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NASA NTRS1979

Long period perturbations of earth satellite orbits

All the equations involved in extending the PS phi solution to include the long periodic and second order secular effects of the zonal harmonics are presented. Topics covered include DSphi elements and relations for their conconical transformation into the PS phi elements; the solution algorithm based on the Von Zeipel method; and the elimination of long periodic terms and analytical integration of primed variables. The equations were entered into the ASOP program, checked out, and verified. Comparisons with numerical integrations show the long period theory to be accurate within several meters after 800 revolutions.

Wang, K. C.↗

NASA NTRS1974

Dynamic techniques for studies of secular variations in position from ranging to satellites

Evaluation of numerous laser range data obtained in orbit determination experiments and by analysis of orbit perturbations due to solid-earth and ocean tides. Results obtained from both a single-laser tracking system and two-laser systems are discussed. With the introduction of radar altimeters, satellite-to-satellite tracking techniques, and more accurate laser data in greater quantities, significant improvements in the gravity field, GM, and station coordinates can be projected such that 10-cm precision relative positioning should be a realizable objective from a single four-pass orbital arc. The use of simultaneous range measurements to a satellite from two stations several hundred km apart is being used to measure the motion between points 900 km apart on opposite sides of the San Andreas fault. Computer simulation of this experiment shows that it will permit determination of the change in baseline (plate motion) to better than 0.5 cm/yr over a seven-year period.

Smith, D. E.↗

NASA NTRS2010

Numerical Mean Element Orbital Analysis with Morbiter

The Morbiter software numerically averages an osculating orbit s equations of motion (EOM) to arrive at the mean orbit s EOMs, which are then numerically propagated to obtain the long-term orbital ephemerides. The long-term evolution characteristics, and stability, of an orbit are best characterized using a mean element propagation of the perturbed, two-body variational equations of motion. The average process eliminates short period terms, leaving only secular and long period effects. Doing this avoids the Fourier series expansions and truncations required by the traditional analytic methods.

Ely, Todd A.↗

NASA NTRS1972

Orbit Perturbations Due to Solar Radiation Pressure

This disturbing force will be important for satellites with a large area to mass ratio and also for those whose orbits are high enough that atmospheric drag is not the more dominate force. The procedure for the analysis is to represent the radiation force as the gradient of a scalar function to be compatible with existing procedures for studying perturbations due to earth's oblateness. From this analysis, solar radiation pressure appears not to be responsible for any secular or long-periodic variations in the semi-major axis of the orbit nor does it provide any secular changes in the eccentricity of the orbit or the angle of inclination of the osculating plane. Solar radiation pressure does produce secular effects in the other orbital elements, but these are in the opposite sense of secularities caused by the gravitational attraction of the sun and tend to reduce the total secularity.

Sawyer, G. A.↗

NASA NTRS1992

A self-consistent field method for galactic dynamics

The present study describes an algorithm for evolving collisionless stellar systems in order to investigate the evolution of systems with density profiles like the R exp 1/4 law, using only a few terms in the expansions. A good fit is obtained for a truncated isothermal distribution, which renders the method appropriate for galaxies with flat rotation curves. Calculations employing N of about 10 exp 6-7 are straightforward on existing supercomputers, making possible simulations having significantly smoother fields than with direct methods such as tree-codes. Orbits are found in a given static or time-dependent gravitational field; the potential, phi(r, t) is revised from the resultant density, rho(r, t). Possible scientific uses of this technique are discussed, including tidal perturbations of dwarf galaxies, the adiabatic growth of central masses in spheroidal galaxies, instabilities in realistic galaxy models, and secular processes in galactic evolution.

Hernquist, Lars↗

DOE OSTI2020

On the Orbital Elements of the Two-body Problem with Slowly Decreasing Mass: The Gyldén–Mestchersky Cases

We study the dynamics of two-body problems with gravitational parameters μ = μ(t) decreasing with the time. In particular we focus our attention on the behavior of the orbital elements in the first two Gyldén–Mestchersky cases: in the first case (GM-I) μ(t)=μ{sub 0}(1+αt){sup −1}, where μ{sub 0} is the constant initial value of the parameter and α a small positive constant. In the second case (GM-II) μ(t)=μ{sub 0}(1+2αt){sup −1/2}. In the GM-I problem, using a suitable transformation of the radius vector and the physical time, which reduces the original problem to a pure Kepler problem, we are able to obtain explicit analytical expressions of the orbital elements that hold true for all t⩾0 and therefore derive their asymptotic behavior. Moreover using the alternative scaled time these expressions show clearly their periodic and secular terms. For the GM-II problem a similar transformation to the GM-I problem leads to a perturbed Kepler problem with a radial direction perturbation. Although exact solutions in terms of elliptic functions may be obtained, the use of some integrals leads to analytical expressions of orbital elements that allow us to study their behavior. Finally, some comparisons between the time evolution of elements in both problems are also included.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1988

Where do the Apollo objects come from?

