Abstract
The existence of asteroid pairs, two bodies on similar heliocentric orbits, reveals an. ongoing process of rotational fission among asteroids. This newly found class of objects has not been studied in detail yet.
Here we choose asteroids (6070) Rheinland and (54827) 2001 NQ8, the most suitable pair for an in-depth analysis. First, we use available optical photometry to determine their rotational state and convex shapes.
Rotational pole of Rheinland is very near the south ecliptic pole with a latitude uncertainty of about 10 degrees. There are two equivalent solutions for the pole of 2001 NQ8, either (72 degrees, -49 degrees) or (242 degrees, -46 degrees) (ecliptic longitude and latitude).
In both cases, the longitude values have about 10 degrees uncertainty and the latitude values have about 15 degrees uncertainty (both 3 sigma uncertainties). The sidereal rotation period of 2001 NQ8 is 5.877186 +/- 0.000002. hr.
Second, we construct a precise numerical integrator to determine the past state vectors of the pair's components, namely their heliocentric positions and velocities, and orientation of their spin vectors. Using this new tool, we investigate the origin of the (6070) Rheinland and (54827) 2001 NQ8 pair.
We find a formal age solution of 16.34 +/- 0.04 kyr. This includes effects of the most massive objects in the asteroid belt (Ceres, Pallas, and Vesta), but the unaccounted gravitational perturbations from other asteroids may imply that the realistic age uncertainty is slightly larger than its formal value.
Analyzing results from our numerical simulation to 250 kya, we argue against a possibility that this pair would allow an older age. Initial spin vectors of the two asteroids, at the moment of their separation, were not collinear, but tilted by 38 degrees +/- 12 degrees.