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At approximate radii of 200-300 km, asteroids transition from oblong `potato'shapes to spheres. This limit is known as the Potato Radius, and has beenproposed as a classification for separating asteroids from dwarf planets. ThePotato Radius can be calculated from first principles based on the elasticproperties and gravity of the asteroid. Similarly, the tallest mountain that aplanet can support is also known to be based on the elastic properties andgravity. In this work, a simple novel method of calculating the Potato Radiusis presented using what is known about the maximum height of mountains andNewtonian gravity for a spherical body. This method does not assume anyknowledge beyond high school level mechanics, and may be appropriate forstudents interested in applications of physics to astronomy.

Calculating the Potato Radius of Asteroids using the Height of Mt. Everest