It has been recognized for some time that large reductions in effective gravity can be achieved aboard an orbital spacecraft. As a consequence, many materials science experiments have been conducted in space in order to minimize or eliminate undesirable effects that might result because of convective motions in fluids driven by buoyancy effects. Of particular interest are the low-frequency accelerations caused by the Earth's gravity gradient field, spacecraft attitude motions, and atmospheric drag, since it is known that these can give rise to sustained fluid motion. In order to gain a limited understanding of the effects of these accelerations, the authors examined their magnitude and orientation and, in particular, have calculated the Stokes' motion of a spherical particle in a fluid for various types of spacecraft attitude motions. In addition, the effect of slowly rotating the experimental system relative to the spacecraft has been assessed. For a restricted set of conditions, it is possible to increase the residence time of the particle in the neighborhood of its initial position.
Nomenclature
Dimensional Variables and Parameters
A= effective cross-sectional area of spacecraft, cm 2 = initial value of the osculating (semimajor) axis, cm = aerodynamic drag coefficient = length scale for the spacecraft, cm = gravitational constant, 6.67 X 10~8 dyne-cm 2 -g~2 = 980cms~2 = mass of Earth, 5.96 X 10 27 g = mass of spacecraft, g Q d GC g M 6 R = radius of spherical particle, cm r 0 = distance of spacecraft mass center from origin of geocentric frame S = Stokes' coefficient, s -1 ; = 4.5ii/(p s R 2 ) ft = effective drag coefficient, cm 2 -g~1 y = G c M e , dyne-cm^g" 1 ju, = viscosity of fluid, dyne-cm 2 -s~l Patm = average mass density of atmosphere, g-cm 3 p f = mass density of fluid, g-cm~3 p s = mass density of spherical particle, g-cm~3 P 0 = reference atmospheric mass density, g-cm 3 u e = rate of rotation of experimental frame relative to spacecraft frame co 0 = angular speed for a circular orbit of radius a 0 /*g =10~6gNondimensional Variables and Parameters a, e, w = osculating elements A KK * = rotation of geocentric frame into spacecraft frame F£ = dimensionless force per unit mass representing Earth's gravitational force G KM = gravity gradient tensor (spacecraft frame) G£*M* = gravity gradient tensor (geocentric frame) G a p = gravity gradient tensor (experimental frame) p a = position of origin of spacecraft frame with respect to origin of experimental frame q£* = position of spacecraft mass center with respect to origin of geocentric inertia! frame Q^ = rate °f rotation, = (dR aK /dt)Rp k r 0 (0 = distance of spacecraft mass center from origin of geocentric frame R aK = rotation of spacecraft frame into experimental frame S = dimensionless Stokes' coefficient, = S/(y/al) l/2 x a = position of particle with respect to origin of experimental frame = position of particle with respect to origin of spacecraft frame = position of particle with respect to origin of geocentric inertia! frame = dimensionless a...
