Russian lunar ephemeris EPM-ERA 2012

The paper describes the lunar ephemeris EPM-ERA 2012. It is a part of the Ephemerides of Planets and the Moon (EPM) developed at the Institute of Applied Astronomy (IAA) of the Russian Academy of Sciences (RAS). In order to construct EPM-ERA 2012, 17580 lunar laser ranging (LLR) observations for 1970–2012 have been processed including 21 observations from the Lunokhod 1 reflector found by the Lunar Reconnaissance Orbiter (LRO) at the end of 2010. EPM-ERA 2012 is compared with American ephemerides DE403, DE405, DE421 ephemeris, and the French ephemeris INPOP10. The possibility of the use of the ephemeris EPM-ERA 2012 to address contemporary problems of ephemeris astronomy is considered.     

Harmonic development of tide-generating potential of terrestrial planets

The aim of this study is to obtain high-accurate harmonic developments of the tide-generating potential (TGP) of Mercury, Venus and Mars. The planets’ TGP values have been first calculated on the base of DE/LE-406 numerical planetary/lunar ephemerides over a long period of time and then processed by a new spectral analysis method. According to this method the development is directly made to Poisson series where both amplitudes and arguments of the series’ terms are high-degree polynomials of time. A new harmonic development of Mars TGP is made over the time period 1900 AD–2100 AD and includes 767 second-order Poisson series’ terms of minimum amplitude equal to 10⁻⁷ m² s⁻². Analogous series composing both Mercury and Venus TGP harmonic models are built over the time period 1000 AD–3000 AD and include 1,061 and 693 terms, respectively. A modification of the standard HW95 format for representation of the terrestrial planets’ TGP is proposed. The number of terms in the planets’ TGP models transformed to the modified HW95 format is 650 for Mercury, 422 for Venus, and 480 for Mars. The quality of the new developments of the terrestrial planets’ TGP is better than that of the similar developments obtained earlier.

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Mass determinations for 27 asteroids by the dynamic method

The masses of 27 asteroids are found from optical and radar observations of perturbed asteroids (test particles). The masses of 18 objects have been previously determined by other authors in the construction of ephemerides EPM2011, DE423, and INPOP10a. Their values are based on observations of the delay time of radio signals from spacecraft. Our values have smaller errors for most of the asteroids. Comparing our results with the latest determinations based only on optical observations of asteroids also shows their accuracy.     

Impact trajectories of the asteroid Apophis in the 21st century

The asteroid Apophis is one of the most hazardous near-Earth asteroids. As a result of the scattering of Apophis?? potential trajectories after its close approach in 2029, and its possible approach in 2036, there are many dangerous trajectories including impact trajectories after 2036. The purpose of this study is to identify and investigate these trajectories. We use the Everhart integrator; the DE405, DE423, and EPM2008 ephemerides; and two sets of initial data for Apophis (those collected by NASA in 2006 and by the IAA in 2010). More than 50 possible encounters in this century are presented, including 13 encounters between 2036 and 2050. The minimum geocentric distances obtained using a different ephemeris and initial conditions differ little between themselves. Analogous results in (Yeomans et al., 2009) are consistent with our results.     

High-Precision Ephemerides of Planets—EPM and Determination of Some Astronomical Constants

The latest version of the planetary part of the numerical ephemerides EPM (Ephemerides of Planets and the Moon) developed at the Institute of Applied Astronomy of the Russian Academy of Sciences is presented. The ephemerides of planets and the Moon were constructed by numerical integration in the post-Newtonian metric over a 140-year interval (from 1880 to 2020). The dynamical model of EPM2004 ephemerides includes the mutual perturbations from major planets and the Moon computed in terms of General Relativity with allowance for effects due to lunar physical libration, perturbations from 301 big asteroids, and dynamic perturbations due to the solar oblateness and the massive asteroid ring with uniform mass distribution in the plane of the ecliptic. The EPM2004 ephemerides resulted from a least-squares adjustment to more than 317000 position observations (1913–2003) of various types, including radiometric measurements of planets and spacecraft, CCD astrometric observations of the outer planets and their satellites, and meridian and photographic observations. The high-precision ephemerides constructed made it possible to determine, from modern radiometric measurements, a wide range of astrometric constants, including the astronomical unit AU = (149597870.6960 ± 0.0001) km, parameters of the rotation of Mars, the masses of the biggest asteroids, the solar quadrupole moment J ₂ = (1.9 ± 0.3) × 10⁻⁷, and the parameters of the PPN formalism β and γ. Also given is a brief summary of the available state-of-the-art ephemerides with the same precision: various versions of EPM and DE ephemerides from the Jet Propulsion Laboratory (JPL) (USA) and the recent versions of these ephemerides—EPM2004 and DE410—are compared. EPM2004 ephemerides are available via FTP at ftp://qua-sar.ipa.nw.ru/incoming/EPM2004.__________Translated from Astronomicheskii Vestnik, Vol. 39, No. 3, 2005, pp. 202–213.Original Russian Text Copyright © 2005 by Pitjeva.     

