Current problems of dynamics of moons of planets and binary asteroids based on observations

The general approach to studying the dynamics of moons of planets and asteroids consists in developing more and more accurate models of motion based on observational data. Not only the necessary ephemerides, but also some physical parameters of planets and moons are obtained this way. It is demonstrated in the present study that progress in this field is driven not only by the increase in accuracy of observations. The accuracy of ephemerides may be increased by expanding the observation time interval. Several problems arise on the way toward this goal. Some of them become apparent only when the procedure of observational data processing and use is examined in detail. The method used to derive astrometric data by processing the results of photometric observations of mutual occultations and eclipses of planetary moons is explained below. The primary contribution to the error of astrometric results is produced by the unaccounted noise level in photometric readings and the inaccuracy of received values of the albedo of moons. It is demonstrated that the current methods do not allow one to eliminate the noise completely. Extensive additional photometric measurements should be performed at different angles of rotation of moons and in different spectral bands of the visible wavelength range in order to obtain correct values of the albedo of moons. Many new distant moons of the major planets have been discovered in the early 21st century. However, the observations of these moons are scarce and were performed over short time intervals; as a result, some of the moons were lost. The necessity of further observations of these Solar System bodies is pointed out in the present study. Insufficient knowledge of asteroid masses is an obstacle to improving the accuracy of the ephemerides of Mars. The basic method for determining the masses of large asteroids consists in analyzing their influence on the motion of Mars, the Earth, and spacecraft. The masses of more than 100 large asteroids were determined this way. One of the principal techniques for Earth-based measurement of the masses of asteroids involves astrometric observations of binary asteroids. The determination of relative coordinates is made rather difficult by the apparent proximity of components. The success of these efforts depends on the availability of instrumentation and the expertise of observers skilled in adaptive optics and speckle interferometry. Collaboration between different research teams and observers is absolutely necessary.     

A planetary system with an escaping Mars

The chaotic behaviour of the motion of the planets in our Solar System is well established. In this work to model a hypothetical extrasolar planetary system our Solar System was modified in such a way that we replaced the Earth by a more massive planet and let the other planets and all the orbital elements unchanged. The major result of former numerical experiments with a modified Solar System was the appearance of a chaotic window at κ _E ∈ (4, 6), where the dynamical state of the system was highly chaotic and even the body with the smallest mass escaped in some cases. On the contrary for very large values of the mass of the Earth, even greater than that of Jupiter regular dynamical behaviour was observed. In this paper the investigations are extended to the complete Solar System and showed, that this chaotic window does still exist. Tests in different ‘Solar Systems’ clarified that including only Jupiter and Saturn with their actual masses together with a more ‘massive’ Earth (4 < κ _E < 6) perturbs the orbit of Mars so that it can even be ejected from the system. Using the results of the Laplace‐Lagrange secular theory we found secular resonances acting between the motions of the nodes of Mars, Jupiter and Saturn. These secular resonances give rise to strong chaos, which is the cause of the appearance of the instability window. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Resonant structures in the solar system

The resonance theory is discussed with respect to the Solar System with a view to show that every triad of successive planets in the Solar System follows Laplace's resonance relation. With rings now known to exist around three of the four major planets, scientists have begun to speculate about the possible existence of ring structure and one or two small planets going around the Sun itself. It is also believed that the ring systems may exist around the planets Neptune and Mars. In this paper an attempt is made to provide a basis to these beliefs using Laplace's resonance relation. The triads of successive innermost objects (rings and/or satellites) in the satellite — systems of Jupiter, Saturn and Uranus are also shown to follow Laplace's resonance relation.     

On the stability of a planet between Mars and the asteroid belt: Implications for the Planet V hypothesis

