Small near-Earth asteroids (NEAs) (< 20 m) are interesting, because they are progenitors for meteorites in our terrestrial collection. The physical characteristics of these small NEAs are crucial to our understanding of the effectiveness of our atmosphere in filtering low-strength impactors. In the past, the characterization of small NEAs has been a challenge, because of the difficulty in detecting them prior to close Earth flyby. In this study, we physically characterized the 2 m diameter NEA 2015 TC25 using ground-based optical, near-infrared and radar assets during a close flyby of the Earth (distance 128,000 km) in 2015 October 12. Our observations suggest that its surface composition is similar to aubrites, a rare class of high-albedo differentiated meteorites. Aubrites make up only 0.14% of all known meteorites in our terrestrial meteorite collection. 2015 TC25 is also a very fast rotator with a period of 133 +/- 6 s. We combined the spectral and dynamical properties of 2015 TC25 and found the best candidate source body in the inner main belt to be the 70 km diameter E-type asteroid (44) Nysa. We attribute the difference in spectral slope between the two objects to the lack of regolith on the surface of 2015 TC25. Using the albedo of E-type asteroids (50%-60%) we refine the diameter of 2015 TC25 to 2 m, making it one of the smallest NEAs ever to be characterized.

Many topics in planetary studies demand an estimate of the collision probability of two objects moving on nearly Keplerian orbits. In the classic works of Opik and Wetherill, the collision probability was derived by linearizing the motion near the collision points, and there is now a vast amount of literature using their method. We present here a simpler and more physically motivated derivation for non-tangential collisions in Keplerian orbits, as well as for tangential collisions that were not previously considered. Our formulas have the added advantage of being manifestly symmetric in the parameters of the two colliding bodies. In common with the Opik-Wetherill treatments, we linearize the motion of the bodies in the vicinity of the point of orbit intersection (or near the points of minimum distance between the two orbits) and assume a uniform distribution of impact parameter within the collision radius. We point out that the linear approximation leads to singular results for the case of tangential encounters. We regularize this singularity by use of a parabolic approximation of the motion in the vicinity of a tangential encounter.

We use a model of aerosol microphysics to investigate the impact of high-altitude photochemical aerosols on the transmission spectra and atmospheric properties of close-in exoplanets, such as HD 209458 b and HD 189733 b. The results depend strongly on the temperature profiles in the middle and upper atmospheres, which are poorly understood. Nevertheless, our model of HD 189733 b, based on the most recently inferred temperature profiles, produces an aerosol distribution that matches the observed transmission spectrum. We argue that the hotter temperature of HD 209458 b inhibits the production of high-altitude aerosols and leads to the appearance of a clearer atmosphere than on HD 189733 b. The aerosol distribution also depends on the particle composition, photochemical production, and atmospheric mixing. Due to degeneracies among these inputs, current data cannot constrain the aerosol properties in detail. Instead, our work highlights the role of different factors in controlling the aerosol distribution that will prove useful in understanding different observations, including those from future missions. For the atmospheric mixing efficiency suggested by general circulation models, we find that the aerosol particles are small (similar to nm) and probably spherical. We further conclude that a composition based on complex hydrocarbons (soots) is the most likely candidate to survive the high temperatures in hot-Jupiter atmospheres. Such particles would have a significant impact on the energy balance of HD 189733 b's atmosphere and should be incorporated in future studies of atmospheric structure. We also evaluate the contribution of external sources to photochemical aerosol formation and find that their spectral signature is not consistent with observations.