Planetary Science

Planets are the most advanced engineering equipment. After all, He made them.

**Ongoing**

**Shapes, stability and interiors of minor planets**

What is an asteroid made of? A chunk of rock? Or, in fact, many chunks sticking together because of their mutual gravitation, i.e. a gravitationally bound granular aggregate? Many people are hedging their bets on the latter. They are late. Uncle Scrooge was there first.

Why should we care? Well, there are a rather large number of these asteroids whose orbits intersect the Earth’s, so that there is a non-vanishing probability that one of them may arrive in your drawing room. That won’t be nice. So, someone, maybe Bruce Willis, may have to blow it up before it hits us. For that, it would be a good idea to know what that object is made of, so that we take up enough TNT. Thus, we would like to know / estimate the strenght and failure characteristics of granular asteroids.

Additionally, knowledge of their internal structure provides clues to the origins of small objects like asteroids, or the inner moons of the giant planets, and, by extension to the origins of the Solar System. And, finally, it is great mechanics -- posing questions that would not arise in routine terrestrial applications, e.g.

- Structural stability of a rotating mass of self-gravitating, frictional grains. Can you use available notions from solid / fluid mechanics? I don't think so (Sharma 2012).
- Bifurcation and failure in such aggregates. How far can you push plasticity theory?
- Can we trace the evolution of the shape of granular aggregates as they take birth from an initial gas cloud? Maybe, see Fig.

**Rings of minor planets : **Recently, some chaps found a ring system about the Centaur Chariklo. This opens up the possibility of small irregular bodies having rings. When can irregular bodies have rings? What will be the dynamics of these rings? Can they be stable? These are the things that bother me. We seek to answer these questions through both theory and simulations.

This research will require/develop familiarity with three-dimensional rigid-body dynamics, granular materials, continuum mechanics and finite/discrete - element methods.

**Dormant**

**Nutational damping:** Goldstein (19.., pp. ) will tell you that a rigid body with internal dissipation will damp into pure rotation about its major principal inertia axis. So? Well, an interesting fact, especially considering their suspected collisional origins, is that asteroids are almost exclusively found in states of pure spin about their maximum inertia axis. This is statistically almost impossible and a majority of asteroids should be found in a tumbling state; unless there is something out there driving asteroids into a state of pure spin about their major principal axis. In fact, they believe that, because nothing in this World is perfect, neither are asteroids. This non-rigidity and general imperfection, caused internal energy dissipation, probably due to cracks opening and closing, or stuff slipping on other stuff, etc. This energy dissipation will then, in accordance with classical predictions, damp the asteroid over time into a state of pure spin.

It is of interest to know over how long this damping takes place, how this damping time-scale depend on the dissipation model, are non-rigid effects on dynamics important, etc. Why? Well planetary for scientists this gives an opportunity to estimate either the age or the interior of the asteroid. Additionally, internal damping is an important controlling tool in artificial satellites, so that this problem finds direct application to the space industry.

This work will require/develop familiarity with three-dimensional rigid-body dynamics, continuum mechanics and finite/discrete - element methods.

**Propellant level gauging for artificial satellites:** It is important to know when a satellite will run out of juice a.k.a propellant. This because in order to cater to our need for a hundred-plus television channels, cable operators have put a huge number of artificial satellites out there. When these satellites run out of fuel, they are mostly junk. Like television. And, there is a lot of junk out there. So much so that orbits are getting congested. Thus, if we could estimate when a satellite is going to run out of fuel, we could take pre-emptive action -- not in the rather violent George Bush sense -- and maneuver this satellite into another, relatively unimportant orbit. However, sensors have proved rather unreliable in relaying accurate information about the amount of fuel in a satellite, and we have to search for an alternate procedure. One option is to relate the effect that the presence of a sloshing liquid fuel has on the dynamics of an otherwise (relatively) rigid spacecraft’s dynamics to the amount of fuel present. This approach holds promise because the attitudinal dynamics of a spacecraft may be very accurately measured. What is required is a good mechanical model of a spacecraft with liquid propellant, including the fuel’s sloshing dynamics, and an ability to correlate observed dynamics of the satellite to controlling parameters in the dynamical model such as the amount of fuel etc.

This work will require/develop familiarity with three-dimensional rigid-body dynamics, continuum mechanics, computational fluid mechanics and estimation methods.

**Related publications**

**Book**

Sharma, I. 2017. Shapes and Dynamics of Granular Minor Planets. Springer.

**Articles**

Sharma, I., J. A. Burns and C. -Y. Hui 2005. Nutational damping in solids of revolution. Mon. Not. R. Astron. **359**, 79-92. pre-print

Sharma, I., Jenkins, J.T., and Burns, J.A. Equilibrium shapes of ellipsoidal soil asteroids, Powders and Grains 2005, 429-432.

Sharma, I., J. T. Jenkins, and J. A. Burns 2006. Tidal encounters of ellipsoidal granular asteroids with planets. Icarus **83**, 312-330. pre-print

Sharma, I., Jenkins, J.T., and Burns J.A., Equilibrium shapes of ellipsoidal soil asteroids, Powders and Grains 2005, 429-432. pre-print

Sharma, I., J. T. Jenkins and J. A. Burns 2009. Dynamical passage to approximate equilibrium shapes for spinning, gravitating rubble asteroids. Icarus **200**, 304-322. pre-print

Sharma, I. 2009. Equilibrium shapes of rubble-pile satellites: The Darwin and Roche ellipsoids for gravitationally held granular aggregates. Icarus **200**, 636-654. pre-print

Sharma, I. 2010. Equilibrium shapes of rubble-pile binaries: The Darwin ellipsoids for for gravitationally held granular aggregates. Icarus **200**, 636-654. pre-print

Sharma, I. 2012. Stability of non-smooth rubble-pile asteroids. J. Fluid Mech. **708**, 71-99. pre-print

Sharma, I. 2013. Structural stability of rubble-pile asteroids. Icarus **223**, 367-382. pre-print

Sharma, I. 2014. Stability of rubble-pile satellites. Icarus **229**, 278-294. pre-print

Sharma, I. 2015. Stability of rubble-pile binaries. Part I: Rigid binaries. Icarus **258**, 438-453. pre-print

Sharma, I. 2016. Stability of rubble-pile binaries. Part II: Rubble-pile binaries. Icarus **277**, 125-140. pre-print

Gupta, A. S. Nadkarni-Ghosh and I. Sharma 2018. Rings of non-spherical, axi-symmetric bodies. Icarus **299**, 97-116.