Kepler developed his second law of motion, known as the law of areas, primarily through accurate measurements of the positions of Mars, obtained from the observations of Tycho Brahe. Therefore, the most appropriate choice is:
B. He made accurate measurements of the positions of all the planets over many years.
Kepler's insights were based on the meticulous positional data collected by Brahe, and he analyzed the motion of Mars to derive his laws of planetary motion, including the second law, which states that a line segment joining a planet to the Sun sweeps out equal areas during equal intervals of time.