Scaling Laws in Nature: The laws that explain the absence of a magnetic field on Mars and why squirrels can jump so high
We know that the interior of Mars is cooler than the interior of the Earth, but why is that the case? Both planets would have been very hot and fully molten during their formation 4.5 billion years ago, but Mars has cooled down faster than the Earth. One of the main reasons for this is that Mars has a smaller volume to surface area ratio than the Earth. What determines an object’s heat energy and cooling rate? The total heat energy in an object is determined by its temperature and mass. If we assume that the Earth and Mars started off with approximately the same temperature and density, then the energy contained within the planets only depends on their volumes. The rate at which an object loses heat (cooling power) is proportional to its surface area. The volume and surface area of a sphere with radius r is given by: If we divide the volume (total energy) by the surface area (cooling power), the resulting ratio tells us how long it takes for the object to lose its heat. Let’s confirm t...