Solar Gravitation Research Articles

Phase angle dependence of the dust cross section in a cometary coma

Context. Rosetta/OSIRIS took optical measurements of the intensity of scattered light from the coma of 67P/Churyumov-Gerasimenko over a wide range of phase angles. These data have been used to measure the phase angle dependent radiance profile of the dust coma. Aims. We want to provide information about the column area densities of the dust coma as seen from Rosetta. This information in combination with the measured OSIRIS phase function can then be used to determine the scattering phase function of the dust particles. Methods. We use a simple numerical model to calculate the dust density in the coma. For this we neglect all forces but solar gravitation and radiation pressure. As this cannot describe particles close to the surface of the comet, we assume starting conditions at a sufficient distance. We evaluate the column area density as observed from Rosetta/OSIRIS and compare the results for different spacecraft positions, dust sizes and surface activity distributions. Results. We find the phase angle dependence of the column area density to be largely independent of particle size and spacecraft positions. The determining factor is the activity distribution across the surface, especially the activity on the night side. For models with no night side activity, we find the column area density at high phase angles to be roughly two orders of magnitude larger than at low phase angles. Conclusions. The radiance profile measured from inside a cometary coma results from the combined effects of a phase angle dependent column area density and the scattering phase function. The radiance profile is therefore strongly dependent on the surface activity distribution, and - unless the dust emission is isotropic - any attempt to infer particle properties (as expressed through the scattering phase function) from such data must take into account and de-bias for this spatial variation of the dust column area density.

Existence and Control of Special Orbits around Asteroid 4 Vesta

This paper focuses on the existence and control of particular types of orbits around asteroid 4 Vesta, including Sun-synchronous orbits, orbits at the critical inclination, repeating ground-track orbits, and stationary orbits. J2, J3, and J4 terms are considered in the gravity model of Vesta. First, the inclination perturbation caused by solar gravitation is studied, and preset and multiple inclination bias methods are proposed to dampen the local time drift at the ascending node. Compared with Vesta, the control periods of the Sun-synchronous orbits of 21 Lutetia and 433 Eros are much longer. Second, Vesta’s orbits with a critical inclination depend on the semi-major axis and eccentricity. If the eccentricity is not greater than 0.2, inclination decreases slowly and monotonically concerning the semi-major axis. If the eccentricity is not smaller than 0.4, inclination increases rapidly and monotonically. Third, Sun-synchronous repeating ground-track circular orbits of Vesta, which do not exist for Lutetia and Eros, are investigated. Finally, the perturbations of stationary orbits caused by solar gravitation and solar radiation pressure are analyzed.

Dynamics and Control of Typical Orbits around Saturn

This paper investigates the dynamics of some typical orbits around Saturn, including sun-synchronous orbits, repeating ground track orbits, frozen orbits, and stationary orbits, and corresponding control methods mainly based on the mean element theory. The leading terms of Saturn’s aspheric gravitational field, J2 and J4 terms, are used when designing the orbits around Saturn. Two control methods of sun-synchronous orbits, including initial inclination-biased method and periodic inclination-biased method, are used to damp the local time drift at the descending node, which is caused by solar gravitation and atmospheric drag. The compensation of semimajor axis and maneuver period to maintain the recursive feature of repeating ground orbits are calculated. While only J2 and J3 terms are taken into account, we examine the argument that the perigee of frozen orbits around Saturn should be 270 deg to promise meaningful eccentricity. The perturbations of inclination and eccentricity of stationary orbits due to solar gravitation and solar radiation pressure are presented. Meanwhile, the preliminary control strategies of inclination perturbation and eccentricity perturbation are naturally introduced.