The orbital evolutions of 1-45 km-diameter Apollo and Amor bodies generated by asteroid belt collisions interior to 2.6 AU are presently traced by Monte Carlo calculations. About 3 percent of the asteroidal fragments of this type and size that are ejected with velocities of 100 m/sec are perturbed into earth-crossing orbits by the 3:1 Jovian commensurability resonance at 2.5 AU, as well as a secular resonance in the innermost asteroid belt. While the initial earth-crossing orbits of these bodies are concentrated near 1 AU, their steady-state orbital distribution is widely dispersed. Additional objects that may be characterized as inactive comets are inferred from strongly suggestive data.

Wetherill, G. W.↗

NASA NTRS2001

Jet Stability and the Generation of Superluminal and Stationary Components

We present a numerical simulation of the response of an expanding relativistic jet to the ejection of a superluminal component. The simulation has been performed with a relativistic time-dependent hydrodynamical code from which simulated radio maps are computed by integrating the transfer equations for synchrotron radiation. The interaction of the superluminal component with the underlying jet results in the formation of multiple conical shocks behind the main perturbation. These trailing components can be easily distinguished because they appear to be released from the primary superluminal component instead of being ejected from the core. Their oblique nature should also result in distinct polarization properties. Those appearing closer to the core show small apparent motions and a very slow secular decrease in brightness and could be identified as stationary components. Those appearing farther downstream are weaker and can reach superluminal apparent motions. The existence of these trailing components indicates that not all observed components necessarily represent major perturbations at the jet inlet; rather, multiple emission components can be generated by a single disturbance in the jet. While the superluminal component associated with the primary perturbation exhibits a rather stable pattern speed, trailing components have velocities that increase with distance from the core but move at less than the jet speed. The trailing components exhibit motion and structure consistent with the triggering of pinch modes by the superluminal component. The increase in velocity of the trailing components is an indirect consequence of the acceleration of the expanding fluid, which is assumed to be relativistically hot; if observed, such accelerations would therefore favor an electron-positron (as opposed to proton rest mass) dominated jet.

Agudo, Ivan↗

NASA NTRS1990

Obliquity histories of Earth and Mars: Influence of inertial and dissipative core-mantle coupling

For both the Earth and Mars, secular variations in the angular separation of the spin axis from the orbit normal are suspected of driving major climatic changes. There is considerable interest in determining the amplitude and timing of these obliquity variations. If the orientation of the orbital plane were inertially fixed, and the planet were to act as a rigid body in it response to precessional torques, the spin axis would simply precess around the orbit at a fixed obliquity and at a uniform angular rate. The precession rate parameter depends on the principal moments of inertia and rotation rate of the perturbed body, and on the gravitational masses and semiminor axes of the perturbing bodies. For Mars, the precession rate is not well known, but probably lies in the interval 8 to 10 arcsec/year. Gravitational interactions between the planets lead to secular motions of the orbit planes. In the rigid body case, the spin axis still attempts to precess about the instantaneous orbit normal, but now the obliquity varies. The hydrostatic figure of a planet represents a compromise between gravitation, which attempts to attain spherical symmetry, and rotation, which prefers cylindrical symmetry. Due to their higher mean densities the cores of the Earth and Mars will be more nearly spherical than the outer layers of these planets. On short time scales it is appropriate to consider the core to be an inviscid fluid constrained to move with the ellipsoidal region bounded by the rigid mantle. The inertial coupling provided by this mechanism is effective whenever the ellipticicy of the container exceeds the ratio of precessional to rotational rates. If the mantle were actually rigid, this would be an extremely effective type of coupling. However, on sufficiently long time scales, the mantle will deform viscously and can accommodate the motions of the core fluid. A fundamentally different type of coupling is provided by electromagnetic or viscous torques. This type of coupling is likely to be most important on longer time scales. In each case, the mantle exerts an equal and opposite torque on the core.

