Asteroid mass determination with the Gaia mission: A simulation of the expected precisions

The ESA astrometric mission Gaia, due for a launch in late 2011, will observe a huge number of asteroids (∼350,000 brighter than V<20) with an unprecedented positional precision (at the sub-milliarcsecond level). This precision will play an important role for the mass determination of about hundred minor planets with a relative precision better than 50%. Presently, due primarily to their perturbations on Mars, the uncertainty in the masses of the largest asteroids is the limiting factor in the accuracy of the solar system ephemerides. Besides, such high precision astrometry will enable to derive direct measurements of the masses of the largest asteroids which are of utmost significance for the knowledge of their physical properties. The method for computing the masses is based on the analysis of orbital perturbations during close encounters between massive asteroids (perturbers) and several smaller minor planets (targets). From given criteria of close approaches selection, we give the list of asteroids for which the mass can be determined, and the expected precision of these masses at mission completion. We next study the possible contribution of the ground-based observations for the mass determination in some special observation cases of close approaches.     

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.     

Astrometric results of observations of mutual occultations and eclipses of the Galilean satellites of Jupiter in 2002-2003

We suggest a new approach and develop an original method for deriving astrometric data from the photometry of mutual occultations and eclipses of planetary satellites. We decide to model not the relative apparent motion of one satellite with respect to another satellite but the deflection of the observed relative motion with respect to the theoretical motion implied by appropriate ephemerides.We have attempted to reduce the results of photometric observations of the Gallilean satellites during their mutual occultations and eclipses in 2002-2003. The data of observation for 319 light curves of 106 mutual events were received from the observers. The reliable 245 light curves were processed with our method. Eighty six apparent relative positions have been obtained.Systematic errors arise inevitably while deriving astrometric data. Most of them are due to factors that are unrelated to the methods for deriving astrometric data. The systematic errors are more likely due to incorrect excluding the effect of background on photometric counts. In the case of mutual occultations, the flux drop is determined to a considerable degree by the ratio of the mean albedos of the two satellites. Some mutual event observations revealed wrong adopted values of the mean albedos.     

Estimates of dynamic parameters and boundaries of habitable zones of selected stars of the Pulkovo program

A list of selected binary stars is presented that have been observed for several decades using a 26-inch refractor at the Pulkovo Observatory. These stars are at a distance from 3.5 to 25 pc from the Sun. They belong to spectral classes F, G, K, and M. Their masses range from 0.3 to 1.5 solar masses. We have analyzed them as possible parent stars for exoplanets taking into account the physical characteristics of these stars. In view of dynamic parameters and orbital elements that we have obtained by Pulkovo observations, ephemerides of positions for the coming years are calculated. The boundaries of the habitable zones around these stars are calculated. The astrometric signal that depends on the gravitational influence of hypothetical planets is estimated. Space telescopes for astrometric observations with microsecond accuracy can be used to detect Earth-like planets near the closest stars of this program. This paper presents an overview of astrometric programs of searches for exoplanets.     

Determining asteroid masses from perturbations on Mars

The orbit of Mars is perturbed more than 5 m, a value compatible with the accuracy of the Viking lander ranging data, by about three dozen asteroids. In addition to larger asteroids throughout the belt, significant perturbations of long period are generated by smaller objects near commensurabilities with Mars. The largest periodic terms induced by 1 Ceres and 2 Pallas have amplitudes of 0.8 and 0.2 km, respectively, both with 10-year periods. Due to a near commensurability, 4 Vesta causes a 5-km, 52-year term. While the Viking ranges will yield significant mass determinations for the largest three asteroids, and some of the smaller bodies should be detectable, it will be difficult to seperate the smaller bodies with useful accuracies. Accurate discrimination must await range data from future missions to Mars or other bodies in the neighborhood of the asteroid belt. The Viking ranges can also yield improved masses for the outer planets (except Pluto), an application which is being exploited by groups analyzing these data. Uncertainties in the asteroid masses limit the ultimate accuracy of the Viking determinations of both the long time scale motion of the system the inner four planets with respect to an inertial frame and the rate of change of the gravitational constant.     

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.     

