Non-gravitational perturbations, regardless being many orders of magnitude weaker than gravity, hold keys to fully understand the evolution of small Solar System bodies. This is because individual bodies, or their entire groups, manifest traces of a long-term accumulated changes by these effects.

For meteoroids and small asteroids in the 10 cm–10 km size range, the principal non-gravitational force and torque arise from an anisotropic thermal emission of the absorbed solar radiation. Related perturbations of the orbital and rotational motion are called the Yarkovsky and YORP effects.

We review the most important Yarkovsky- and YORP-driven processes, in the Main Asteroid Belt. These include: steady and size-dependent semimajor axis drift, secular changes of rotational period and obliquity, efficient transport towards low-order resonances, interaction with weaker higher-order resonances, captures in secular and spin-orbit resonances.

Many independent observations can be naturally interpreted in the framework of Yarkov-sky/YORP models, like cosmic ray exposure ages of meteorites, current population and size-distribution of near-Earth objects, the existence of unstable resonant asteroids or the structure of asteroid families.

In the next generation surveys, the discovery of moving objects can be successful only if an observation strategy and the identification/orbit determination procedure are appropriate for the diverse apparent motions of the target sub-populations. The observations must accurately measure the displacement over a short interval of time; observations believed to belong to the same object have to be connected into tracklets. Information contained in tracklets is in most cases not sufficient to compute an orbit: two or more of them must be identified to provide an orbit. We have developed a method for recursive identification of tracklets allowing an unbiased orbit determination for all sub-populations and efficient enough to cope with the data flow expected from the next generation surveys. The success of the new algorithms can be easily measured only in a simulation, by consulting a posteriori some “ground truth”.

We present here the results of a simulation of the orbit determination for one month of operations of the future Pan-STARRS survey, based upon a Solar System Model with a downsized population of Main Belt asteroids and a full size populations of Trojans, NEO, Centaurs, Comets and TNO. The results indicate that the method already developed and tested to find identifications of NEO and Main Belt asteroids are directly applicable to Trojans. The more distant objects often require modified algorithms, fitting orbits with only 4 parameters in a coordinate system specially adapted to handle very short arcs of observations. These orbits are mostly used as intermediate results, allowing to find full solutions as more tracklets are identified.

When the number density of detections is as large as expected from the next generation surveys, both joining observations into tracklets and identifying tracklets can produce some false results. The only reliable way to remove them is a procedure of tracklet/identification management. It compares the tracklets and the identifications with a complex logic, allowing to discard almost all the false tracklets and all the false identifications. However, the distant objects still present a challenge for orbit determination: they require three tracklets in separate nights. If this requirement is met we have found no problem in achieving an unbiased orbit determination for all populations. Further work will lead to more advanced simulations, in particular by introducing a realistic model for astrometric and photometric errors.

We examine the origin of water in the terrestrial planets. We list various geochemical measurements that may be used to discriminate between different endogenous and exogenous sources of water. Late stage delivery of significant quantities of water from asteroidal and cometary sources appears to be ruled out by isotopic and molecular ratio considerations, unless either comets and asteroids currently sampled spectroscopically and by meteorites are unlike those falling to Earth 4.5 Ga ago or our measurements are not representative of those bodies. The dust in the accretion disk from which terrestrial planets formed was bathed in a gas of H, He and O. The dominant gas phase species were H2O, He, H2O, and CO. Thus grains in the accretion disk must have been exposed to and adsorbed H2 and water. We examine the efficacy of nebular gas adsorption as a mechanism by which the terrestrial planets accreted “wet”. A simple model suggests that grains accreted to Earth could have adsorbed 1 - 3 Earth oceans of water. The fraction of this water retained during accretion is unknown, but these results suggest that at least some of the water in the terrestrial planets may have originated by adsorption.

The population of small bodies of the outer Solar System is composed by objects of different kind and size, such as comets, Kuiper Belt objects and Centaurs, all sharing however a common characteristic, that is to be rich in ices and other volatiles. The knowledge of the composition and properties of these bodies would help in better understanding the processes that shaped the solar nebula at large heliocentric distances and determined the formation and evolution of the planets. A large number of observational results are now available on these bodies, due to successful space missions and increasingly powerful telescopes, but all our instruments are unable to probe the interiors. However, we are beginning to see how these seemingly different populations are related to each other by dynamical and genetic relationships. In this paper we try to see what could be their thermal evolution and how and when it brings to their internal differentiation. In fact, in this way we can try to foresee what should be the surface expression of their differentiation and evolution and try to link the surface properties, as probed by instruments, with the interior properties. One thing to note about the cometary activity is that it is well interpreted when assuming that the comets are small, fragile, volatile-rich and low-density objects. This view, despite of the strong differences noted in the few comet nuclei observed in situ, has not been disproved. On the other side, the observations of the Kuiper belt objects are possibly indicating that they are large, probably collisionally evolved objects (Farinella & Davis 1996), maybe with larger densities. We are now facing a kind of paradox: we have from one side the comets, and from the other side a population of much denser and larger objects; we know that a dynamical link exists between them, but how can we go from one type of population to another? In this paper the current status of our knowledge on the subject is reviewed, taking into account the results of thermal modeling and the results of observations.