Solar wind energy flux observations in the inner heliosphere: first results from Parker Solar Probe

Aims.We investigate the solar wind energy flux in the inner heliosphere using 12-day observations around each perihelion of Encounter One (E01), Two (E02), Four (E04), and Five (E05) of Parker Solar Probe (PSP), respectively, with a minimum heliocentric distance of 27.8 solar radii (R⊙).Methods.Energy flux was calculated based on electron parameters (densityne, core electron temperatureTc, and suprathermal electron temperatureTh) obtained from the simplified analysis of the plasma quasi-thermal noise (QTN) spectrum measured by RFS/FIELDS and the bulk proton parameters (bulk speedVpand temperatureTp) measured by the Faraday Cup onboard PSP, SPC/SWEAP.Results.Combining observations from E01, E02, E04, and E05, the averaged energy flux value normalized to 1R⊙plus the energy necessary to overcome the solar gravitation (WR⊙) is about 70 ± 14 W m−2, which is similar to the average value (79 ± 18 W m−2) derived by Le Chat, G., Issautier, K., & Meyer-Vernet, N. (2012, Sol. Phys., 279, 197) from 24-yr observations by Helios, Ulysses, and Wind at various distances and heliolatitudes. It is remarkable that the distributions ofWR⊙are nearly symmetrical and well fitted by Gaussians, much more so than at 1 AU, which may imply that the small heliocentric distance limits the interactions with transient plasma structures.

Effects of Dispersion of the Dust Velocity in the LISM on the Interstellar Dust Distribution inside the Heliosphere

Interstellar dust (ISD) penetrates into the heliosphere due to the relative motion of the Sun and the local interstellar medium (LISM). Inside the heliosphere and at the boundaries, where solar wind interacts with the LISM, distribution of ISD is modified due to the action of the electromagnetic forces, the solar gravitation and the radiation pressure. These forces make the distribution of the ISD particles in the heliosphere inhomogeneous. In previous work we demonstrated the existence of singularities in the ISD density distribution at 0.03 - 10 a.u. north and south with respect to the heliospheric current sheet. In this paper we show that dispersion in the ISD velocity distribution strongly affects the singularities. Even small values of dispersion have the drastic impact on the density distribution and smooth the high density layers discovered previously.

Analysis of the IBEX-Lo interstellar hydrogen fluxes collected in 2009–2018 as a tool for sensing of the solar radiation pressure and the hydrogen ionization rate

ABSTRACT The Interstellar Boundary Explorer (IBEX) has been measuring interstellar hydrogen fluxes at 1 au since 2009. In this paper, we analysed all available data obtained with the IBEX-Lo instrument at energies 11–41 eV using our numerical kinetic model of the interstellar hydrogen distribution in the heliosphere. We performed a fitting of the data to find independently the model parameters: the ratio of the solar radiation pressure to the solar gravitation (μ0), ionization rate of hydrogen atoms at 1 au (β0), parameters of the secondary interstellar atoms at 70 au from the Sun, which provide the best agreement with the data by minimization of metric χ2. We also analysed temporal variations of the ratio of the fluxes measured in a fixed direction at energy bin 1 and energy bin 2. It is found that in 2009–2011 and 2017–2016 the ratio provided by the model is smaller than in the IBEX-Lo data, while in 2012–2015, oppositely, the model ratio is larger compared to the data. This might be caused by the incorrect separation of the measured fluxes between energy channels in the data, or by some additional physical factors that are omitted in the model. Understanding this issue may be important for the preparation of future Interstellar Mapping and Acceleration Probe mission. At this stage, we relied on the sum of the fluxes measured in energy bins 1 and 2 for comparison to model predictions.

Lagrangian fluid approach for the modeling of peculiarities of the interstellar dust distribution in the astrospheres/heliosphere

Abstract Interstellar dust penetrates into the heliosphere/astrosphere due to relative motion of the Sun and the local interstellar medium (LISM). Inside the heliosphere/astrosphere and at the heliospheric boundaries, where the solar/stellar wind interacts with LISM, distribution of the interstellar dust is modified due to an action of electromagnetic forces, the solar gravitation and radiation pressure. In this paper we show that the distribution of the interstellar dust particles in the heliosphere has peculiarities of high density layers. In order to understand the nature of the peculiarities Osiptsov’s Lagrangian method has been employed and developed for the case when the force acting on the particles has discontinuity as it is for the electromagnetic force at the helioshperic current sheet. In the result of the modeling we demonstrate existence of multiple layers of high density of the interstellar dust located at 0.03 - 10 AU north and south with respect to the heliospheric current sheet.