Detecting the errors in solar system ephemeris by pulsar timing

Pulsar timing uses planetary ephemerides to convert the measured pulse arrival time at an observatory to the arrival time at the Solar System barycenter(SSB). Since these planetary ephemerides cannot be perfect, a method of detecting the associated errors based on a pulsar timing array is developed. By using observations made by an array of 18 millisecond pulsars from the Parkes Pulsar Timing Array, we estimated the vector uncertainty from the Earth to the SSB of JPL DE421, which reflects the offset of the ephemeris origin with respect to the ideal SSB, in different piecewise intervals of pulsar timing data, and found consistent results. To investigate the stability and reliability of our method, we divided all the pulsars into two groups. Both groups yield largely consistent results, and the uncertainty of the Earth-SSB vector is several hundred meters, which is consistent with the accuracy of JPL DE421. As an improvement in the observational accuracy, pulsar timing will be helpful to improve the solar system ephemeris in the future.     

Enhancing the Accuracy of Numerical Integration of the Equations of Asteroid Motion with Perturbations from Major Planets and the Moon from the DE Ephemerides

The discontinuous behavior of coordinates of planets and the Moon and their derivatives, which are determined from their modern ephemerides, at the boundaries of adjacent interpolation intervals is illustrated using the example of the DE436 ephemerides. The numerical integration of the equations of motion of two asteroids demonstrates that the integration accuracy increases by several orders of magnitude if the step of numerical integration is matched to the boundaries of ephemeris interpolation intervals. In addition, an algorithm for ephemeris smoothing at the boundaries of interpolation intervals is developed and applied in order to eliminate the jumps of coordinates and their first-order derivatives emerging in extended- and quadprecision calculations. This algorithm allows one to remove the jumps of coordinates and their derivatives up to any given order. It is demonstrated that the use of ephemerides smoothed to the first-order derivatives in quad-precision calculations increases the accuracy of numerical integration by ~10 orders of magnitude.     

Comparison study of magnetic flux ropes in the ionospheres of Venus, Mars and Titan

Magnetic flux ropes are created in the ionosphere of Venus and Mars during the interaction of the solar wind with their ionospheres and also at Titan during the interaction of the Saturnian magnetospheric plasma flow with Titan’s ionosphere. The flux ropes at Venus and Mars were extensively studied from Pioneer Venus Orbiter and Mars Global Surveyor observations respectively during solar maximum. Based on the statistical properties of the observed flux ropes at Venus and Mars, the formation of a flux rope in the ionosphere is thought first to arise near the boundary between the magnetic barrier and the ionosphere and later to sink into the lower ionosphere. Venus flux ropes are also observed during solar minimum by Venus Express and the observations of developing and mature flux ropes are consistent with the proposed mechanism. With the knowledge of flux rope structure in the Venus ionosphere, the twisted fields in the lower ionosphere of Titan from Cassini observations are studied and are found to resemble the Venus flux ropes.     

Effects of impacts on the atmospheric evolution: Comparison between Mars, Earth, and Venus

Classified as a terrestrial planet, Venus, Mars, and Earth are similar in several aspects such as bulk composition and density. Their atmospheres on the other hand have significant differences. Venus has the densest atmosphere, composed of CO₂ mainly, with atmospheric pressure at the planet's surface 92 times that of the Earth, while Mars has the thinnest atmosphere, composed also essentially of CO₂, with only several millibars of atmospheric surface pressure. In the past, both Mars and Venus could have possessed Earth-like climate permitting the presence of surface liquid water reservoirs. Impacts by asteroids and comets could have played a significant role in the evolution of the early atmospheres of the Earth, Mars, and Venus, not only by causing atmospheric erosion but also by delivering material and volatiles to the planets. Here we investigate the atmospheric loss and the delivery of volatiles for the three terrestrial planets using a parameterized model that takes into account the impact simulation results and the flux of impactors given in the literature. We show that the dimensions of the planets, the initial atmospheric surface pressures and the volatiles contents of the impactors are of high importance for the impact delivery and erosion, and that they might be responsible for the differences in the atmospheric evolution of Mars, Earth and Venus.     

