A Computational Study of the Mechanics of Gravity-induced Torque on Cells

In this paper we use Nace’s previous work in order to model the effects of gravity in cells and similar objects. In the presence of the gravitational field of a primary body, the gravity vector can result in numerous effects, some of which are tension, shear, and finally torque. To model the torque effect we use a complete expression for the gravitational acceleration, as this is given on the surface of a planetary body as well as in orbit around it. In particular, on the surface of the Earth the acceleration is corrected for the effect of oblateness and rotation. In the gravitational acceleration the effect of oblateness can be modeled with the inclusion of a term that contains the J₂ harmonic coefficient, as well as a term that depends on the square of angular velocity of the Earth. In orbit the acceleration of gravity at the point of the spacecraft is a function of the orbital elements and includes, only in our case, the J₂ harmonic since no Coriolis force is felt by the spacecraft. We derive analytical expressions and calculate the resulting torque effects for various geocentric latitudes, as well as circular and elliptical orbits of various eccentricities and inclinations. We find that elliptical polar orbits result in higher torques, and that higher eccentricities result in higher the torque effects. To any measurable extent, our results do not drastically impact any existing biophysical conclusions.