The stability of an additional planet between the orbit of Mars and the asteroid belt is examined in the context of the Planet V hypothesis. In this model, the Solar System initially contained a fifth terrestrial planet, “Planet V,” which was removed after ∼700 Myr, a possible trigger for the late heavy bombardment on the inner planets. The model is investigated using 96 N-body integrations of the 8 major planets with an additional body between Mars and the asteroid belt. In more than 1/4 of simulations, Planet V survives for 1000 Myr. In most other cases, Planet V collides with the Sun or hits another planet after several hundred Myr, leaving 4 surviving terrestrial planets. In 24/96 simulations, Planet V is lost by ejection or collision with the Sun while the other four terrestrial planets survive without undergoing a collision. In 18 cases, Planet V is removed at least 200 Myr after the beginning of the simulation. The endstate depends sensitively on the mass of Planet V. Collision with the Sun is likely when Planet V's mass is 0.25 Mars masses or less. When Planet V is more massive than this, collisions involving it and/or other terrestrial planets become commonplace. In unstable systems, the times of first encounter and first collision/ejection depend on the initial aphelion distance of Mars. Reducing Mars's aphelion distance increases these times and also increases the fraction of systems surviving for 1000 Myr. When Mars's current orbit is used, the stability of Planet V increases when these two planets are widely separated initially. Planet V's aphelion distance Q typically begins to cross the asteroid belt within a few tens to a few hundred Myr, and its orbit last leaves the belt several hundred Myr later in most cases. The total time spent with Q>2.1 AU is typically less than 200 Myr.     

Automated design of gravity-assist trajectories to Mars and the outer planets

In this paper, a new approach to planetary mission design is described which automates the search for gravity-assist trajectories. This method finds all conic solutions given a range of launch dates, a range of launch energies and a set of target planets. The new design tool is applied to the problems of finding multiple encounter trajectories to the outer planets and Venus gravity-assist trajectories to Mars. The last four-planet grand tour opportunity (until the year 2153) is identified. It requires an Earth launch in 1996 and encounters Jupiter, Uranus, Neptune, and Pluto. Venus gravity-assist trajectories to Mars for the 30 year period 1995–2024 are examined. It is shown that in many cases these trajectories require less launch energy to reach Mars than direct ballistic trajectories.Assistant Professor, School of Aeronautics and AstronauticsGraduate Student, School of Aeronautics and Astronautics     

Inner Solar System dynamical analogs of plutinos

By studying orbits of asteroids potentially in 3:2 exterior mean motion resonance with Earth, Venus, and Mars, we have found plutino analogs. We identify at least 27 objects in the inner Solar System dynamically protected from encounter through this resonance. These are four objects associated with Venus, six with Earth, and seventeen with Mars. Bodies in the 3:2 exterior resonance (including those in the plutino resonance associated with Neptune) orbit the Sun twice for every three orbits of the associated planet, in such a way that with sufficiently low libration amplitude close approaches to the planet are impossible. As many as 15% of Kuiper Belt objects share the 3:2 resonance, but are poorly observed. One of several resonance sweeping mechanisms during planetary migration is likely needed to explain the origin and properties of 3:2 resonant Kuiper Belt objects. Such a mechanism likely did not operate in the inner Solar System. We suggest that scattering by the next planet out allows entry to, and exit from, 3:2 resonance for objects associated with Venus or Earth. 3:2 resonators of Mars, on the other hand, do not cross the paths of other planets, and have a long lifetime. There may exist some objects trapped in the 3:2 Mars resonance which are primordial, with our tests on the most promising objects known to date indicating lifetimes of at least tens of millions of years. Identifying 3:2 resonant systems in the inner Solar System permits this resonance to be studied on shorter timescales and with better determined orbits than has been possible to date, and introduces new mechanisms for entry into the resonant configuration.     

Origin of water in the inner Solar System: A kinetic Monte Carlo study of water adsorption on forsterite

The origin of water in the inner Solar System is not well understood. It is believed that temperatures were too high in the accretion disk in the region of the terrestrial planets for hydrous phases to be thermodynamically stable. Suggested sources of water include direct adsorption of hydrogen from the nebula into magma oceans after the terrestrial planets formed, and delivery of asteroidal or cometary material from beyond the zone of the terrestrial planets. We explore a new idea, direct adsorption of water onto grains prior to planetary accretion. This hypothesis is motivated by the observation that the accretion disk from which our planetary system formed was composed of solid grains bathed in a gas dominated by hydrogen, helium, and oxygen. Some of that hydrogen and oxygen combined to make water vapor. We examine quantitatively adsorption of water onto grains in the inner Solar System accretion disk by exploring the adsorption dynamics of water molecules onto forsterite surfaces via kinetic Monte Carlo simulations. We conclude that many Earth oceans of water could be adsorbed.     

