The Yarkovsky effect describes a small but significant force that affects the orbital motion of meteoroids and asteroids smaller than $30-40$ kilometers in diameter. It is caused by sunlight; when these bodies heat up in the Sun, they eventually re-radiate the energy away in the thermal waveband, which in turn creates a tiny thrust. This recoil acceleration is much weaker than solar and planetary gravitational forces, but it can produce measurable orbital changes over decades and substantial orbital effects over millions to billions of years. The same physical phenomenon also creates a thermal torque that, complemented by a torque produced by scattered sunlight, can modify the rotation rates and obliquities of small bodies as well. This rotational variant has been coined the Yarkovsky-O'Keefe-Radzievskii-Paddack (YORP) effect. During the past decade or so, the Yarkovsky and YORP effects have been used to explore and potentially resolve a number of unsolved mysteries in planetary science dealing with small bodies. Here we review the main results to date, and preview the goals for future work.Comment: Chapter to appear in the Space Science Series Book: Asteroids I

We present a technique to adaptively bin sparse data using weighted Voronoi tessellations (WVTs). WVT binning is a generalization of the Voronoi binning algorithm by Cappellari & Copin, developed for integral field spectroscopy. WVT binning is applicable to many types of data and creates unbiased binning structures with compact bins that do not lead the eye. We apply the algorithm to simulated data, as well as several X-ray data sets, to create adaptively binned intensity images, hardness ratio maps and temperature maps with constant signal-tonoise ratio per bin. We also illustrate the separation of diffuse gas emission from contributions of unresolved point sources in elliptical galaxies. We compare the performance of WVT binning with other adaptive binning and adaptive smoothing techniques. We find that the csmooth tool in CIAO versions 1.1-3.1 creates serious artefacts and advise against its use to interpret diffuse X-ray emission.

Radiation recoil (YORP) torques are shown to be extremely sensitive to small-scale surface topography, using numerical simulations. Starting from a set of "base objects" representative of the near-Earth object population, random realizations of three types of small-scale topography are added: Gaussian surface fluctuations, craters, and boulders. For each, the expected relative errors in the spin and obliquity components of the YORP torque caused by the observationally unresolved small-scale topography are computed. Gaussian power, at angular scales below an observational limit, produces expected errors of order 100% if observations constrain the surface to a spherical harmonic order l 10. For errors under 10%, the surface must be constrained to at least l = 20. A single crater with diameter roughly half the object's mean radius, placed at random locations, results in expected errors of several tens of percent. The errors scale with crater diameter D as D 2 for D > 0.3 and as D 3 for D < 0.3 mean radii. Objects that are identical except for the location of a single large crater can differ by factors of several in YORP torque, while being photometrically indistinguishable at the level of hundredths of a magnitude. Boulders placed randomly on identical base objects create torque errors roughly 3 times larger than do craters of the same diameter, with errors scaling as the square of the boulder diameter. A single boulder comparable to Yoshinodai on 25143 Itokawa, moved by as little as twice its own diameter, can alter the magnitude of the torque by factors of several, and change the sign of its spin component at all obliquities. Most of the total torque error produced by multiple unresolved craters is contributed by the handful of largest craters; but both large and small boulders contribute comparably to the total boulder-induced error. A YORP torque prediction derived from groundbased data can be expected to be in error by of order 100% due to unresolved topography. Small surface changes caused by slow spin-up or spin-down may have significant stochastic effects on the spin evolution of small bodies. For rotation periods between roughly 2 and 10 hours, these unpredictable changes may reverse the sign of the YORP torque. Objects in this spin regime may random-walk up and down in spin rate before the rubble-pile limit is exceeded and fissioning or loss of surface objects occurs. Similar behavior may be expected at rotation rates approaching the limiting values for tensile-strength dominated objects.

The Double Asteroid Redirection Test (DART) is a Planetary Defense mission, designed to demonstrate the kinetic impactor technique on (65803) Didymos I Dimorphos, the secondary of the (65803) Didymos system. DART has four level 1 requirements to meet in order to declare mission success: (1) impact Dimorphos between 2022 September 25 and October 2, (2) cause at least a 73 s change in its binary orbit period via the impact, (3) measure the change in binary period to an uncertainty of 7.3 s or less, and (4) measure the momentum transfer efficiency (β) of the impact and characterize the resulting effects of the impact. The data necessary to achieve these requirements will be obtained and analyzed by the DART Investigation Team. We discuss the rationales for the data to be gathered, the analyses to be undertaken, and how mission success will be achieved.

We have measured the stellar kinematic proÐles of NGC 3379 along four position angles, using absorption lines in spectra obtained with the Multiple Mirror Telescope. We derive a far more detailed description of the kinematic Ðelds through the main body of the galaxy than could be obtained from previous work. Our data extend 90A from the center, at essentially seeing-limited resolution out to 17A. The derived mean velocities and dispersions have total errors (internal and systematic) better than^10 km s~1, and frequently better than 5 km s~1, out to 55A. We Ðnd very weak (3 km s~1) rotation on the minor axis interior to 12A and no detectable rotation above 6 km s~1 from 12A to 50A or above 16 km s~1 out to 90A (95% conÐdence limits). However, a Fourier reconstruction of the mean velocity Ðeld from all four sampled PAs does indicate a D5¡ twist of the kinematic major axis, in the direction opposite to the known isophotal twist. The and parameters are found to be generally small over h 3 h 4 the entire observed region. The azimuthally averaged dispersion proÐle joins smoothly at large radii with the velocity dispersions of planetary nebulae. Unexpectedly, we Ðnd sharp bends in the major axis rotation curve, also visible (though less pronounced) on the diagonal position angles. The outermost bend closely coincides in position with other sharp kinematic features : an abrupt Ñattening of the dispersion proÐle, and local peaks in and All of these features are in a photometrically interesting region in h 3 h 4 . which the surface brightness proÐle departs signiÐcantly from an r1@4 law. Features such as these are not generally known in elliptical galaxies owing to a lack of data at comparable resolution. Very similar behavior, however, is seen the kinematics of the edge-on S0 galaxy NGC 3115. We discuss the suggestion that NGC 3379 could be a misclassiÐed S0 galaxy ; preliminary results from dynamical modeling indicate that it may be a Ñattened, weakly triaxial system seen in an orientation that makes it appear round.