File:Visualization of relevant sets and their distances - two notions of distance for the problem of learning Kepler’s third law of planetary motion from solar-system data and background theory.webp

English: "The numerical data, background theory, and a discovered model are depicted for Kepler’s third law of planetary motion giving the orbital period of a planet in the solar system. The data consists of measurements (m1, m2, d, p) of the mass of the sun m1, the orbital period p and mass m2 for each planet and its distance d from the sun. The background theory amounts to Newton’s laws of motion, i.e., the formulae for centrifugal force, gravitational force, and equilibrium conditions. The 4-tuples (m1, m2, d, p) are projected into (m1 + m2, d, p). The blue manifold represents solutions of fB, which is the function derivable from the background-theory axioms that represents the variable of interest. The gray manifold represents solutions of the discovered model f. The double arrows indicate the distances β ( f ) and ε( f )."