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

TL;DR

This paper presents a simple, physics-based method to estimate the Potato Radius of asteroids by relating it to the maximum height of mountains supported by gravity and elastic properties, accessible to high school students.

Contribution

It introduces a novel, accessible approach to calculating the Potato Radius using basic physics principles without advanced assumptions.

Findings

The Potato Radius is approximately 200-300 km.

Maximum mountain height relates to asteroid gravity and elastic properties.

Method is suitable for educational purposes and introductory astronomy.

Abstract

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 been proposed as a classification for separating asteroids from dwarf planets. The Potato Radius can be calculated from first principles based on the elastic properties and gravity of the asteroid. Similarly, the tallest mountain that a planet can support is also known to be based on the elastic properties and gravity. In this work, a simple novel method of calculating the Potato Radius is presented using what is known about the maximum height of mountains and Newtonian gravity for a spherical body. This method does not assume any knowledge beyond high school level mechanics, and may be appropriate for students interested in applications of physics to astronomy.