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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.

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NASA NTRS2004

Unstable Resonant Orbits near Earth and Their Applications in Planetary Missions

This paper explores the uses of planar, simple-periodic symmetrical families of orbits in mission designs in the Earth-Moon system. This classification is defined as the planar periodic orbits that pierce the x-axis in the rotating frame exactly twice per orbit where each piercing is orthogonal to the x-axis. A continuation method has been used to explore several families of this class of orbit in the Earth-Moon restricted three-body system. The invariant manifolds of the unstable orbits in each of these families are then produced and several mission designs are discussed that take advantage of these manifolds. Focus is given to mission designs that implement resonant orbits that periodically fly by the moon.

invariant manifolds↗
NASA NTRS1987

Orbital resonances, unusual configurations and exotic rotation states among planetary satellites

Several examples of satellite dynamics are presented where significant progress has been made in understanding a complex problem, where a long-standing problem has finally been solved, where newly discovered configurations have motivated novel descriptions or where an entirely new phenomenon has been revealed. The origin of orbital resonances in satellites and the solution of the problem of the origin and evolution of the three body Laplace resonance among the Galilean satellites are among the topics discussed.

Peale, S. J.↗
NASA NTRS1984

Orbital resonances among Saturn's satellites

When orbital properties constituted most of our knowledge of Saturn's satellites, resonances provided important clues to physical properties and history. With the discoveries of the 1980s, including close-up direct observations of physical and geological properties, resonances are more important than ever. This chapter reviews the kinetics of the various classes of resonances represented among the classical and newly discovered satellites and describes how resonances have played a fundamental role in shaping the Saturn system as it is seen today.

Greenberg, R.↗
NASA NTRS2021

Computation and Analysis of Jupiter-Europa and Jupiter-Ganymede Resonant Orbits in the Planar Concentric Circular Restricted 4-body Problem

Many unstable periodic orbits of the planar circular restricted 3-body problem (PCRTBP) persist as invariant tori when a periodic forcing is added to the equa- tions of motion. In this study, we compute tori corresponding to exterior Jupiter- Europa and interior Jupiter-Ganymede PCRTBP resonant periodic orbits in a con- centric circular restricted 4-body problem (CCR4BP). Motivated by the 2:1 Laplace resonance between Europa and Ganymede’s orbits, we then attempt the continu- ation of a Jupiter-Europa 3:4 resonant orbit from the CCR4BP into the Jupiter- Ganymede PCRTBP. We strongly believe that the resulting dynamical object is a KAM torus lying near but not on the 3:2 Jupiter-Ganymede resonance.

Gunter, Brian↗
NASA NTRS1991

Charged dust dynamics - Orbital resonance due to planetary shadows

The dynamics of a weakly charged dust grain orbiting in the equatorial plane of a planet surrounded by a rigidly corotating magnetospehre is examined. It is shown that an introduction of an effectilve 1D potential causes a perturbation due to electrostatic forces, which induces a motion of the pericenter, similar to the effect of the planetary oblateness. A case is examined where the charge varies periodically due to the modulation of the photoelectron current occurring as the grain enters and leaves the planetary shadow, causing the electromagnetic perturbation to resonate with the orbital period and to modify the size and eccentricity of the orbit. This effect is demonstrated both numerically and analytically for small grains comprising the Jovian ring, showing that their resulting changes are periodic, and their amplitude is much larger than that of the periodic changes due to light-pressure perturbation or the secular changes due to resonant charge variations that develop over a comparable time span.

Horanyi, M.↗
NASA NTRS1976

Dynamical study of the Hilda asteroids. I - Resonant orbital motion of the PLS objects from the Palomar-Leiden Survey

Schubart's (1968) model of a planar elliptic restricted three-body problem is used to study the orbital motion of the Hilda asteroids from the Palomar-Leiden Survey. The 3:2 resonant coupling to Jupiter of some of these small asteroids is found to be stable. However, some of the small asteroids with absolute magnitude greater than 15 have large amplitude of variation in their orbital elements in one libration period. Since the lifetime scales against catastrophic collision of the Hilda asteroids are estimated to be several times larger than those of the main-belt objects, a significant portion of these resonant asteroids could be the original members of the Hilda group. From this point of view, it is suggested that such 'size dependence' of resonant orbital motions might be the result of cosmogonic effects of jet-stream accretion.