Bills, Bruce G.↗

NASA NTRS1974

Effect of resonance-oblateness coupling on a satellite orbit

Second order effects of the coupling between geopotential resonance and oblateness on a satellite orbit are calculated. Results show that: (1) these effects arise from the interaction of resonance with the secular changes of the orbit's node, perigee, and mean anomaly; (2) they have the same period and phase as first order resonance perturbations; and (3) their amplitudes are proportional to the square of the period and dominate the first order effects as the orbit becomes commensurate. A striking example of this coupling is seen in the 18 day resonance variation of the node of the orbit of the first earth resources technology satellite. Analysis of this one arc second (31m) variation yielded a strong 14th order constraint to the geopotential for odd degree terms. This constraint is poorly predicted by current models.

Wagner, C. A.↗

NASA NTRS1975

Effect of resonance-oblateness coupling on a satellite orbit

Second-order effects of the coupling between geopotential resonance and oblateness on a satellite orbit are calculated. These effects arise from the interaction of resonance with the secular changes of the orbit's node, perigee, and mean anomaly. They have the same period and phase as first-order resonance perturbations. But their amplitudes are proportional to the square of the period and dominate the first-order effects as the orbit becomes commensurate. A striking example of this coupling is seen in the 18-day resonance variation of the node of the orbit of the first earth resources technology satellite. Analysis of this 1 arc sec (31 m) variation yields a strong fourteenth-order constraint to the geopotential field for odd degree terms. This constraint (lumped coefficient) is poorly predicted by most current models.

Wagner, C. A.↗

DOE OSTI2022

Stellar populations with MEGARA: The inner regions of NGC 7025

This paper aims to determine the capabilities of the MEGARA spectrograph at the Gran Telescopio Canarias (GTC), which is an optical integral-field unit, for studying stellar populations. We also aim to exploit its combination of high spectral (R ~ 6000, 12 000 and 20 000) and spatial (0.62") resolution within its 12".5 × 11".3 field of view. We do this by analysing the commissioning data of the nearby S0a galaxy NGC 7025. We establish a systematic method through which we can determine the properties of the stellar populations in the observations made with MEGARA, more specifically, within the MEGADES legacy project. For this paper in particular, we determine the properties of the stellar populations of NGC 7025. We used MEGARA observations of galaxy NGC 7025 that were taken during the commissioning phase of the instrument. We applied different approaches to estimate the properties of the stellar populations with the highest possible certainty. In addition to the specific study of NGC 7025 and in the context of the MEGADES survey, we have carried out a number of tests to determine the expected errors (including potential biases) in these star formation history (SFH) derivations as a function of these parameters, namely spectral setup, signal-to-noise ratio, σ, and the SFH itself. All the studies we conduct (both full spectral fitting and absorption line indices) of the stellar populations of NGC 7025 indicate that the stars that form its bulge have supersolar metallicity and considerably old ages (~10 Gyr) in general. Using three different combinations of MEGARA spectral setups, we determined that the bulge of NGC 7025 has smild negative mass-weighted age gradient. For the more detailed SFH, our results indicate that in addition to a rather constant star formation at early epochs, a peak in the formation history of the stars in the bulge is also found 3.5–4.5 Gyr ago. This partly explains the mass-weighted age gradients we measured. The scenario presented in NGC 7025 is that of an isolated galaxy under secular evolution that about 3.5–4.5 Gyr ago likely experienced a minor merger (mass ratio 1/10) that induced an increase in star formation and also perturbed the morphology of its outer disc. In addition to these specific results for NGC 7025, we report different lessons learned for the ongoing exploitation of the MEGADES survey with the GTC, such as the need to obtain combined observations in the LR-B + LR-V setups and a signal-to-noise ratio of at least 20 per Å.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1984

Orbital stability in combined uniform axial and three-dimensional wiggler magnetic fields for free-electron lasers

Zachary Phys. Rev. A 29 (6), 3224 (1984) recently analyzed the instability of relativistic-electron helical trajectories in combined uniform axial and helical wiggler magnetic fields when the radial variation of the wiggler field is taken into account. It is shown here that the type 2 instability comprised of secular terms growing linearly in time, identified by Zachary and earlier by Diament Phys. Rev. A 23 (5), 2537 (1981), is an artifact of simple perturbation theory. A multiple-time-scale perturbation analysis reveals a nonsecular evolution on a slower time scale which accommodates an arbitrary initial perturbation. It is shown that, in the absence of exponential instability, the electron seeks a modified helical orbit more appropriate to its perturbed state and oscillates stably about it. Thus, the perturbed motion is oscillatory but nonsecular, and hence the helical orbits are stable.