Effect of topographic bias on geoid and reference ellipsoid of Venus, Mars, and the Moon

Since the continuation of an external gravity field inside topographic masses by a harmonic function results in topographic bias, geoid computation by means of global gravity models (GGMs) in terms of external-type series of spherical harmonics, at locations where the GGMs are evaluated inside the topographic masses, will be biased. Consequently, if the reference ellipsoid is defined based on the geoid, it will also be biased. In this paper, the effects of topographic bias on the geoid and reference ellipsoid of Venus, Mars, and the Moon are studied. Moreover, a thorough error analysis in the geoid and reference ellipsoid computation is presented, and it is shown that the estimated standard deviation (STD) of the geoid potential value, the geoidal heights, and the semimajor and semiminor axes of the reference ellipsoid are independent of the topographic bias. According to the results, the effects of topographic bias on the geoid potential value and the semimajor and semiminor axes of the reference ellipsoid in comparison with their estimated STDs are insignificant for Venus, Mars, and the Moon. Moreover, the effect of topographic bias on the geoidal heights of Venus as compared with the estimated STD of its geoidal heights is insignificant. However, the effects of topographic bias on the geoidal heights of Mars and the Moon can be significant, especially in high mountains such as the Tharsis volcanic region on Mars.     

Ionospheric photoelectrons: Comparing Venus, Earth, Mars and Titan

The sunlit portion of planetary ionospheres is sustained by photoionization. This was first confirmed using measurements and modelling at Earth, but recently the Mars Express, Venus Express and Cassini-Huygens missions have revealed the importance of this process at Mars, Venus and Titan, respectively. The primary neutral atmospheric constituents involved (O and CO₂ in the case of Venus and Mars, O and N₂ in the case of Earth and N₂ in the case of Titan) are ionized at each object by EUV solar photons. This process produces photoelectrons with particular spectral characteristics. The electron spectrometers on Venus Express and Mars Express (part of ASPERA-3 and 4, respectively) were designed with excellent energy resolution (ΔE/E=8%) specifically in order to examine the photoelectron spectrum. In addition, the Cassini CAPS electron spectrometer at Saturn also has adequate resolution (ΔE/E=16.7%) to study this population at Titan. At Earth, photoelectrons are well established by in situ measurements, and are even seen in the magnetosphere at up to 7R_E. At Mars, photoelectrons are seen in situ in the ionosphere, but also in the tail at distances out to the Mars Express apoapsis (∼3R_M). At both Venus and Titan, photoelectrons are seen in situ in the ionosphere and in the tail (at up to 1.45R_V and 6.8R_T, respectively). Here, we compare photoelectron measurements at Earth, Venus, Mars and Titan, and in particular show examples of their observation at remote locations from their production point in the dayside ionosphere. This process is found to be common between magnetized and unmagnetized objects. We discuss the role of photoelectrons as tracers of the magnetic connection to the dayside ionosphere, and their possible role in enhancing ion escape.     

Modern Numerical Ephemerides of Planets and the Importance of Ranging Observations for Their Creation

The JPL planetary and lunar ephemerides – DE200/LE200, DE403/LE403, DE405/LE405 and the planetary and lunar ephemerides, EPM87, EPM98, and EPM2000, constructed in the Institute of Applied Astronomy of RAS are described. Common properties and differences of the various ephemerides are given. Graphical comparisons of the DE ephemerides with each other and with the EPM ephemerides are presented. A fairly good agreement of planetary orbits is between DE403, DE405 and EPM98, EPM2000, respectively, over the interval of 120 years (1886–2006) covered by EPM98 and EPM2000. Some differences are explained by a slight disagreement in representing the orbits of Ceres, Pallas, and Vesta as they affect the planets. The accurate radar observations of planets and spacecraft make it possible not only to improve the orbital elements of planets but to determine a broad set of astronomical constants as well: km/AU, parameters of Mars rotation including its precessional rate, the masses of Jupiter, Ceres, Pallas, and Vesta, relativistic parameters of the PPN formalism, the variability of the gravitational constant G. These have been obtained in the fitting process of the DE405 and EPM2000 ephemerides to observational data, including nearly 80000 American and Russian radar observations of planets (1961–1997), ranging and doppler to the Viking and Pathfinder landers, and other miscellaneous measurements from various sources and spacecraft.     

