Gregory W. Ojakangas (Drury University/LZ Technology), H. Cowardin (ESCG/Jacobs)
Keywords: Orbital Debris
Abstract:
In order for Active Debris Removal to be accomplished, it is critically important to understand the probable rotation states of orbiting, spent rocket bodies (RBs). However, rotational dynamics is non-intuitive and misconceptions are common. Determinations of rotation and precession rates from light curves have been published that are inconsistent with the theory presented here. In a state of free precession, the total angular momentum of the object is constant, while kinetic energy decreases due to internal friction, approaching rotation about the axis of maximum inertia. For solid internal friction the timescale is hundreds to thousands of years for quality factors of ~100 and assuming metallic rigidities, but for friction in partially-filled liquid fuel tanks we predict that the preferred rotational state is approached rapidly, within days to months. However, history has shown that theoretical predictions of the timescale have been notoriously inaccurate. In free precession, the 3-1-3 Euler angle rates dphi/dt (precession rate of long axis about fixed angular momentum with cone angle theta) and dpsi/dt (roll rate around long axis) have comparable magnitudes until very close to theta=pi/2, so that otherwise the true rotation period is not simply twice the primary light curve period. Furthermore dtheta/dt, nonzero due to friction, becomes asymptotically smaller as theta=pi/2 is approached, so that theta can linger within several degrees of flat spin for a relatively long time. Such a condition is likely common, and cannot be distinguished from the wobble of a cylinder with a skewed inertia tensor unless the RB has non-axisymmetric reflectivity characteristics. For an RB of known dimensions, a given value of theta fixes the relative values of dpsi/dt and dphi/dt. In forced precession, the angular momentum precesses about a symmetry axis defined by the relevant torque. However, in LEO, only gravity gradient and magnetic eddy current torques are dominant, and these cannot cause precession periods shorter than a week, or more likely, months. Thus forced precession is probably not observable over observation campaigns spanning a few days or less. Spin-orbit resonances are likely for low rotation rates approaching the mean motion, possibly causing large deviations between the symmetry axis and the geocentric direction. An expression for the eddy current torque on an arbitrarily rotating cylinder, hitherto not available in the literature, is presented here. Numerical integrations of the equations of motion for a cylindrical RB in LEO with arbitrary initial conditions and subject to eddy current and gravity gradient torques as well as prescribed internal dissipation are in progress. Acknowledgements: This work was produced under NASA contract NNJ05HI05.
Date of Conference: September 11-14, 2012
Track: Orbital Debris