbit (HEO), geosynchronous orbit (GEO), the Moon, near-Earth objects (NEOs), which > 95% are asteroidal bodies, Phobos, Deimos, Mars, and beyond. The HEDS technology roadmap will strategically guide NASA and other U.S. Government agency technology investments that will result in capabilities enabling human exploration missions to diverse destinations generating high returns on investments.

Kennedy, Kriss J.↗

NASA NTRS2020

Orbit Selection for the Proposed Lynx Observatory Mission

The Advanced Concepts Office design team performed several analyses and trades in support of orbit selection for the proposed Lynx mission, an x-ray observatory being submitted to the Astro2020 Decadal Survey. Though the descriptions in this Technical Memorandum (TM) focus on the Lynx mission, the approach and process for selecting the final orbit is applicable to a variety of proposed science and exploration missions. To select the best orbit for the Lynx science, mission designers assembled a team of subsystem and discipline experts, in addition to mission analysts, to evaluate several candidate orbits. These discipline experts included members of the science and instrument team, power and avionics, thermal, propulsion, and environments. The goal was to clearly show the benefits and weaknesses of each orbit in the trade space and provide sound justification for the final selection. Discipline experts conducted trades and evaluated the results using a variety of methods including engineering judgement, rough estimates, and detailed calculations, and rolled the results into a final grade using a weighted grading method. The orbit options could then be ranked. The principal investigator (PI) for the mission, along with the science team, was given the task of final orbit selection. The result of the trades indicated that a halo orbit about the second Sun-Earth Lagrange point (SE-L2), similar to the planned orbit for the James Webb Space Telescope (JWST), was the best choice for the Lynx mission. Details of how the team arrived at this selection are below.

Hopkins, R. C.↗

NASA NTRS1985

Development and application of a unified balancing approach with multiple constraints

The development of a general analytic approach to constrained balancing that is consistent with past influence coefficient methods is described. The approach uses Lagrange multipliers to impose orbit and/or weight constraints; these constraints are combined with the least squares minimization process to provide a set of coupled equations that result in a single solution form for determining correction weights. Proper selection of constraints results in the capability to: (1) balance higher speeds without disturbing previously balanced modes, thru the use of modal trial weight sets; (2) balance off-critical speeds; and (3) balance decoupled modes by use of a single balance plane. If no constraints are imposed, this solution form reduces to the general weighted least squares influence coefficient method. A test facility used to examine the use of the general constrained balancing procedure and application of modal trial weight ratios is also described.

Zorzi, E. S.↗

NASA NTRS1988

Interplanetary magnetic field orientations associated with bidirectional electron heat fluxes detected at ISEE 3

A statistical survey of interplanetary magnetic field orientations associated with bidirectional electron heat fluxes observed at ISEE 3 in orbit about the Sunward Lagrange point indicates that magnetic connection of the spacecraft to the earth's shock was frequently the source of the bidirectionality. When the interplanetary magnetic field was oriented within 5 deg of the earth-spacecraft line, backstreaming electrons from the bow shock were clearly observed approximately 18 percent of the time, and connections apparently occurred for angles as large as about 30-35 deg.

Stansberry, J. A.↗

NASA NTRS1991

Geomagnetic activity associated with earth passage of interplanetary shock disturbances and coronal mass ejections

Coronal mass ejection events (CMEs) are important occasional sources of plasma and magnetic field in the solar wind at 1 AU, accounting for approximately 10 percent of all solar wind measurements in the ecliptic plane during the last solar activity maximum. Using a recently appreciated capability for distinguishing CMEs in solar wind data in the form of counterstreaming solar wind electron events, this paper explores the overall effectiveness of shock wave disturbances and CMFs in general in stimulating geomagnetic activity. The study is confined to the interval from mid-August 1978 through mid-October 1982, spanning the last solar activity maximum, when ISEE 3 was in orbit about the L1 Lagrange point 220 Re upstream from earth. It is found that all but one of the 37 largest geomagnetic storms in that era were associated with earth passage of CMEs and/or shock disturbances, with the large majority of these storms (27 out of 37) being associated with interplanetary events where earth encountered both a shock and the CME driving the shock (shock/CME events). Although CMEs and/or shock disturbances were increasingly the cause of geomagnetic activity as the level of geomagnetic activity increased, many smaller geomagnetic disturbances were unrelated to these events.