Nonuniform cratering of the Moon and a revised crater chronology of the inner Solar System

We model the cratering of the Moon and terrestrial planets from the present knowledge of the orbital and size distribution of asteroids and comets in the inner Solar System, in order to refine the crater chronology method. Impact occurrences, locations, velocities and incidence angles are calculated semi-analytically, and scaling laws are used to convert impactor sizes into crater sizes. Our approach is generalizable to other moons or planets. The lunar cratering rate varies with both latitude and longitude: with respect to the global average, it is about 25% lower at (±65°N, 90°E) and larger by the same amount at the apex of motion (0°N, 90°W) for the present Earth-Moon separation. The measured size-frequency distributions of lunar craters are reconciled with the observed population of near-Earth objects under the assumption that craters smaller than a few kilometers in diameter form in a porous megaregolith. Varying depths of this megaregolith between the mare and highlands is a plausible partial explanation for differences in previously reported measured size-frequency distributions. We give a revised analytical relationship between the number of craters and the age of a lunar surface. For the inner planets, expected size-frequency crater distributions are calculated that account for differences in impact conditions, and the age of a few key geologic units is given. We estimate the Orientale and Caloris basins to be 3.73 Ga old, and the surface of Venus to be 240 Ma old. The terrestrial cratering record is consistent with the revised chronology and a constant impact rate over the last 400 Ma. Better knowledge of the orbital dynamics, crater scaling laws and megaregolith properties are needed to confidently assess the net uncertainty of the model ages that result from the combination of numerous steps, from the observation of asteroids to the formation of craters. Our model may be inaccurate for periods prior to 3.5 Ga because of a different impactor population, or for craters smaller than a few kilometers on Mars and Mercury, due to the presence of subsurface ice and to the abundance of large secondaries, respectively. Standard parameter values allow for the first time to naturally reproduce both the size distribution and absolute number of lunar craters up to 3.5 Ga ago, and give self-consistent estimates of the planetary cratering rates relative to the Moon.     

Libration celestial mechanics experiment

The exploration of planet moons and minor bodies (Avduevskii et al., 1996) is a basic task for comprehending the nature of the processes occurring in our Solar System. Knowing the current state of the moons, we can better describe their past and look into the future. This knowledge is important, first of all, for understanding the origin of the Solar System. Interest in the Martian moon Phobos has been displayed during recent decades. The interest is caused by some questions to which there have been no answers up until now (Sagdeev et al., 1988; 1989). For example, there is a question regarding the origin of the moon: whether it is an asteroid captured by Mars’ gravitational field or it is an accumulated body in the Martian orbit. In connection with this, it is interesting to conduct studies aimed at answering this question. If Phobos appears to be an asteroid, then investigations regarding the chemical and isotopic compositions of the moon as the primary matter of the Solar System as well as its evolution are of great interest.     