Ip, W.-H.↗
NASA NTRS1984

Stability of the Galilean Satellites in Deep Orbital Resonance

The Galilean satellites are locked in the Laplace resonance, which is responsible for forcing their significant orbital eccentricites. The eccentricites in turn result in tidal energy dissipation within the satellites that is responsible for the great thermal activity on Io, including both volcanism observed by Voyager and heat flux measured from Earth. The resonance results from the nearly 2:1 commensurability of orbital periods (or equivalently of mean motions) taken by pairs. These geometrical relations enhance the mutual gravitational effects. Yoder pointed out that tides raised on Io tend to drive the system out of resonance (toward greater nu and correspondingly smaller eccentricities) while tides raised on Jupiter tend to drive the system towards deeper resonance (smaller nu and larger forced eccentricities). The possible behavior of the system in deep resonance is investigated.

Richard Greenburg↗
NASA NTRS2022

Adiabatic Evolution Due to the Conservative Scalar Self-force During Orbital Resonances

We calculate the scalar self-force experienced by a scalar point-charge orbiting a Kerr black holealongrθ-resonant geodesics. We use the self-force to calculate the averaged rate of change of thecharge’s orbital energy⟨ ̇E⟩, angular momentum⟨ ̇Lz⟩, and Carter constant⟨ ̇Q⟩, which togethercapture the leading-order adiabatic, secular evolution of the point-charge. Away from resonances,only the dissipative (time antisymmetric) components of the self-force contribute to⟨ ̇E⟩,⟨ ̇Lz⟩, and⟨ ̇Q⟩. We demonstrate, using a new numerical code, that duringrθresonances conservative (timesymmetric) scalar perturbations also contribute to⟨ ̇Q⟩and, thus, help drive the adiabatic evolutionof the orbit. Furthermore, we observe that the relative impact of these conservative contributionsto⟨ ̇Q⟩is particularly strong for eccentric 2:3 resonances. These results provide the first conclusivenumerical evidence that conservative scalar perturbations of Kerr spacetime are nonintegrable duringrθresonances.

Zachary Nasipak↗
NASA NTRS1985

Orbital Resonances and Planetary Accretion in the Solar Nebula

Planetesimal orbital evolution in a resisting medium near an accreting protoplanet was studied to explore mechanisms for capture into Trojan and satellite orbits. Various mechanisms for capture into libration were proposed, e.g., increase in Jupiter/Sun mass ratio, change in Jovian orbital radius, and collisions of asteroids with interplanetary dust. Studies include effects of solar nebula gas drag on orbital evolution. In general, the gas deviates from Keplerian motion, causing secular decay of planetesimal orbits, as well as damping eccentricity. The motion of bodies near Jupiter under the effect of a resisting medium was numerically explored. The equations of motion were integrated using the formalism of the planar restricted three body problem, modified to include effects by gas drag and a growing Jupiter.

Weidenschilling, S. J.↗
NASA NTRS1985

Orbital resonances in the solar nebula - Implications for planetary accretion

The influence of gas drag and gravitational perturbations by a planetary embryo on the orbit of a planetesimal in the solar nebula was examined. Non-Keplerian rotation of the gas causes secular decay of the orbit. If the planetesimal's orbit is exterior to the perturber's, resonant perturbations oppose this drag and can cause it to be trapped in a stable orbit at a commensurability of order j/(j + 1), where j is an integer. Numerical and analytical demonstrations show that resonant trapping occurs for wide ranges of perturbing mass, planetesimal size, and j. Induced eccentricities are large, causing overlap of orbits for bodies in different resonances with j greater than 2. Collisions between planetesimals in different resonances, or between resonant and nonresonant bodies, result in their disruption. Fragments smaller than a critical size can pass through resonances under the influence of drag and be accreted by the embryo. This effect speeds accretion and tends to prevent dynamical isolation of planetary embryos, making gas-rich scenarios for planetary formation more plausible.

Weidenschilling, S. J.↗
NASA NTRS1975

Gravitational Harmonics from Shallow Resonant Orbits

Five gravitational constraints were derived for the GEOS 2 orbit (order 13, to 30th degree) whose principal resonant period is 6 days. The constraints explain the sinusoidal variation with argument of perigee of a lumped harmonic found from 41 6-day arcs of optical and laser data. The condition equations, derived from elementary perturbation theory are shown to account for almost all of the resonant information in the tracking data.