Accurate Mars Express orbits to improve the determination of the mass and ephemeris of the Martian moons

The determination of the ephemeris of the Martian moons has benefited from observations of their plane-of-sky positions derived from images taken by cameras onboard spacecraft orbiting Mars. Images obtained by the Super Resolution Camera (SRC) onboard Mars Express (MEX) have been used to derive moon positions relative to Mars on the basis of a fit of a complete dynamical model of their motion around Mars. Since, these positions are computed from the relative position of the spacecraft when the images are taken, those positions need to be known as accurately as possible. An accurate MEX orbit is obtained by fitting two years of tracking data of the Mars Express Radio Science (MaRS) experiment onboard MEX. The average accuracy of the orbits has been estimated to be around 20–25 m. From these orbits, we have re-derived the positions of Phobos and Deimos at the epoch of the SRC observations and compared them with the positions derived by using the MEX orbits provided by the ESOC navigation team. After fit of the orbital model of Phobos and Deimos, the gain in precision in the Phobos position is roughly 30 m, corresponding to the estimated gain of accuracy of the MEX orbits. A new solution of the GM of the Martian moons has also been obtained from the accurate MEX orbits, which is consistent with previous solutions and, for Phobos, is more precise than the solution from the Mars Global Surveyor (MGS) and Mars Odyssey (ODY) tracking data. It will be further improved with data from MEX-Phobos closer encounters (at a distance less than 300 km). This study also demonstrates the advantage of combining observations of the moon positions from a spacecraft and from the Earth to assess the real accuracy of the spacecraft orbit. In turn, the natural satellite ephemerides can be improved and participate to a better knowledge of the origin and evolution of the Martian moons.     

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.     

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.     

Comet and asteroid ephemerides for spacecraft encounters

To a significant degree, the success of spacecraft missions to comets and asteroids depends upon the accuracy of the target body ephemerides. In turn, accurate ephemerides depend upon the quality of the astrometric data set used in determining the object's orbit and the accuracy with which the target body's motion can be modelled. Using error analyses studies of the target bodies for the NEAR, Muses-C, Clementine 2, Stardust, and Rosetta missions, conclusions are drawn as to how to minimize target body position uncertainties at the times of encounter, In general, these uncertainties will be minimized when the object has a good number of optical observations spread over several orbital periods. If a target body lacks a lengthy data interval, its ephemeris uncertainties can be dramatically reduced with the use of radar Doppler and delay data taken when the body is relatively close to the Earth. The combination of radar and optical angle data taken at close Earth distances just before a spacecraft encounter can result in surprisingly small target body ephemeris uncertainties.     

Some results from the National Observatory of Turkey, Kazan State University, and Nikolaev Astronomical Observatory on small bodies of the solar system

A scientific collaboration between TÜB?TAK National Observatory (Turkey), Kazan State University (Russia) and Nikolaev Astronomical Observatory (Ukraine) involves observations of minor planets and near-Earth asteroids (NEAs) with the 1.5 m Russian-Turkish telescope (RTT150). Regular observations of selected asteroids in the range of 11-18 magnitudes began in 2004 with the view of determining masses of selected asteroids, improving the orbits of the NEAs, and studying physical characteristics of selected asteroids from photometric observations. More than 3000 positions of 53 selected asteroids and 11 NEAs have been obtained with an internal error in the range of 30-300 mas for a single determination. Photometric reductions of more than 4000 CCD frames are in progress. Masses of 21 asteroids were estimated through dynamical method using the ground-based optical observations, mainly from the RTT150 and Minor Planet Center. A comparison of the observational results from the RTT150 in 2004-2005 with observations of the same objects at other observatories allows us to conclude that RTT150 can be used for ground-based support in astrometry for the space mission GAIA.     