Atmospheric angular momentum variations of Earth, Mars and Venus at seasonal time scales

Atmospheric angular momentum variations of a planet are associated with the global atmospheric mass redistribution and the wind variability. The exchange of angular momentum between the fluid layers and the solid planet is the main cause for the variations of the planetary rotation at seasonal time scales. In the present study, we investigate the angular momentum variations of the Earth, Mars and Venus, using geodetic observations, output of state-of-the-art global circulation models as well as assimilated data. We discuss the similarities and differences in angular momentum variations, planetary rotation and angular momentum exchange for the three terrestrial planets. We show that the atmospheric angular momentum variations for Mars and Earth are mainly annual and semi-annual whereas they are expected to be “diurnal” on Venus. The wind terms have the largest contributions to the LOD changes of the Earth and Venus whereas the matter term is dominant on Mars due to the CO₂ sublimation/condensation. The corresponding LOD variations (ΔLOD) have similar amplitudes on Mars and Earth but are much larger on Venus, though more difficult to observe.     

Updated IAA RAS planetary ephemerides-EPM2011 and their use in scientific research

The EPM (Ephemerides of Planets and the Moon) numerical ephemerides were first created in the 1970s in support of Russian space flight missions and since then have been constantly improved at IAA RAS. In the following work, the latest version of the planetary part of the EPM2011 numerical ephemerides is presented. The EPM2011 ephemerides are computed using an updated dynamical model, new values of the parameters, and an extended observation database that contains about 680000 positional measurements of various types obtained from 1913 to 2011. The dynamical model takes into account mutual perturbations of the major planets, the Sun, the Moon, 301 massive asteroids, and 21 of the largest trans-Neptunian objects (TNOs), as well as perturbations from the other main-belt asteroids and other TNOs. The EPM ephemerides are computed by numerical integration of the equations of motion of celestial bodies in the parameterized post-Newtonian n-body metric in the BCRS coordinate system for the TDB time scale over a 400-year interval. The ephemerides were oriented to the ICRF system using 213 VLBI observations (taken from 1989 to 2010) of spacecraft near planets with background quasars, the coordinates of which are given in the ICRF system. The accuracy of the constructed ephemerides was verified by comparison with observations and the JPL independent ephemerides DE424. The EPM ephemerides are used in astronavigation (they form the basis of the Astronomical Yearbook and are planned to be utilized in GLONASS and LUNA-RESURS programs) and various research, including the estimation of the solar oblateness, the parameters of the rotation of Mars, and the total mass of the asteroid main belt and TNOs, as well as the verification of general relativity, the secular variations of the Sun’s mass and the gravitational constant, and the limits on the dark matter density in the Solar System. The EPM ephemerides, together with the corresponding time differences TT — TDB and the coordinates of seven additional objects (Ceres, Pallas, Vesta, Eris, Haumea, Makemake, and Sedna), are available at ftp://quasar.ipa.nw.ru/incoming/EPM.     

Venusian saltation

Estimates of the trajectories of saltating particles on Venus show the level of saltation on Ve low when compared to either Earth or Mars. Particles in saltation on Venus obtain maximum heights of only 1 cm over a wide range in particle size and surface wind speeds. Their path lenghts are only a few centimeters at the wind speed of 1 and 2 m/sec. The entire saltation process and particle trajectories are insensitive to changes in surface pressure over the range from 70 to 100 bars and to changes in surface temperature over the range from 600 to 900°K. Secondly, the net rate of surface material transport due to saltation on Venus is small when compared to Earth or Mars. This result is due to the dense Venusian atmosphere. It is estimated that approximately 10 times more surface materials is transported by saltation on Earth than on Venus for dynamically similar conditions. And approximately 250 times more material is moved by the saltation process on Mars than on Venus, again for dynamically similar conditions. Both these estimates apply over a wide range of particle diameter, from 0.01 to 7 mm. Thirdly, the ripple wavelenghts may be small, such that thay may not be detected by the high-resolution radar images of the surface of Venus.     

Atmospheric ion wakes of Venus and Mars in the solar wind

A model has been developed for the currents induced in the ionospheres of Venus and Mars by the flowing magnetized solar wind in a previous paper (Cloutier and Daniell, 1973). The altitudes of the ionopauses on both planets, determined from the electrodynamical models of the previous paper, are used here to calculate the total rates of atmospheric mass loss to the solar wind for Venus and Mars. These loss rates are compared to the rates calculated by Michel (1971) based upon the limit of mass loading of the solar wind flow determined from hydrodynamic constraints. The distributions of planetary ions in the downstream wakes of Venus and Mars are calculated, and the interpretation of ion spectrometer measurements from close planetary encounters is discussed.     

