Astronomy & Space Sciences
Title : | Stability and dynamics of granular minor planets during their formation and break-up |
Area of research : | Astronomy & Space Sciences |
Focus area : | Planetary Science |
Principal Investigator : | Prof. Ishan Sharma, Indian Institute Of Technology Kanpur (IITK), Uttar Pradesh |
Timeline Start Year : | 2024 |
Timeline End Year : | 2027 |
Contact info : | ishans@iitk.ac.in |
Details
Executive Summary : | Many minor planets (asteroids, small moons and trans-Neptunian objects) are known to be rubble piles — spinning granular aggregates held together mainly by self-gravity. These objects are meters to kilometers in size. It is remarkable that their very low self-gravity keeps them together. Study of these objects has technological importance (space missions, resources), is crucial for disaster management (asteroid impact) and poses challenging questions (Solar System formation). We will develop detailed mathematical models for two fundamental geophysical processes — formation and break-up — of such rubble-pile minor planets. 1. Formation: Grains in a loose rotating cloud agglomerate due to self-gravity and dissipative collisions. This process may lead to monolithic or bifurcated objects (e.g. asteroid Itokawa), or even separated binaries (e.g. asteroid Antiope). We will employ affine dynamics along with a constitutive law for dense granular gases to follow the agglomeration of a rotating spherical cloud of grains. This will provide us with a sequence of nominal ellipsoidal shapes that a granular cloud will go through as it collapses. However, these nominal ellipsoidal shapes may be unstable to perturbations that are not admitted by the assumption of affine dynamics. Such instabilities, if present, may cause the agglomerating granular cloud to ultimately form a bifurcated non-ellipsoidal shape or even divide into a binary. Stability of the nominal ellipsoidal shapes will be assessed through the method of moments. The ellipsoidal shape will be subjected to increasingly complex, non-ellipsoidal kinematic perturbations. The linearized equations will be then be analyzed for growing eigenmodes. The aggregate’s constitutive law — which depends on the grain’s size, mass and restitution coefficient — and kinetic parameters (e.g. initial angular momentum) will control when the instability is initiated and its severity. Further, we will also directly integrate the full moment equations to follow the dynamical evolution of the granular cloud and test the predictions of the stability analysis. 2. Break-up: Once formed, a rubble pile is a rotating, dense grain collective that does not deform much, but is inherently weaker than a monolithic solid body. Such rubble piles may thus be torn apart due to external effects, e.g tides. To characterize break-up we need to first estimate when yielding is initiated and then check if the body becomes unstable post-yield. So far this is done by finding the average (zeroth moment) bulk stress within the rubble pile and testing for its yielding and post-yield stability to homogenous (first-order) perturbations alone. We will significantly improve this analysis by (a) computing higher moments of the stress distribution and (b) investigating the post-break up stability and dynamics in the presence of high-order kinematic fields. Whenever possible, we will support our predictions by discrete and finite element simulations. |
Total Budget (INR): | 6,60,000 |
Organizations involved