Astrometric observations of planetary satellites at the Abastumani Astrophysical Observatory

We present and discuss the results of the astrometry project during which we observed the satellites of Mars, Jupiter, Saturn, Uranus, and Neptune at the Abastumani Astrophysical Observatory (Georgia) between 1983 and 1994. Observations at the Abastumani Observatory were performed with the double Zeiss astrograph (DZA: D/F = 400/3024 mm) and AZT-11 telescope (F = 16 m). We processed a large array of observations and determined exact coordinates of the planets and their satellites in a system of reference stars of modern catalogues as well as relative coordinates of the satellites. The results were compared with modern ephemerides using the MULTI-SAT software. The comparison enabled us to estimate the accuracy of observations (their random and systematic uncertainties) and the accuracy of modern theories of the motion of planets and their satellites. Random uncertainties of observations are estimated to be 0.10??C0.40?? for various objects and observational conditions. Observational results obtained for Uranus, Neptune and the satellites Titania and Oberon were shown to deviate appreciably and systematically from theories of their motion. The results of observations are presented in the Pulkovo database for Solar System bodies that is available at the website http://www.puldb.ru.     

Long-Lived Near-Earth Asteroid 2013 RB6

The search for asteroids that maintain stable motion in the zone between the Earth and Mars has been performed. The near-Earth object 2013 RB6, which has avoided close encounters with the planets for a long period of time, has been found. Integration of the equations of motion of the object shows that its dynamical lifetime in the zone between the Earth and Mars significantly exceeds 100 Myr. 2013 RB6 moves away from orbital resonances with the planets, but is in the secular resonance ν₅. Solving the question of its origin requires further observations.     

Determination of asteroid masses from their close encounters with Mars

An obstacle to the asteroid mass determination lies in the difficulty in isolating the gravitational perturbation exerted by a single asteroid on the planets, being strongly correlated and mixed up with those of many other asteroids. This hindrance may be avoided by the method of analysis presented here: an asteroid mass is estimated in correspondence with its close encounters with Mars where the acceleration it induces on the planet can be sufficiently disentangled from those generated by the remaining asteroid masses to calculate. We test this technique in the analysis of range observations to Mars Global Surveyor and Mars Express performed from 1999 to 2007. For this purpose, we adopt the dynamical model of the planetary ephemeris INPOP06 (Fienga et al., 2008), which includes the gravitational influences of the 300 most perturbing asteroids of the Martian orbit. We obtain the solutions of 10 asteroid masses that have the largest effects on this orbit over the period examined: they are generally in good agreement with determinations recently published.     

The astrometric signal of microlensing events caused by free floating planets

Astrometric observations of microlensing events can be used to obtain important information about lenses. During these events, the shift of the position of the multiple image centroid with respect to the source star location can be measured. This effect, which is expected to occur on scales from micro-arcseconds to milli-arcseconds, depends on the lens-source-observer system physical parameters. Here, we consider the astrometric and photometric observations by space and ground-based telescopes of microlensing events towards the Galactic bulge caused by free floating planets (FFPs). We show that the efficiency of astrometric signal on photometrically detected microlensing events tends to increase for higher FFP masses in our Galaxy. In addition, we estimate that during five years of the Gaia observations, about a dozen of microlensing events caused by FFPs are expected to be detectable.     

Astrometry of Iapetus, Ariel, Umbriel, and Titania from eclipses and occultations

Highly accurate astrometric positions obtained from eclipses and occultations of planetary satellites are reported. These measurements may be used to test existing ephemerides, to improve upon them, and to fit system constants such as satellite masses and planetary zonal harmonics. Eclipse and occultation photometry of 5 uranian satellite mutual events has resulted in precise astrometry for 3 of these moons. Relative satellite positions were determined with an uncertainty of less than 10 milli-arcseconds for 4 of the events. These observations plus two additional data from C. Miller and N.J. Chanover (private communication) indicate that predictions based on the SPICE [Acton, C.H., 1996. Planet. Space Sci. 44, 65-70] ephemeris URA083 and those from the LA06 ephemeris in a paper by Arlot et al. [Arlot, J.-E., Lainey, V., Thuillot, W., 2006. Astron. Astrophys. 456, 1173-1179] are significantly more accurate than predictions generated by Christou [Christou, A.A., 2005. Icarus 178, 171-178] using the GUST86 ephemeris in the along-track component of motion. The observations indicate that Ariel, Umbriel and Titania are lagging behind their predicted positions for all of the ephemerides, but by varying distances and significance levels. Analysis of data recorded by Hidas et al. [Hidas, M.G., Christou, A.A., Brown, T.M., 2008. Mon. Not. R. Astron. Soc. 384, L38-L40] suggests a similar lag for Oberon. Photometry recorded during the ingress portion of a saturnian eclipse of Iapetus on 2007 May 5 indicates that the middle of the event occurred at geocentric UTC 02:14:58. At that moment the center of the satellite disk facing the Sun was intersected by a solar-centered ray refracted at a minimum altitude of 240 km above the 1-bar pressure level in the planet's atmosphere. The uncertainty in the timings due to observational scatter was only 5 s which equates to 16 km of Iapetus motion, but other factors increased the overall uncertainty to 111 km or 16 milli-arcseconds at the distance of Saturn from the Sun. The astrometric result is fit very well by the SPICE ephemeris SAT288.     

