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Trajectories of ballistic impact ejecta on a rotating Earth

On an airless, slowly rotating planetary body like the Moon, ejecta particles from an impact follow simple ballistic trajectories. If gaseous interactions in the fireball are ignored, ejecta particles follow elliptical orbits with the center of the planetary body at one focus until they encounter the surface at the point of reimpact. The partial elliptical orbit of the ejecta particle lies in a plane in inertial (galactic) coordinates. Because of the slow rotation rate (for example, 360 degrees/28 days for the Moon), the intersection of the orbital plane and the surface remains nearly a great circle during the flight time of the ejecta. For this reason, lunar rays, representing concentrations of ejecta with the same azimuth but different velocities and/or ejecta angles, lie essentially along great circles. Ejecta from airless but more rapidly rotating bodies will follow more complicated, curving trajectories when plotted in the coordinate frame of the rotating planet or viewed as rays on the planetary surface. The curvature of trajectories of ejecta particles can be treated as a manifestation of the Coriolis effect, with the particles being accelerated by Coriolis pseudoforces. However, it is more straightforward to calculate the elliptical orbit in inertial space and then determine how far the planet rotates beneath the orbiting ejecta particle before reimpact. The Earth's eastward rotation affects ballistic ejecta in two ways: (1) the eastward velocity component increases the velocity of eastbound ejecta and reduces the velocity of westbound ejecta; and (2) the Earth turns underneath inflight ejecta, so that although the latitude of reimpact is not changed, the longitude is displaced westward, with the displacement increasing as a function of the time the ejecta remains aloft.

Alvarez, W.

Understanding Neutron Stars using Thermonuclear X-ray Bursts

Studies of thermonuclear X-ray bursts can be very useful to constrain the spin rate, mass and radius of a neutron star = EOS model of high density cold matter in the neutron star cores. Extensive observation and analysis of the data from the rising portions of the bursts = modeling of burst oscillations and thermonuclear flame spreading. Theoretical study of thermonuclear flame spreading on the rapidly spinning neutron stars should be done considering all the main physical effects (including magnetic field, nuclear energy generation, Coriolis effect, strong gravity, etc.).

Bhattacharyya, S.

Neutron Stars and Thermonuclear X-ray Bursts

Studies of thermonuclear X-ray bursts can be very useful to constrain the spin rate, mass and radius of a neutron star approaching EOS model of high density cold matter in the neutron star cores. +k Extensive observation and analysis of the data from the rising portions of the bursts - modeling of burst oscillations and thermonuclear flame spreading. +k Theoretical study of thermonuclear flame spreading on the rapidly spinning neutron stars should be done considering all the main physical effects (including magnetic field, nuclear energy generation, Coriolis effect, strong gravity, etc.).

Bhattacharyya, Sudip

Climates of Warm Earth-like Planets. II. Rotational "Goldilocks" Zones for Fractional Habitability and Silicate Weathering

Planetary rotation rate has a significant effect on atmospheric circulation, where the strength of the Coriolis effect in part determines the efficiency of latitudinal heat transport, altering cloud distributions, surface temperatures, and precipitation patterns. In this study, we use the ROCKE-3D dynamic ocean general circulation model to study the effects of slow rotations and increased insolations on the "fractional habitability" and silicate weathering rate of an Earth-like world. Defining the fractional habitability f(sub h) to be the percentage of a planet's surface that falls in the 0 ≤ T ≤ 100 °C temperature regime, we find a moderate increase in f(sub h) with a 10% and 20% increase in insolation and a possible maximum in f(sub h) at sidereal day lengths between 8 and 32 times that of the modern Earth. By tracking precipitation and runoff, we further determine that there is a rotational regime centered on a 4 day period in which the silicate weathering rate is maximized and is particularly strongly peaked at higher overall insolations. Because of weathering's integral role in the long-term carbonate–silicate cycle, we suggest that climate stability may be strongly affected by the anticipated rotational evolution of temperate terrestrial-type worlds and should be considered a major factor in their study. In light of our results, we argue that planetary rotation period is an important factor to consider when determining the habitability of terrestrial worlds.