The Architectural Design Rules of Solar Systems Based on the New Perspective

In this paper I present a new perspective of the birth and evolution of Planetary Systems. This new perspective presents an all encompassing and self consistent Paradigm of the birth and evolution of the solar systems. In doing so it redefines astronomy and rewrites astronomical principles. Kepler and Newton defined a stable and non-evolving elliptical orbits. While this perspective defines a collapsing or expanding spiral orbit of planets except for Brown Dwarfs. Brown Dwarfs are significant fraction of the central star. Hence they rapidly evolve from non-Keplerian state to the end point which is a Keplerian state where it is in stable elliptical orbits. On the basis of the Lunar Laser Ranging Data released by NASA on the Silver Jubilee Celebration of Man’s Landing on Moon on 21st July 1969–1994, theoretical formulation of Earth-Moon tidal interaction was carried out and Planetary Satellite Dynamics was established. It was found that this mathematical analysis could as well be applied to Star and Planets system and since every star could potentially contain an extra-solar system, hence we have a large ensemble of exo-planets to test our new perspective on the birth and evolution of solar systems. Till date 403 exo-planets have been discovered in 390 extra-solar systems by radial velocity method, by transiting planet method, by gravitational lensing method, by direct imaging method and by timing method. I have taken 12 single planet systems, four Brown Dwarf—Star systems and two Brown Dwarf pairs. Following architectural design rules are corroborated through this study of exo-planets. All planets are born at inner Clarke’s Orbit what we refer to as inner geo-synchronous orbit in case of Earth-Moon System. The inner Clarke’s Orbit is an orbit of unstable equilibrium. By any perturbative force such as cosmic particles or radiation pressure, the planet gets tipped long of a_G1 or short of a_G1. Here a_G1 is inner Clarke’s Orbit. If planet is long of a_G1 then it is said to be in extra-synchronous orbit. Here Gravitational Sling Shot effect is in play. In gravity assist planet fly-by maneuver in space flights, gravitational sling shot is routinely used to boost the space craft to its destination. The exo-planet can either be launched on death spiral as CLOSE HOT JUPITERS or can be launched on an expanding spiral path as the planets in our Solar System are. In death spiral, exo-planet less than 5 m_J will get pulverized and vaporized in close proximity to the host star. If the mass is between 5 and 7.5 m_J then it will be partially vaporized and partially engulfed by the host star and if it is greater than 7.5 m_J, then it will be completely ingested by the host star. In the process the planet will deposit all its material and angular momentum in the Host Star. This will leave tell-tale imprints of ingestion: in such cases host Star will have higher ⁷Li, host star will become a rapidly rotating progenitor and the host star will have excess IR. All these have been confirmed by observations of Transiting Planets. It was also found that if the exo-planet are significant fraction of the host star then those exo-planets rapidly migrate from a_G1 to a_G2 and have very short Time Constant of Evolution as Brown Dwarfs have. But if exo-planets are insignificant fraction of the host star as our terrestrial planets are then they are stay put in their original orbit of birth. By corollary this implies that Giant exo-planets reach nearly Unity Evolution Factor in a fraction of the life span of a solar system. This is particularly true for brown dwarfs orbiting main sequence stars. In this study four star systems hosting Brown Dwarfs, two Brown Dwarf pairs and 12 extrasolar systems hosting Jupiter sized planets are selected. In Brown Dwarfs evolution factor is invariably UNITY or near UNITY irrespective of their respective age and Time Constant of Evolution is very short of the order of year or tens of years. In case of 12 exo-planets system with increasing mass ratio evolution factor increases and time constant of evolution shortens from Gy to My though there are two exceptions. TW Hydrae is a special case. This Solar System is newly born system which is only 9 million years old. Hence its exo-planet has just been born and it is very near its birth place just as predicted by my hypothesis. In fact it is only slightly greater than a_G1. This vindicates our basic premise that planets are always born at inner Clarke’s Orbit. This study vindicates the design rules which had been postulated at 35th COSPAR Scientific Assembly in 2004 at Paris, France, under the title “New Perspective on the Birth & Evolution of Solar Systems”.     

What makes a planet habitable?

This work reviews factors which are important for the evolution of habitable Earth-like planets such as the effects of the host star dependent radiation and particle fluxes on the evolution of atmospheres and initial water inventories. We discuss the geodynamical and geophysical environments which are necessary for planets where plate tectonics remain active over geological time scales and for planets which evolve to one-plate planets. The discoveries of methane–ethane surface lakes on Saturn’s large moon Titan, subsurface water oceans or reservoirs inside the moons of Solar System gas giants such as Europa, Ganymede, Titan and Enceladus and more than 335 exoplanets, indicate that the classical definition of the habitable zone concept neglects more exotic habitats and may fail to be adequate for stars which are different from our Sun. A classification of four habitat types is proposed. Class I habitats represent bodies on which stellar and geophysical conditions allow Earth-analog planets to evolve so that complex multi-cellular life forms may originate. Class II habitats includes bodies on which life may evolve but due to stellar and geophysical conditions that are different from the class I habitats, the planets rather evolve toward Venus- or Mars-type worlds where complex life-forms may not develop. Class III habitats are planetary bodies where subsurface water oceans exist which interact directly with a silicate-rich core, while class IV habitats have liquid water layers between two ice layers, or liquids above ice. Furthermore, we discuss from the present viewpoint how life may have originated on early Earth, the possibilities that life may evolve on such Earth-like bodies and how future space missions may discover manifestations of extraterrestrial life.     

