Thoughts on Solution to Spherical Liquid Planet and Pressure problem

Imagine the atoms in the planet as bowling balls (also basically not compressible). Would you rather be under 1, 10, or 100 bowling balls, that is, nearer the surface or nearer the center? Most people would prefer to be under less weight/mass, because the weight (pressure) on them would be less; here, weight is the same as pressure. (The question did not mention temperature, so we can take a temperature as close to 0 Kelvin as we wish, which makes the analogy of the liquid's atoms to a bowling ball, basically not moving, more apt, and removes other possible causes of pressure.) Although gravity in a sphere acts as if all mass were concentrated at the center, because gravitational attraction in all other directions than radially tend to cancel out, the mass actually remains distributed evenly throughout the sphere in this problem, so there is mass/weight to be on top of you if you are within the sphere; you'd prefer as little as possible (less pressure). So intuitively, the pressure is least near the surface and greater at the center. The apparent concentration of all mass at the center means that the gravitational force, which decreases by the square of distance from that point, is greatest nearer the center.

Note by Jed Somit
3 months ago

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