Atmospheric effects

Climates of Warm Earth-like Planets. II. Rotational "Goldilocks" Zones for Fractional Habitability and Silicate Weathering

Planetary rotation rate has a significant effect on atmospheric circulation, where the strength of the Coriolis effect in part determines the efficiency of latitudinal heat transport, altering cloud distributions, surface temperatures, and precipitation patterns. In this study, we use the ROCKE-3D dynamic ocean general circulation model to study the effects of slow rotations and increased insolations on the "fractional habitability" and silicate weathering rate of an Earth-like world. Defining the fractional habitability f (h) to be the percentage of a planet's surface that falls in the 0 ≤ T ≤ 100 °C temperature regime, we find a moderate increase in f (h) with a 10% and 20% increase in insolation and a possible maximum in f (h) at sidereal day lengths between 8 and 32 times that of the modern Earth. By tracking precipitation and runoff, we further determine that there is a rotational regime centered on a 4 day period in which the silicate weathering rate is maximized and is particularly strongly peaked at higher overall insolations. Because of weathering's integral role in the long-term carbonate–silicate cycle, we suggest that climate stability may be strongly affected by the anticipated rotational evolution of temperate terrestrial-type worlds and should be considered a major factor in their study. In light of our results, we argue that planetary rotation period is an important factor to consider when determining the habitability of terrestrial worlds.

atmospheric effects

Forces and Motion: Dynamics of the Tethered Satellite

In this 'Lift off to Learning' series, Loren Shriver, commander of STS 46, and the other members of the mission (Claude Nicollier, Marsha Ivins, Andrew Allen, Jeffrey Hoffman, Franklin Chiang-Diaz, and Franco Maerba) use computer graphics, and physical experiments to explain how the tethered satellite to be deployed during their mission will be raised, how it works, the influence of the Shuttle on the satellite and the satellite's influence on the Shuttle's orbit, the gravitational effects, and other effects concerning the Theoretical Physics used to plan this mission (gravity gradient force, center of mass, angular momentum, centrifugal force, and coriolis effect). This video ends with a discussion of the technology transfer and utilization of this tethered satellite concept and design.

Source record

Simulation-Based Analysis and Prediction of Thrust Vector Servoelastic Coupling

A method of analysis and prediction of servoelastic coupling in launch vehicles is presented, surveying the discovery and subsequent resolution of a predicted servoelastic resonance phenomenon affecting the NASA Space Launch System launch vehicle at specific flight conditions. A physics-based linearized multibody mechanization of the governing equations is combined with first principles analysis to demonstrate that antisymmetric bending of the solid rocket motors leads to a reduction of equivalent viscous modal damping through coupling with the thrust vector control actuators. The sensitivity to parameters and the effects of the resonance phenomenon on flight control performance and stability are confirmed through extensive simulation verification in the time and frequency domain. A novel enhancement in model fidelity that accounts for Coriolis effects of fluid flow on bending within the solid rocket motor case and nozzle is shown to add sufficient damping to reduce the risk of adverse control-structure interaction.

Jeb S Orr

The Puzzling Structure of Solar Convection: Window into the Dynamo

The operation of the solar dynamo, with all of its remarkable spatio-temporal ordering, remains an outstanding problem of modern solar physics. A number of mechanisms that might plausibly contribute to its operation have been proposed, but the relative role played by each remains unclear. This uncertainty stems from continuing questions concerning the speed and structure of deep-seated convective flows. Those flows are in-turn thought to sustain both the Sun’s turbulent EMF and the large-scale flows of differential rotation and meridional circulation suspected of influencing the dynamo’s organization and timing. Ultimately, the convective and large-scale flow structure derive from the Coriolis force. When the Coriolis effect is weak (rapid convective flow), convection exhibits little organization in its spatial structure, and the meridional flow is expected to assume a single-celled profile within each hemisphere. Convection subject to strong Coriolis forces instead organizes into compact, spiraling columnar structures and sustains meridional flows that possess multiple cells in latitude and radius. The implications for the dynamo in these two regimes are substantial, impacting the flux-transport properties of any assumed meridional flow and the convectively-driven EMF. Continued progress in this area is complicated by (i) inconsistencies between helioseismic measurements of convective and meridional flow made with different techniques and instruments, and (ii) a lack of high-latitude data for convection, differential rotation, and meridional flow. We suggest that the path forward to resolving these difficulties is twofold. First, the acquisition of long-term helioseismic and emissivity measurements obtained from a polar vantage point is vital to complete our picture of the Sun’s outer convection zone. Second, sustained and expanded investment in theory-oriented and combined theory/observational research initiatives will be crucial to fully exploit these new observations and to resolve inconsistencies between existing measurements.