Although it is presently not possible to extract the true composition of a comet nucleus from its coma composition, the distribution of physical and chemical coma properties among comets may be expedient to establish a comet classification scheme that reflects their origin and/or evolution. Most of the coma species visible in the optical were extensively observed in the past. The analysis of these gas coma constituents, mainly daughter products produced for the most part by photolytic destruction of their parent species, is therefore of major importance, if we want to draw conclusions on diversities and similarities of comets in terms of coma composition on a statistically relevant basis. Hundreds of gas and dust production rates are published, but have never been combined into a single database that would allow identifying whether and how the abundances of coma species differ from comet to comet and how they vary with heliocentric distance and with the number of apparitions. A common database can however only be established if the production rates are re-calculated with a common model and set of parameters.

Classically, comets from the outer solar system (beyond the orbit of Neptune), are expected to be icy, and thus active near the Sun, while asteroids in the inner solar system (interior to the orbit of Jupiter) are expected to be relatively ice-deficient, and thus inert. Studies of anomalous objects, most recently 133P/Elst-Pizarro, challenge this classical picture, however, and suggest that either (1) subsurface ice can in fact be preserved over billions of years in small bodies in the inner solar system but still be close enough to the surface to be excavated by an impact by another body, or (2) non-gravitational dynamical evolution (primarily driven by asymmetrical outgassing) of icy bodies from the outer solar system can drive these cometary bodies onto thoroughly asteroid-like orbits, erasing all dynamical signs of their trans-Neptunian origins in the process. The question thus boils down to whether occasionally sublimating icy bodies on stable asteroid-like orbits in the inner solar system, particularly in the main asteroid belt, may in fact be native to the region or whether they must necessarily be recent arrivals.

Over the past 25 years the number of reliably determined rotation rates of asteroids has increased by an order of magnitude, from 157 in 1979 to 1686 in 2005. As the numbers have increased, various special classes and features have emerged. Asteroids larger than $\sim 50 \,\rm{km}$ diameter have a dispersion of spin rates that is well represented by a single Maxwellian distribution. Smaller asteroids have a more dispersed distribution, with both slow and fast spinning populations. We see a “spin rate barrier” in the size range of 1–10 km diameter that suggests that even rather small asteroids are “rubble piles”. Among the very slow rotators are some (but not all) that are “tumbling” in non-principal axis rotation states. Among the smallest asteroids (less than a few hundred m diameter) are some that spin dramatically faster than the “spin barrier”, indicating that they must have some tensile strength rather than consisting of loose regolith. In the last few years it has been recognized that the spins of asteroids smaller than a few tens of km diameter are affected by radiation pressure torques that tend to either speed up or slow down asteroid spin rates, thus providing an explanation for the dispersion of small asteroid spins, and also their non-random axis orientations. Lightcurves have also revealed the presence of binary asteroids among both Near-Earth and Main-Belt populations. Automated robotic observatories and next-generation survey instruments promise to increase the rate of production of asteroid lightcurves so that we may soon have tens of thousands of lightcurve results, extending down to even smaller sizes. In contrast, there are only about 20 rotation rates known for comets, and 15 for TNOs. Very little can be said from such meager statistics; the mean spin rate of TNOs appears to be comparable to that of asteroids, without extremes of fast or slow rotation; the mean spin rate of comets appears to be a bit slower than asteroids, perhaps due to lower mean density, and there may be an excess of slow rotators, probably due to gas jetting effects. The future is promising for studies of these objects as larger telescopes become available to do photometry to fainter magnitudes, so that comet nuclei can be studied at greater heliocentric distance with less coma interference, and more TNOs can be observed.

While the physical characterization of near-Earth objects (NEOs) is progressing at a much slower rate than that of discovery, a substantial body of thermal-infrared data has been gathered over the past few years. A wide variety of taxonomic classes in the NEO population have now been sampled by means of thermal-infrared spectrophotometric observations. The resulting albedo information, together with the distribution of taxonomic types from spectroscopic investigations and the rapidly increasing catalog of orbits and absolute magnitudes derived from NEO search programs, such as LINEAR, facilitates more accurate estimates of the size distribution of the NEO population and the magnitude of the impact hazard. Despite our rapidly increasing knowledge of the NEO population, many questions and uncertainties remain, such as: How does the albedo distribution of NEOs compare with that of main-belt asteroids, and does space weathering play a role? How does the surface structure and regolith coverage of NEOs vary with size and taxonomic type? What fraction of NEOs are extinct comets? A property of particular interest is the surface thermal inertia of small asteroids, which is an indicator of the presence or lack of a thermally-insulating surface layer. Large asteroids can accumulate regolith, but can very small asteroids retain thermally-insulating collisional debris or at least a dust layer? Knowledge of thermal inertia is important for accurate calculations of the Yarkovsky effect, which can significantly influence the orbital evolution of potentially hazardous NEOs, and for the design of instruments for lander missions. Contrary to earlier expectations, evidence appears to be accumulating that even sub-kilometer asteroids often have a significant thermally-insulating surface layer. Recent results from thermal-infrared investigations of NEOs are reviewed and implications for the surface properties of small asteroids discussed.