C/2010 U3 (Boattini): A Bizarre Comet Active at Record Heliocentric Distance

Abstract We present a photometric and dynamical study of comet C/2010 U3 (Boattini), which was seen active in prediscovery data as early as 2005 November at a new inbound record heliocentric distance of r H = 25.8 au. Two outburst events around 2009 and 2017 were observed. The coma and tail of the comet consist of dust grains of ∼10 μm in radius, ejected protractedly at speeds ≲50 m s−1 near the subsolar point, and are subjected to the Lorentz force, solar gravitation, and radiation pressure force all together. The prolonged activity indicates that sublimation of supervolatiles (e.g., CO, CO2) is at play, causing a net mass-loss rate ≳1 kg s−1. To sustain the mass loss, the nucleus radius has to be ≳0.1 km. The color of the cometary dust, similar to other long-period comets, is redder than the solar colors, but we also observed potential color variations when the comet was at 10 < r H < 15 au, concurrent with the onset of crystallization of amorphous water ice, if at all. Using publicly available and our refined astrometric measurements, we estimated the precise trajectory of the comet and propagated it backward to its previous perihelion. We found that the comet visited the planetary region 1.96 ± 0.04 Myr ago, with barycentric perihelion distance q = 8.364 ± 0.004 au. Thus, C/2010 U3 (Boattini) is almost certainly a dynamically old comet from the Oort cloud, and the observed activity cannot be caused by retained heat from the previous apparition.

Earth–Moon transfer with near-optimal lunar capture in the restricted four-body problem

In this paper, the low energy transfer (LET) from low Earth orbit to a permanent lunar orbit is investigated under the Sun–Earth–Moon-spacecraft restricted four-body problem (RFBP). Based on the near-optimal lunar capture, we propose an optimization method to construct the three-impulse Earth–Moon transfer in the RFBP. In the design process, a hybrid model is used to reduce the difficulty of the optimization problem. Compared with the Weak Stability Boundary transfer, the transfer orbit obtained has more chances to insert the spacecraft into low lunar orbit. Besides, compared with the patched-conic transfers, the LETs obtained can efficiently reduce the propellant costs, but the transfer durations apparently increase. Finally, the effect of solar gravitation on the transfer is analyzed.

Возмущения от Солнца при многовитковых перелетах на геостационарную орбиту космического аппарата с малой тягой

Возмущения от Солнца при многовитковых перелетах на геостационарную орбиту космического аппарата с малой тягой

INTERSTELLAR HYDROGEN FLUXES MEASURED BY IBEX -LO IN 2009: NUMERICAL MODELING AND COMPARISON WITH THE DATA

In this paper, we perform numerical modeling of the interstellar hydrogen fluxes measured by IBEX-Lo during orbit 23 (spring 2009) using a state-of-the-art kinetic model of the interstellar neutral hydrogen distribution in the heliosphere. This model takes into account the temporal and heliolatitudinal variations of the solar parameters as well as non-Maxwellian kinetic properties of the hydrogen distribution due to charge exchange in the heliospheric interface. We found that there is a qualitative difference between the IBEX-Lo data and the modeling results obtained with the three-dimensional, time-dependent model. Namely, the model predicts a larger count rate in energy bin~2 (20-41 eV) than in energy bin~1 (11-21 eV), while the data shows the opposite case. We perform study of the model parameter effects on the IBEX-Lo fluxes and the ratio of fluxes in two energy channels. We shown that the most important parameter, which has a major influence on the ratio of the fluxes in the two energy bins, is the solar radiation pressure. The parameter fitting procedure shows that the best agreement between the model result and the data occurs in the case when the ratio of the solar radiation pressure to the solar gravitation, $\mu_0$, is 1.26$^{+0.06}_{-0.076}$, and the total ionization rate of hydrogen at 1 AU is $\beta_{E,0}=3.7^{+0.39}_{-0.35}\times 10^{-7}$~s$^{-1}$. We have found that the value of $\mu_0$ is much larger than $\mu_0=0.89$, which is the value derived from the integrated solar Lyman-alpha flux data for the period of time studied. We discuss possible reasons for the differences.

