Final answer:
The least gravitational potential energy between the prairie dog and Earth would be stored when the prairie dog was resting in its burrow, as it is likely to be at the lowest point relative to Earth's surface.
Step-by-step explanation:
When the question asks about the least gravitational potential energy stored between the prairie dog and Earth, we are looking for the point at which the prairie dog is closest to the reference level, typically Earth's surface. Gravitational potential energy is given by the formula PE = mgh, where PE is potential energy, m is mass, g is the acceleration due to gravity, and h is the height above the reference level. Since the mass of the prairie dog does not change, the gravitational potential energy depends only on the height.
Option A, when the prairie dog was resting in its burrow, would likely be at a lower elevation than the flat field, meaning the prairie dog is closer to the reference level (presumably ground level) and therefore has the least gravitational potential energy. The prairie dog being hungry or stopping in the grass (options B and C) does not affect the gravitational potential energy unless those actions change its vertical position relative to the ground. However, based on the information given, there's no evidence that the prairie dog's elevation changed when it got hungry or when it stopped in the grass.
Therefore, the least gravitational potential energy would be stored when the prairie dog was resting in its burrow (assuming the burrow is below the flat field).