Planetary ENA Imaging: Venus and a comparison with Mars

We present simulated images of energetic neutral atoms (ENAs) produced in charge exchange collisions between solar wind protons and neutral atoms in the exosphere of Venus, and make a comparison with earlier results for Mars. The images are found to be dominated by two local maxima. One produced by charge exchange collisions in the solar wind, upstream of the bow shock, and the other close to the dayside ionopause. The simulated ENA fluxes at Venus are lower than those obtained in similar simulations of ENA images at Mars at solar minimum conditions, and close to the fluxes at Mars at solar maximum. Our numerical study shows that the ENA flux decreases with an increasing ionopause altitude. The influence of the Venus nighttime hydrogen bulge on the ENA emission is small.     

Characterization of terrestrial exoplanets based on the phase curves and albedos of Mercury, Venus and Mars

The empirically derived phase curves of terrestrial planets strongly distinguish between airless Mercury, cloud-covered Venus, and the intermediate case of Mars. The function for Mercury is steeply peaked near phase angle zero due to powerful backscattering from its surface, while that for Venus has 100 times less contrast and exhibits a brightness excess near 170° due to Mie scattering from droplets in the atmosphere. The phase curve of Mars falls between those of Mercury and Venus, and there are variations in luminosity due to the planet’s rotation, seasons, and atmospheric states. The phase function and geometric albedo of the Earth are estimated from published albedos values. The curves for Mercury, Venus and Mars are compared to that of the Earth as well as theoretical phase functions for giant planets. The parameters of these different phase functions can be used to characterize exoplanets.     

On the classification of comet plasma tails

The investigation of plasma tails of comets is an important part of comet research. Different classifications of plasma tails of comets are proposed. Plasma acceleration in the tails is investigated in sufficient detail. Several cometary forms are explained. Plasma tails of Mars and Venus were observed during the first studies of these planets. They are associated with the capture of ionized atoms and exosphere molecules by the solar wind magnetized plasma flow. Distinct plasma tails of Mars and Venus are caused by the mass loading of the solar wind with heavy ions. It was shown that the transverse dimension of the tails of Mars, Venus, and comets can be quite accurately determined by production rate of the obstacle to the solar wind flow. While plasma tails of Mars and Venus are investigated by in situ measurements from spacecraft, observations of comet tails from the Earth make it possible to see the entire object under study and to monitor changes in its structure. A certain similarity of cometary and planetary tails can be explained by the nonmagnetic nature of both types of bodies. Thus, it is reasonable to suppose that investigations of plasma tails of comets can supplement the information obtained by in situ methods of the study of the planets. In this paper, plasma tails of comets, presumably analogous to the plasma tails of Mars and Venus, have been identified on modern photographs of comets (more than 1500 photographs viewed). Only quasi-steady laminar tails are considered. They are divided into two types: double structures and outflows. The paper attempts to define the 3D structure of double structures and to determine certain characteristics of outflows.     

Comparative study of ion cyclotron waves at Mars, Venus and Earth

Ion cyclotron waves are generated in the solar wind when it picks up freshly ionized planetary exospheric ions. These waves grow from the free energy of the highly anisotropic distribution of fresh pickup ions, and are observed in the spacecraft frame with left-handed polarization and a wave frequency near the ion’s gyrofrequency. At Mars and Venus and in the Earth’s polar cusp, the solar wind directly interacts with the planetary exospheres. Ion cyclotron waves with many similar properties are observed in these diverse plasma environments. The ion cyclotron waves at Mars indicate its hydrogen exosphere to be extensive and asymmetric in the direction of the interplanetary electric field. The production of fast neutrals plays an important role in forming an extended exosphere in the shape and size observed. At Venus, the region of exospheric proton cyclotron wave production may be restricted to the magnetosheath. The waves observed in the solar wind at Venus appear to be largely produced by the solar-wind-Venus interaction, with some waves at higher frequencies formed near the Sun and carried outward by the solar wind to Venus. These waves have some similarity to the expected properties of exospherically produced proton pickup waves but are characterized by magnetic connection to the bow shock or by a lack of correlation with local solar wind properties respectively. Any confusion of solar derived waves with exospherically derived ion pickup waves is not an issue at Mars because the solar-produced waves are generally at much higher frequencies than the local pickup waves and the solar waves should be mostly absorbed when convected to Mars distance as the proton cyclotron frequency in the plasma frame approaches the frequency of the solar-produced waves. In the Earth’s polar cusp, the wave properties of ion cyclotron waves are quite variable. Spatial gradients in the magnetic field may cause this variation as the background field changes between the regions in which the fast neutrals are produced and where they are re-ionized and picked up. While these waves were discovered early in the magnetospheric exploration, their generation was not understood until after we had observed similar waves in the exospheres of Mars and Venus.