Lyman-alpha Radiation Pressure in the Heliosphere: Results from a 3D Monte Carlo Radiative Transfer Simulation

Global models of the heliosphere and its interaction with the local interstellar medium have evolved to fit spacecraft observations since the beginning of their development. It is now understood that neutral hydrogen plays a very important role in the modification of the shape and location of the heliopause. Comparisons of simulations to observations have often led to the need for a more accurate treatment of a particular process. We bring attention to a long-held assumption that radiation pressure on neutral hydrogen atoms due to Lyman-alpha absorption and emission falls off with heliocentric distance at the same rate as solar gravitation. These have generally been combined into a single term. Through our Monte Carlo simulation of Lyman-alpha radiative transfer in the heliosphere, we show that the radiation pressure 1) falls off at a slower rate than r-2 and 2) is not isotropic. We find that the radiation pressure in the upwind direction falls off with heliocentric distance with a power of approximately -1.80 between ~6 and 75 AU, while the downwind direction falls of with a much slower rate and more variability over heliocentric distance. We discuss our methods and results as well as the implications below.

Spectral properties of backscattered solar Ly- α radiation in the heliosphere: A search for heliospheric boundary effects

We explore the imprints of the solar wind interaction with the local interstellar medium on spectral properties of backscattered solar Ly- α radiation. We employ a newly developed effective model for the interstellar H atom velocity distribution function in the heliosphere ( Katushkina and Izmodenov, 2011). The model takes into account both global effects of H atom perturbations at the heliospheric boundaries and local (i.e. within 10–20 AU from the Sun) effects of the solar ionization, charge exchange, solar gravitation and radiation pressure. Backscattered solar Ly- α profiles, intensities, line-shifts and line-widths were computed at 1 AU for the anti-solar lines-of-sight. Then the intensities, line-shifts and line-widths are compared with those calculated by using more simplified one-component and two-component hot models. The largest differences between the new model and hot models are seen in the line-width of the backscattered Ly- α profiles. The line-width is very sensitive to the kinetic properties of the H atom distribution function after passing the interaction region between the solar wind and the interstellar medium.

Analysis of high area-to-mass ratio (HAMR) GEO space object orbit determination and prediction performance: Initial strategies to recover and predict HAMR GEO trajectories with no a priori information

Optical deep space surveys are focusing on the study of a class of near Geosynchronous (GEO) objects characterized by high area-to-mass ratio (HAMR). Consistent cataloging and study of these HAMR objects requires repeated follow-up and tracking. The combination of lunar–solar gravitation, unmodeled solar radiation pressure dynamics, thermal emissions, and possibly passive electrostatic charging of the object interacting with the weak magnetic field at GEO results in unknown perturbations to the its trajectory. When these effects are combined with their apparent dim, time-varying reflective light intensity magnitudes, correctly identifying/associating tracks to the HAMR object is non-trivial. The focus of this work is to quantify the effects of the unmodeled accelerations on the reconstructed and predicted HAMR trajectory. Optical angle tracking data for several candidate HAMR objects were reduced and analyzed, and compared with results derived from the reduction of simulated optical angles data generated from the same sites, over comparable durations and using known dynamical models. Comparison of the orbit determination results provides insight into the effects of unmodeled errors on the estimated orbit parameters and their associated uncertainties. The results conclude that the orbit errors resulting from unmodeled rotational dynamics are significant, and can require the addition of process noise to properly account for the force model uncertainties to the total state error distribution. The results further demonstrate that the longer term solar radiation pressure effects are well determined with adequate observations, but determination of shorter term variations due to rotational dynamics are dependent on the area-to-mass ratio, measurement quality and estimation sampling interval.