Wagner, C. A.↗
NASA NTRS1975

The resonant orbit of the Lost City meteorite

An integration of the long-period perturbations of Jupiter and Saturn on the orbit of the Lost City meteorite shows that the average nodal rate of the meteorite was nearly the same as the nodal rates of Jupiter and Saturn. This near equality of rates led to a large resonant variation in the inclination of the meteorite's orbit with a period on the order of 1 million years. The resonance makes the orbital evolution too sensitive to the deficiencies of the perturbation calculations and to the values of the elements at impact to allow definitive calculations. It is shown that an orbit similar to the meteorite's orbit can spend approximately 88% of its time with an eccentricity too small to allow for intersections with the earth's orbit. The ordinary cosmic ray exposure age of the Lost City meteorite does not suggest that its collisional lifetime was unusual, but the role of resonances in determining the lifetime of typical meteorites is unknown.

Williams, J. G.↗
NASA NTRS1993

Orbital resonances and Poynting-Robertson drag

The phenomenon of resonance trapping with Poynting-Robertson drag in the simplest case - the circular restricted three-body problem - is elucidated. Attention is given to what determines whether a grain of a given size passes through a given resonance or is trapped there, to how and why a trapped particle's orbit evolves with time, and to why Poynting-Robertson drag resonances are only temporary, while gas-drag resonances appear to be stable. The possibility of trapping a grain into resonance with a planet depends on the combination of the following parameters: the ratio of radiation pressure force to solar gravity, the mass of the perturbing planet normalized to the solar mass, an integer, and eccentricity. In general, the peak eccentricity and sometimes the threshold value are large enough so that crossing orbits and close approaches to the planet can inhibit capture and aid escape from resonance.

Weidenschilling, S. J.↗
NASA NTRS1993

Cross-tail current - Resonant orbits

A technique to generate self-consistent 1D current sheets is described. Groups of monoenergetic protons were followed in a modified Harris magnetic field. This sample current sheet is characterized by resonant quasi-adiabatic orbits. The magnetic moment of a quasi-adiabatic ion which is injected from outside a current sheet changes substantially during the orbit but returns to almost its initial value by the time the ion leaves. Several ion and electron groups were combined to produce a plasma sheet in which the charged particles carry the currents needed to generate the magnetic field in which the orbits were traced. An electric field also is required to maintain charge neutrality. Three distinct orbit types, one involving untrapped ions and two composed of trapped ions, were identified. Limitations associated with the use of a 1D model also were investigated; it can provide a good physical picture of an important component of the cross-tail current, but cannot adequately describe any region of the magnetotail in which the principal current sheet is separated from the plasma sheet boundary layer by a nearly isotropic outer position of the central plasma sheet.

Kaufmann, Richard L.↗
NASA NTRS1975

Adiabatic invariants and phase equilibria for first-order orbital resonances

In the planar circular restricted three-body problem, the evolution of near-commensurable orbits is studied under change in the mass ratio, mu. The evolution involves preservation of two adiabatic invariants. Transition from circulation to libration may occur; such transitions are of two types. Type I transition occurs when the evolutionary track in phase space passes through near-zero eccentricity; as in the ordinary case (no transition), pre- and post-evolutionary states are linked by solution of a two-point boundary-value problem. Type II transition occurs when the evolutionary track encounters an unstable phase equilibrium or periodic orbit. There is then a discontinuous change in one adiabatic invariant, and pre- and post-evolutionary states are linked by solution of a three-point boundary-value problem. No evolutionary track can encounter a stable phase equilibrium, but the class of all stable phase equilibria is mapped into itself under mu change.

Heppenheimer, T. A.↗
NASA NTRS1975

Thirteenth-order orbital resonance on a Diademe 2 fragment

A strong thirteenth-order resonance has been observed in an analysis which is based on U.S. Navy tracking data regarding the slowly decaying orbit of a Diademe 2 fragment. The exact commensurability for the orbit occurred in late 1973. The major changes due to the resonance were over by late 1974. Approaches for a significant improvement of thirteenth-order geopotential terms are discussed.

Wagner, C. A.↗