Astronomy Without A Telescope – One Potato, Two Potato

Sometimes it’s good to take a break from mind-stretching cosmology models, quantum entanglements or events at 10^-23 seconds after the big bang and get back to some astronomy basics. For example, the vexing issue of the potato radius. 

At the recent 2010 Australian Space Science Conference, it was proposed by Lineweaver and Norman that all naturally occurring objects in the universe adopt one of five basic shapes depending on their size, mass and dynamics. Small and low mass objects can be considered Dust – being irregular shapes governed primarily by electromagnetic forces. 

Next up are Potatoes, being objects where accretion by gravity begins to have some effect, though not as much as in the more massive Spheres – which, to quote the International Astronomical Union’s second law of planets, has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape. 

Objects of the scale of molecular dust clouds will collapse down into Disks where the sheer volume of accreting material means that much of it can only rotate in a holding pattern around and towards the centre of mass. Such objects may evolve into a star with orbiting planets (or not), but the initial disk structure seems to be a mandatory step in the formation of objects at this scale. 

At the galactic scale you may still have disk structures, such as a spiral galaxy, but usually such large scale structures are too diffuse to form accretion disks and instead cluster in Halos – of which the central bulge of a spiral galaxy is one example. Other examples are globular clusters, elliptical galaxies and even galactic clusters. 

The authors then investigated the potato radius, or R_pot, to identify the transition point from Potato to Sphere, which would also represent the transition point from small celestial object to dwarf planet. Two key issues emerged in their analysis. 

Firstly, it is not necessary to assume a surface gravity of a magnitude necessary to generate hydrostatic equilibrium. For example, on Earth such rock crushing forces only act at 10 kilometres or more below the surface – or to look at it another way you can have a mountain on Earth the size of Everest (9 kilometres), but anything higher will begin to collapse back towards the planet’s roughly spheroid shape. So, there is an acceptable margin where a sphere can still be considered a sphere even if it does not demonstrate complete hydrostatic equilibrium across its entire structure. 

Secondly, the differential strength of molecular bonds affects the yield strength of a particular material (i.e. its resistance to gravitational collapse). 

On this basis, the authors conclude that R_pot for rocky objects is 300 kilometres. However, R_pot for icy objects is only 200 kilometres, due to their weaker yield strength, meaning they more easily conform to a spheroidal shape with less self-gravity. 

Since Ceres is the only asteroid with a radius that is greater than R_pot for rocky objects we should not expect any more dwarf planets to be identified in the asteroid belt. But applying the 200 kilometre R_pot for icy bodies, means there may be a whole bunch of trans-Neptunian objects out there that are ready to take on the title.