Relativistic effects and solar oblateness from radar observations of planets and spacecraft

We used more than 250 000 high-precision American and Russian radar observations of the inner planets and spacecraft obtained in the period 1961–2003 to test the relativistic parameters and to estimate the solar oblateness. Our analysis of the observations was based on the EPM ephemerides of the Institute of Applied Astronomy, Russian Academy of Sciences, constructed by the simultaneous numerical integration of the equations of motion for the nine major planets, the Sun, and the Moon in the post-Newtonian approximation. The gravitational noise introduced by asteroids into the orbits of the inner planets was reduced significantly by including 301 large asteroids and the perturbations from the massive ring of small asteroids in the simultaneous integration of the equations of motion. Since the post-Newtonian parameters and the solar oblateness produce various secular and periodic effects in the orbital elements of all planets, these were estimated from the simultaneous solution: the post-Newtonian parameters are β = 1.0000 ± 0.0001 and γ = 0.9999 ± 0.0002, the gravitational quadrupole moment of the Sun is J₂ = (1.9 ± 0.3) × 10^?7, and the variation of the gravitational constant is ?/G = (?2 ± 5) × 10^?14 yr^?1. The results obtained show a remarkable correspondence of the planetary motions and the propagation of light to General Relativity and narrow significantly the range of possible values for alternative theories of gravitation.     

The origin of the Martian moons revisited

The origin of the Martian moons, Phobos and Deimos, is still an open issue: either they are asteroids captured by Mars or they formed in situ from a circum-Mars debris disk. The capture scenario mainly relies on the remote-sensing observations of their surfaces, which suggest that the moon material is similar to outer-belt asteroid material. This scenario, however, requires high tidal dissipation rates inside the moons to account for their current orbits around Mars. Although the in situ formation scenarios have not been studied in great details, no observational constraints argue against them. Little attention has been paid to the internal structure of the moons, yet it is pertinent for explaining their origin. The low density of the moons indicates that their interior contains significant amounts of porous material and/or water ice. The porous content is estimated to be in the range of 30?C60% of the volume for both moons. This high porosity enhances the tidal dissipation rate but not sufficiently to meet the requirement of the capture scenario. On the other hand, a large porosity is a natural consequence of re-accretion of debris at Mars?? orbit, thus providing support to the in situ formation scenarios. The low density also allows for abundant water ice inside the moons, which might significantly increase the tidal dissipation rate in their interiors, possibly to a sufficient level for the capture scenario. Precise measurements of the rotation and gravity field of the moons are needed to tightly constrain their internal structure in order to help answering the question of the origin.     

Asteroid mass determination at Nikolaev Observatory

Masses of asteroids are topical for research in ephemerides computations and density evaluations. Details of the dynamical method are given for asteroid mass determinations. Preliminary masses of 13 asteroids, obtained with relative errors less than 50%, are presented from non-weighted least squares. Accuracy improvement of mass values for dynamical computations is evident using contemporary observations of 1999-2006. Statistics of the fitting ephemerides to the observations is also discussed.     

Numerical theories of motion of Triton and Nereid

The ephemerides of satellites of major planets are needed in planning spacecraft missions both for studying the satellites themselves and for navigational support during the flights of spacecraft in the vicinity of planets. In addition, accurate numerical theories of motion of the natural satellites of major planets make it possible to increase the accuracy of the ephemerides of their central planets based on positional (photographic and CCD) observations of the satellites. Numerical theories of Neptune’s satellites, Triton and Nereid, constructed within the framework of the ERA software package developed at the Institute of Applied Astronomy of the Russian Academy of Sciences are presented.