How did the search to explain planetary orbits exemplify the scientific method and use of methods?

The answer depends on her definition of the spheres of the earth. You need to know those three sphere definitions before you can answer the question.

Planetary orbit system theories include heliocentric and geocentric theories. Heliocentric theory says the sun is the center of our solar system. Geocentric theory says the earth is the center of our solar system. One aspect of the scientific method is the necessity to suspend judgment in order to entertain the possibility of other answers. This helps us to reduce and minimize the effect of prejudice and emotion as we try to be as logical as possible in our fact gathering. Although we all see the sun rise and fall every day and it appears the earth is flat, it was not until we could suspend judgment and consider other possibilities that we could become more enlightened about the larger picture which includes other planets, the solar system, the galaxy, and the universe. Although it appears the sun orbits the earth, now we know that we orbit the sun. Waxing and waning of moons and planets provide clues to the sun as the center of our solar system and not the earth.

The moon was excised from the earth in a relatively gentle event involving a chain of meteors perforating our ancient equator. The moon then left the earth and succumbed to gravitational influence of the earth so that its one side always faces us as the earth revolves. There was very little angular momentum imparted to the moon when it was created so it left no debris field or ring around the earth and it "locked into phase" with the earth so it does not rotate relative to the earth. The gentleness of the moon's creation also explains why it has no iron from the earths core in it.