Analytical solution of a satellite orbit disturbed by lunar and solar gravitation

In this paper, we derive to the second order (5 x 10- 6 ) the analytical solution of a satellite orbit disturbed by the lunar gravitational force. The force vector is first expanded to omit terms smaller than the third order (10 -9 ). Then, four terms of potential functions are derived from the expanded force vector and set into the Lagrangian equations of satellite motion to obtain the theoretical solutions. For the first term of the potential functions, the solutions are derived directly. For the second term, mathematical expansions and transformations are used to separate disturbances into three parts: short-periodic terms with triangular functions of M, long-periodic terms with triangular functions of (ω, i, Ω) and secular terms with non-periodic functions of (a, e). The integrations are then carried out with respect to M, (ω, i, Ω) and t, to obtain the analytical solutions of satellite orbits with a program using mathematical symbolic operation software. The third potential function differs from the second by a factor and the fourth is simpler than the second. Therefore, the solutions are derived similarly using slightly modified programs, respectively. The results show that only two Keplerian elements (ω, M) are linearly perturbed by lunar gravitation; that is, the lunar attracting force will cause a linear regression (delay) of the perigee (orientation of the ellipse) and a linear delay of the position (mean anomaly) on an Earth satellite. The Keplerian element a (semimajor axis of the ellipse) is not perturbed long periodically as the others. The derived solutions are also valid for solar and planetary gravitational disturbances. Because of the distance differences between the Moon, the Sun and the planets to the Earth or an Earth satellite, the solutions are of third and fourth orders for solar and planetary gravitational disturbances on an Earth satellite, respectively.

Pickup Ions and Cosmic Rays from Dust in the Heliosphere

The combination of recent observational and theoretical work has completed the catalog of the sources of heliospheric Pickup Ions (PUIs). These PUIs are the seed population for Anomalous Cosmic Rays (ACRs), which are accelerated to high energies at or beyond the Termination Shock (TS). For elements with high First Ionization Potentials (high-FIP atoms: e.g., H, He, Ne, etc.), the dominant source of PUIs and ACRs is from neutral atoms that drift into the heliosphere from the Local Interstellar Medium (LISM) and, prior to ionization, are influenced primarily by solar gravitation and radiation pressure (for H). After ionization, these interstellar ions are pickup up by the solar wind, swept out, and are either accelerated near the TS or beyond it. Elements with low first ionization potentials (low-FIP atoms: e.g., C, Si, Mg, Fe, etc.) are also observed as PUIs by Ulysses and as ACRs by Wind and Voyager. But the low-FIP composition of this additional component reveals a very different origin. Low-FIP interstellar atoms are predominantly ionized in the LISM and therefore excluded from the heliosphere by the solar wind. Remarkably, a low-FIP component of PUIs was hypothesized by Banks (J. Geophys. Res. 76, 4341, 1971) over twenty years prior to its direct detection by Ulysses/SWICS (Geiss et al., J. Geophys. Res. 100(23), 373, 1995) The leading concept for the generation of Inner Source PUIs involves an effective recycling of solar wind on grains near the Sun, as originally suggested by Banks. Voyager and Wind also observe low-FIP ACRs, and a grain-related source appears likely and necessary. Two concepts have been proposed to explain these low-FIP ACRs: the first concept involves the acceleration of the Inner Source of PUIs, and the second involves a so-called Outer Source of PUIs generated from solar wind interaction with the large population of grains in the Kuiper Belt. We review here the observational and theoretical work over the last decade that shows how solar wind and heliospheric grains interact to produce pickup ions, and, in turn, anomalous cosmic rays. The inner and outer sources of pickup ions and anomalous cosmic rays exemplify dusty plasma interactions that are fundamental throughout the cosmos for the production of energetic particles and the formation of stellar systems.