Johnston, S.↗

NASA NTRS1986

The possibility of estimating tidal perturbations of Jupiter's Galilean satellites

Recent measurements in the IR of the energy emitted by Io suggest that if the observed emission is due to tidal dissipation in Io, then one should observe a very large secular acceleration of Io in its orbit. The purpose of this paper is to investigate the observational evidence which might be examined to verify that hypothesis. The authors have assembled the largest collection of eclipse observations extant and investigated the possibility of observing secular drifts in the period of Io. Preliminary results suggest that large tidal accelerations of Jupiter's satellites do not exist at the suggested magnitude and hence the heat flux measurements probably represent an episodic occurrence.

Lieske, Jay H.↗

NASA NTRS1977

Effects of solar radiation pressure on the orbit of the Solar Power Satellite

The surface area-to-weight ratio of the Solar Power Satellite (SPS) is of the order of sq m/kg. Therefore, solar radiation pressure will be an important perturbation on the orbit, causing large variations in eccentricity. An analytical solution is developed for the motion of eccentricity and the line of apsides. Included is a secular term due to the earth's orbital eccentricity. Several initial conditions are considered. For some cases, the eccentricity is nearly constant over a few years. General characteristics of the motion are discussed. Long-term (30 years) effects of gravity are investigated by using a numerical integration method. Eccentricities of approximately 0.08 can be expected for uncorrected SPS orbits.

Graf, O. F., Jr.↗

NASA NTRS2001

Integrated Orbit, Attitude, and Structural Control Systems Design for Space Solar Power Satellites

The major objective of this study is to develop an integrated orbit, attitude, and structural control systems architecture for very large Space Solar Power Satellites (SSPS) in geosynchronous orbit. This study focuses on the 1.2-GW Abacus SSPS concept characterized by a 3.2 x 3.2 km solar-array platform, a 500-m diameter microwave beam transmitting antenna, and a 500 x 700 m earth-tracking reflector. For this baseline Abacus SSPS configuration, we derive and analyze a complete set of mathematical models, including external disturbances such as solar radiation pressure, microwave radiation, gravity-gradient torque, and other orbit perturbation effects. The proposed control systems architecture utilizes a minimum of 500 1-N electric thrusters to counter, simultaneously, the cyclic pitch gravity-gradient torque, the secular roll torque caused by an offset of the center-of-mass and center-of-pressure, the cyclic roll/yaw microwave radiation torque, and the solar radiation pressure force whose average value is about 60 N.

Wie, Bong↗

NASA NTRS2004

Long Period Variations in Tidal and Librational Forcing of Europa

The gravitational field of Jupiter exerts a profound influence on the energy balance, thermal evolution, and stress regime of Europa. It widely appreciated that dissipation associated with the spheroidal tidal deformation is a major source of heat. Another possibly important source of dissipation is the toroidal deformation field associated with forced librations. Both tidal and librational deformations depend on the distance and direction Jupiter, as seen from Europa. These quantities vary with time as a result of the finite values of orbital eccentricity and spin pole obliquity, though the obliquity effects have been ignored in most previous studies. Variations in eccentricity and obliquity of the Galilean satellites occur on a very wide range of time scales, as angular momentum is exchanged among the orbital and rotational components of the coupled system. The orbital periods are only a few days in length, and the secular changes in orbital period associated with tidal and librational dissipation have characteristic time scales of 10-9 years or longer. On intermediate time scales, the satellites perturb each other, and the Sun and Saturn make additional contributions. The present values of satellite orbital inclinations and obliquities are not particularly representative their respective longer term variations. As a result, the tidal stress and dissipation regimes at present may not provide adequate explanation of the sources of surface features seen on the satellites.

Bills, Bruce G.↗

NASA NTRS2001

Integrated Orbit, Attitude, and Structural Control System Design for Space Solar Power Satellites

The major objective of this study is to develop an integrated orbit, attitude, and structural control system architecture for very large Space Solar Power Satellites (SSPS) in geosynchronous orbit. This study focuses on the 1.2-GW Abacus SSPS concept characterized by a 3.2 x 3.2 km solar-array platform, a 500-m diameter microwave beam transmitting antenna, and a 500 700 m earth-tracking reflector. For this baseline Abacus SSPS configuration, we derive and analyze a complete set of mathematical models, including external disturbances such as solar radiation pressure, microwave radiation, gravity-gradient torque, and other orbit perturbation effects. The proposed control system architecture utilizes a minimum of 500 1-N electric thrusters to counter, simultaneously, the cyclic pitch gravity-gradient torque, the secular roll torque caused by an o.set of the center-of-mass and center-of-pressure, the cyclic roll/yaw microwave radiation torque, and the solar radiation pressure force whose average value is about 60 N.

Wie, Bong↗