On the stability of Earth-like planets in multi-planet systems

We present a continuation of our numerical study on planetary systems with similar characteristics to the Solar System. This time we examine the influence of three giant planets on the motion of terrestrial-like planets in the habitable zone (HZ). Using the Jupiter–Saturn–Uranus configuration we create similar fictitious systems by varying Saturn’s semi-major axis from 8 to 11 AU and increasing its mass by factors of 2–30. The analysis of the different systems shows the following interesting results: (i) Using the masses of the Solar System for the three giant planets, our study indicates a maximum eccentricity (max-e) of nearly 0.3 for a test-planet placed at the position of Venus. Such a high eccentricity was already found in our previous study of Jupiter–Saturn systems. Perturbations associated with the secular frequency g ₅ are again responsible for this high eccentricity. (ii) An increase of the Saturn-mass causes stronger perturbations around the position of the Earth and in the outer HZ. The latter is certainly due to gravitational interaction between Saturn and Uranus. (iii) The Saturn-mass increased by a factor 5 or higher indicates high eccentricities for a test-planet placed at the position of Mars. So that a crossing of the Earth’ orbit might occur in some cases. Furthermore, we present the maximum eccentricity of a test-planet placed in the Earth’ orbit for all positions (from 8 to 11 AU) and masses (increased up to a factor of 30) of Saturn. It can be seen that already a double-mass Saturn moving in its actual orbit causes an increase of the eccentricity up to 0.2 of a test-planet placed at Earth’s position. A more massive Saturn orbiting the Sun outside the 5:2 mean motion resonance (a _S  ≥9.7 AU) increases the eccentricity of a test-planet up to 0.4.     

The effect of radiative transfer on shear-flow instability in the atmospheres on mars and venus

The results of two theoretical investigations concerning the destabilizing effects of radiative transfer on stably stratified shear flows are applied to the CO₂ atmospheres Mars and Venus. It is found that radiatively modified critical Richardson numbers remain below plausible atmospheric values throughout the stratospheres of both planets. Above certain altitudes, however, in the upper stratospheres of these planets (≈50 km on Mars and ≈100 km on Venus), critical Richardson numbers begin to increase significantly above the nonradiating critical value. This trend continues until, in the lower thermosphere, critical Richardson numbers eventually surpass atmospheric values. This effect could lead to observably greater turbulent mixing in the upper atmospheres of Mars and Venus than might be expected from terrestrial observation and from nonradiating theoretical calculations.     

A half-century of terrestrial analog studies: From craters on the Moon to searching for life on Mars

Terrestrial analogs to the Moon and Mars have been used to advance knowledge in planetary science for over a half-century. They are useful in studies of comparative geology of the terrestrial planets and rocky moons, in astronaut training and testing of exploration technologies, and in developing hypotheses and exploration strategies in astrobiology. In fact, the use of terrestrial analogs can be traced back to the origins of comparative geology and astrobiology, and to the early phases of the Apollo astronaut program. Terrestrial analog studies feature prominently throughout the history of both NASA and the USGS’ Astrogeology Research Program. In light of current international plans for a return missions to the Moon, and eventually to send sample return and manned missions to Mars, as well as the recent creation of various analog research and development programs, this historical perspective is timely.     

Keck Observations of Solar System Objects: Perspectives for Extremely Large Telescopes

From differential tracking techniques, required for appulse observations of KBOs with Laser Guide Star Adaptive Optics (LGSAO), to developing methods for collecting spectra at the precise moment of a predicted impact, each Solar System observation conducted on a large telescope presents a unique set of challenges. We present operational details and some key science results from our science program, adaptive optics observations of main belt asteroids and near earth objects; as well as the technical and operational details of several Keck Solar System observations conducted by other teams: the impact of Shoemaker-Levy 9 on Jupiter, volcanoes on Io, the Deep Impact mission to Comet 9P/Tempel 1, and recent observations of Pluto’s moons Nix and Hydra. For each of these observations, we draw from our Keck experience to predict what challenges may lie ahead when similar observations are conducted on next generation telescopes.     

The importance of radical density in cosmic chemistry

In various laboratory experiments chemical processes induced by ionizing radiation have been simulated which occur in the outer layers of comets, in interstellar clouds, and in the atmospheres of planets and moons of our Solar System. An obvious problem for the interpretation of the results is that the duration of the experiments is by many orders of magnitude shorter than the time intervals of the simulated systems. Hence in most ice and gas phase experiments much higher dose rates of ionizing radiation are applied in order to obtain a total absorbed dose which is realistic for the simulated system.In this paper the influence of the dose rate on reactions in gaseous systems shall be discussed as well as the influence of linear energy transfer and of scavengers on the reactions and their yields. The central parameter is the density of reactive species.Some consequences for ice systems will be given.     