CN, C 2 radicals and dust in Comets Shoemaker–Levy 1991 T2 and P/deVico 1995 S1

The results of the multiaperture photometry of Comet Shoemaker–Levy 1991 T2 in the pre-perihelion and P/deVico in the post-perihelion period with the narrowband CN, C 2 and Blue Continuum (BC) IHW filters are presented. A Haser model of the molecular coma was used for the determination of the parent and daughter scale-lengths and production rates of the radicals. The comets showed some substantial differences between their parent scale-lengths. The CN parent scale-length (at 1.0 AU) was 16 × 10 3 km for Comet Shoemaker–Levy and 39 × 10 3 for P/deVico, the C 2 parent scale-lengths were respectively 29 × 10 3 and 54 × 10 3 km . Such divergences could be interpreted in the frame of different scenarios of emission of cometary parents, either from a nucleus or from a volume source. The daughter scale-lengths for these comets were quite similar, namely: 306 × 10 3 and 318 × 10 3 km for CN and 69 × 10 3 and 66 × 10 3 km for C 2. We determined the Afρ parameter for apertures of different radii. A Monte Carlo model of the dust coma was used to obtain the dust ejection velocity. It was of the order of 0.1 km s −1 for both comets. The power index of the distribution of the β-parameter of dust particles (ratio of light pressure to the solar gravitation) was of the order of 3 for C/Shoemaker–Levy and close to 2 for P/deVico. The dependence on heliocentric distance ( r h ) of the radical and dust production rates for P/deVico in the range of 0.7–1.0 AU was described by the power law function r h − α with a power index equal to: 5.55 ± 0.14 for CN, 5.70 ± 0.24 for C 2 and 5.22 ± 0.19 for dust. Relative abundances of the dynamically new Comet Shoemaker–Levy and short-period P/deVico were quite similar with an enhancement of C 2 comparing with standard values taken from A'Hearn et al. (1995).

Synchronization of seismoacoustic emission with deformation of the Earth’s upper crust

Long-term geoacoustic observations revealed an explicit synchronization in the Earth’s upper crust between the amplitude of acoustic noise at a frequency of 28‐35 Hz, which is related to seismoacoustic emission (SAE), and the calculated value (a squared rate of variation in the volume strain of the earth’s crust due to solar gravitation [1]). A joint study of these two processes, the observed SAE, and the calculated tidal deformation established that the average background seismic noise has a relatively high correlation coefficient (0.6‐0.8) with a solar component of tidal deformation (SD), but lacks stable correlation with the lunar component of tidal deformation (LD) or total deformation due to lunar‐solar tide (LSD). We found out previously that variation in SAE intensity within the mentioned frequency band at a depth of about 2000 m has good agreement (in terms of amplitude and phase) with the rate of variation in lunar‐solar disturbance of gravity [2]. As a result of a posteriori detailed analysis of data obtained in 1988 in a borehole at a depth of 390 m [3], the SAE intensity was found to have the best correlation with the sum of squared rates of variations in volume strain due to solar and lunar gravitation components (LD + SD), i.e., with the total power of the Earth’s tide. It is evident from the cited data that correlation coefficients of SAE intensity and calculated power of individual components of the tidal process in the Earth’s crust are rather significant for LD and SD components, but the correlation coefficient with the squared rate of deformation due to total lunar‐solar gravitation (LSD) yields negative values. This is evident from the following correlation coefficients between SAE and components, as follows:

Sun-perturbed earth-to-moon transfers with low energy and moderate flight time

We construct a spacecraft transfer with low cost and moderate flight time from the Earth to the Moon. The motion of the spacecraft is modeled by the planar circular restricted three-body problem including a perturbation due to the solar gravitation. Our approach is to reduce computation of optimal transfers to a non-linear boundary value problem. Using a computer software called AUTO, we solve it and continue its solutions numerically to obtain the optimal transfers. Our result also shows that the use of the solar gravitation can further lower the transfer cost drastically.

A study of the orbital evolution of near-earth asteroids

This paper describes some basic results obtained in our research on the orbital evolutioin of near Earth asteroids (NEAs) over the past several years. We emphasize the use of the reasonable dynamical model and an effective algorithm in the numerical work. The model includes all possible factors that affect the motion of NEAs, including the gravitation of all the larger bodies and the four larger main-belt asteroids, the effect of oblateness of the bodies and the post-Newtonian effect of the solar gravitation. By using the orbital elements of the Moon as the variables in the integration a single step size can be used. The times and distances of closest approach for NEAs that approach the Earth during the 21st century are calculated and are found to agree closely with the results published by the MPC.