Gosling, J. T.↗

NASA NTRS1992

Power transmission by laser beam from lunar-synchronous satellites to a lunar rover

This study addresses the possibility of beaming laser power from synchronous lunar orbits (L1 and L2 LaGrange points) to a manned long-range lunar rover. The rover and two versions of a satellite system (one powered by a nuclear reactor; the other by photovoltaics) are described in terms of their masses, geometry, power needs, mission and technological capabilities. Laser beam power is generated by a laser diode array in the satellite and converted to 30 kW of electrical power at the rover. Present technological capabilities, with some extrapolation to near future capabilities, are used in the descriptions. The advantages of the two satellite/rover systems over other such systems and over rovers with on-board power are discussed along with the possibility of enabling other missions.

Williams, M. D.↗

NASA NTRS1998

Using Sequential Earth Images to Determine the Orientation of a Satellite at L1

This paper introduces a method for determining the three-axis attitude (orientation) of a spacecraft from a sequence of Earth images taken while in orbit about the stationary Lagrange point between the Earth and the sun (LI). Two axes of information can be obtained simply by monitoring the Earth's position within the field-of-view of the camera. The third axis is obtained by correlating sequential Earth images in such a way as to detect the flow of the features within the Earth's disk over time. When taken correctly, this measurement is perpendicular to the Earth's spin axis and, consequently, locates the Earth's spin axis within the images. This is equivalent to determining the orientation of the spacecraft about the instrument's boresight. Actual data from the Galileo spacecraft is used to test the algorithms outlined in this paper.

Houghton, Martin B.↗

NASA NTRS2003

The James Webb Telescope Instrument Suite Layout: Optical System Engineering Considerations for a Large, Deployable Space Telescope

The James Webb Space Telescope (JWST) is a space-based, infrared observatory designed to study the early stages of galaxy formation in the Universe. The telescope will be launched into an elliptical orbit about the second Lagrange point and passively cooled to 30-50 K to enable astronomical observations from 0.6 to 28 microns. A group from the NASA Goddard Space Flight Center and the Northrop Grumman Space Technology prime contractor team has developed an optical and mechanical layout for the science instruments within the JWST field of view that satisfies the telescope s high-level performance requirements. Four instruments required accommodation within the telescope's field of view: a Near-Infrared Camera (NIRCam) provided by the University of Arizona; a Near-Mared Spectrometer (NIRSpec) provided by the European Space Agency; a Mid-Infrared Instrument (MIRI) provided by the Jet Propulsion Laboratory and a European consortium; and a Fine Guidance Sensor (FGS) with a tunable filter module provided by the Canadian Space Agency. The size and position of each instrument's field of view allocation were developed through an iterative, concurrent engineering process involving the key observatory stakeholders. While some of the system design considerations were those typically encountered during the development of an infrared observatory, others were unique to the deployable and controllable nature of JWST. This paper describes the optical and mechanical issues considered during the field of view layout development, as well as the supporting modeling and analysis activities.

Bos, Brent↗

NASA NTRS2019

DSCOVR-EPIC MAIAC AOD - A Proxy for Understanding Aerosol Diurnal Patterns from Space

The Deep Space Climate Observatory (DSCOVR) spacecraft was launched on 11 February 2015 and in June 2015 achieved its orbit at the first Lagrange point (L1), 1.5 million km from Earth toward the sun. The Earth Polychromatic Imaging Camera (EPIC) onboard DSCOVR views the entire sunlit Earth from sunrise to sunset, every 1-2 hours, at scattering angles between 168.5° and 175.5° with 10 narrowband filters in the range of 317-779 nm. NASA Multiangle Implementation of Atmospheric Correction (MAIAC) algorithm, originally developed for MODIS, has been applied to EPIC data with an Aerosol Optical Depth (AOD) product at 440nm with a 10km spatial resolution. This high temporal resolution product is a unique dataset for investigating diurnal patterns in aerosols from space. Our work analyzed the capability of the satellite-borne data to capture the aerosol diurnal variation by associating it with AERONET AOD at 440nm data over the contiguous US. We validated the DSCOVR MAIAC AOD data over 100 AERONET stations during 2015-2018, and examined the contribution of the surface reflectance and relevant acquisition angles, derived by the MAIAC algorithm, to the predicted error. We used over 180,000 hourly DSCOVR-EPIC MAIAC AOD observations with collocated with AERONET AOD observations averaged over +-30 minutes from the satellite overpass time. The AERONET and DSCOVR AOD temporal patterns show that the diurnal variation is different across US AERONET sites, with higher diurnal variation in the DSCOVR dataset in general.

Sorek-Hamer, Meytar↗