Results of astrometrical observations of the Sun and major planets at the mountain astronomical station of the Pulkovo Observatory

A series of daytime observations of the Sun and major planets are obtained at the mountain astronomical station of the Pulkovo Observatory using the Ertel-Struve meridian instruments. A series of declinations of Solar System bodies and major planets includes 4057 positions and that of right ascensions of Solar System bodies comprising 2057 positions. Based on the joint processing of observations of the Sun, Mercury, Venus, and Mars obtained with the Ertel-Struve vertical circle and large transit instrument, the orientation elements of the DE200/LE200 dynamic coordinate system, namely, a correction for the right ascensions of FK5 stars ΔA = +0.127″ ± 0.033″, a correction for declinations of FK5 stars ΔD = +0.056″ ± 0.011″, a correction for the ecliptic inclination Δɛ = −0.044″ ± 0.012″, and a correction for the average longitude of the Sun ΔL = −0.083″±0.035″, are determined with respect to the stellar coordinate system.     

Water and related chemistry in the solar system. A guaranteed time key programme for Herschel

“Water and related chemistry in the Solar System” is a Herschel Space Observatory Guaranteed-Time Key Programme. This project, approved by the European Space Agency, aims at determining the distribution, the evolution and the origin of water in Mars, the outer planets, Titan, Enceladus and the comets. It addresses the broad topic of water and its isotopologues in planetary and cometary atmospheres. The nature of cometary activity and the thermodynamics of cometary comae will be investigated by studying water excitation in a sample of comets. The D/H ratio, the key parameter for constraining the origin and evolution of Solar System species, will be measured for the first time in a Jupiter-family comet. A comparison with existing and new measurements of D/H in Oort-cloud comets will constrain the composition of pre-solar cometary grains and possibly the dynamics of the protosolar nebula. New measurements of D/H in giant planets, similarly constraining the composition of proto-planetary ices, will be obtained. The D/H and other isotopic ratios, diagnostic of Mars’ atmosphere evolution, will be accurately measured in H₂O and CO. The role of water vapor in Mars’ atmospheric chemistry will be studied by monitoring vertical profiles of H₂O and HDO and by searching for several other species (and CO and H₂O isotopes). A detailed study of the source of water in the upper atmosphere of the Giant Planets and Titan will be performed. By monitoring the water abundance, vertical profile, and input fluxes in the various objects, and when possible with the help of mapping observations, we will discriminate between the possible sources of water in the outer planets (interplanetary dust particles, cometary impacts, and local sources). In addition to these inter-connected objectives, serendipitous searches will enhance our knowledge of the composition of planetary and cometary atmospheres.     

Influence of the largest asteroids on the orbital motions of terrestrial planets: application to the Earth and Mars

The level of precision of modern numerical ephemeris of the Solar System necessitates taking into account the gravitational influence of the largest asteroids on the terrestrial planets. This can be done in a straightforward manner when assuming that the mass of the asteroid is well known. Nevertheless, this is rarely the case, even for the largest asteroids. In this paper, we use recent determinations of the masses of Ceres, Pallas, and Vesta to both qualitatively and quantitatively determine the action of these asteroids on the orbital parameters of the Earth and Mars. This is done by the numerical integration by comparing the orbital motions of the perturbed planet when adding or not the perturbing asteroid to the classical 9 bodies problem (the Sun + the eight planets). Some preliminary results are discussed. Published in Russian in Astronomicheskii Vestnik, 2009, Vol. 43, No. 1, pp. 83–86. The text was submitted by the autors in English.     

Simultaneous solution for the masses of the principal planets from analysis of optical,radar, and radio tracking data

The Jet Propulsion Laboratory has developed a set of computer programs known as the Solar System Data Processing System (SSDPS) which is employed in improving the ephemerides of the major planets and for improving the values of several associated astronomical constants. A group of solutions for the masses of the major planets, together with the AU and radii of Mercury, Venus, and Mars, is presented. These solutions based upon optical, radar, and spacecraft radio tracking data are preliminary. The relative power of radar and radio tracking data vis-à-vis purely optical data in a solution is shown. The problems which could arise by adopting solutions based upon a single data type are demonstrated.Presented at IAU Colloquium No. 9, the IAU System of Astronomical Constants' Heidelberg, Germany, August 12–14, 1970.This paper presents the results of one phase of research carried out at the Jet Propulsion Laboratory, California Institute of Technology, under Contract No. NAS 7-100, sponsored by the National Aeronautics and Space Administration.