Modeling the sodium potassium droplet interactions with the low earth orbit space debris environment

The NASA/JSC sodium potassium (NaK) RORSAT coolant source and propagation model has been extended to 1 mm in diameter via a size distribution, which is an inverse power law fit that has been modified to damp out in the large size regime. This function matches the observed Haystack NaK population down to diameters of about 6 mm. The extrapolated function takes the population to arbitrarily small sizes all the while retaining the mass dominance of the 1–3 cm droplets that is observed in the Haystack data. This result is physically satisfying since the mechanism of NaK ejection appears to be a nonviolent release at low relative velocities. We propose that any NaK particles smaller than about 1 mm that exist would not be due to that mechanism. Instead, we show that such a population could be the result of subsequent collisions of NaK droplets with larger resident space objects and the micrometeoroid population. Our preliminary analysis shows that collisions between these populations are likely in the time period of 1980 through present-day. Though the result of such collisions is generally unknown it is probable that some ejecta of NaK enter the low Earth orbit (LEO) environment as a result. It is these secondary NaK droplets/particles that we contend are the likely impactors noted on returned surfaces.     

Stability of resonance rotation of a satellite with respect to its center of mass in the orbit plane

The stability of resonance oscillations and rotations of a satellite in the plane of its orbit in the case when the difference of the moments of inertia with respect to the principal axes lying in the orbit plane is small is determined at a given rotation number m by the sign of function Φ_m(e), introduced by F.L. Chernous’ko in 1963. In this paper, convenient analytical representations of functions Φ_m(e) are described in the form of integrals and series of Bessel functions regular at e → 1^?. Values of Φ_m(1) are calculated in explicit form. A theorem about the double asymptotic form of functions Φ_m(e) at m → ∞ and e → 1^? is proved by the saddlepoint method.