SMD

Sea breezes and advective effects in southwest James Bay

Observations from a transect extending 100 km inland during the Northern Wetlands Study (NOWES) in 1990 show that the sea breeze develops on approximately 25% of days during summer and may penetrate up to 100 km inland on occasions. The sea breeze exhibits a marked diurnal clockwise rotation as a result of the Coriolis effect along the unobstructed coastline. The marine advective effect is shown to depend on gradient wind direction. With northwesterly upper level flow the sea breeze tends to be northeasterly in direction and is associated with decreased temperatures and vapor pressure deficits (VPD). With southwesterly upper level flow the sea breeze tends to have a southeasterly direction and less effect on temperatures and VPD. This is attributed to shorter residence times of air parcels over water. For two cases, Colorado State University mesoscale model simulations show good agreement with surface wind observations and suggest that under northwesterly gradient flow, Bowen ratios are increased in the onshore flow along western James Bay, while during southwesterly gradient flow these effects are negligible. These results have implications for the interpretation of local climate, ecology, and hydrology as well as land-based and airborne turbulent flux measurements made during NOWES.

Mckendry, Ian

Integration of Libration Point Orbit Dynamics into a Universal 3-D Autonomous Formation Flying Algorithm

The autonomous formation flying control algorithm developed by the Goddard Space Flight Center (GSFC) for the New Millennium Program (NMP) Earth Observing-1 (EO-1) mission is investigated for applicability to libration point orbit formations. In the EO-1 formation-flying algorithm, control is accomplished via linearization about a reference transfer orbit with a state transition matrix (STM) computed from state inputs. The effect of libration point orbit dynamics on this algorithm architecture is explored via computation of STMs using the flight proven code, a monodromy matrix developed from a N-body model of a libration orbit, and a standard STM developed from the gravitational and coriolis effects as measured at the libration point. A comparison of formation flying Delta-Vs calculated from these methods is made to a standard linear quadratic regulator (LQR) method. The universal 3-D approach is optimal in the sense that it can be accommodated as an open-loop or closed-loop control using only state information.

Folta, David

Adaptation in a rotating artificial gravity environment

The centripetal force generated by a rotating space vehicle is a potential source of artificial gravity. Minimizing the cost of such a vehicle dictates using the smallest radius and highest rotation rate possible, but head movements made at high rotation rates generate disorienting, nauseogenic cross-coupled semicircular canal stimulation. Early studies suggested 3 or 4 rpm as the highest rate at which humans could adapt to this vestibular stimulus. These studies neglected the concomitant Coriolis force actions on the head/neck system. We assessed non-vestibular Coriolis effects by measuring arm and leg movements made in the center of a rotating room turning at 10 rpm and found that movement endpoints and trajectories are initially deviated; however, subjects readily adapt with 10-20 additional movements, even without seeing their errors. Equilibrium point theories of motor control errantly predict that Coriolis forces will not cause movement endpoint errors so that subjects will not have to adapt their reaching movements during rotation. Adaptation of movement trajectory acquired during Coriolis force perturbations of one arm transfers to the unexposed arm but there is no intermanual transfer of endpoint adaptation indicating that neuromotor representations of movement endpoint and trajectory are separable and can adapt independently, also contradictory to equilibrium point theories. Touching a surface at the end of reaching movements is required for complete endpoint adaptation in darkness but trajectory adapts completely with or without terminal contact. We have also made the first kinematic measurements of unconstrained head movements during rotation, these movements show rapid adaptation to Coriolis force perturbations. Our results point to methods for achieving full compensation for rotation up to 10 rpm. Copyright 1998 Published by Elsevier Science B.V.

Non-NASA Center