Final answer:
The heliocentric solar system model, specifically the Copernican model, answered questions such as the behavior of Mercury and Venus near the Sun which could not be explained by the geocentric model. The Big Bang theory is supported by the observation that galaxies are moving away from each other. Earth supports life due to its hydrosphere and atmosphere maintaining life-sustaining conditions.
Step-by-step explanation:
The question regarding the heliocentric solar system model that could not be answered with a geocentric model is: Why do Mercury and Venus always appear near the Sun? The Ptolemaic geocentric model had Earth at the center and could not explain the observed behaviors of Mercury and Venus without adding increasingly complex circles or epicycles. In contrast, the Copernican heliocentric model with the Sun at the center provided a simpler and more accurate explanation, describing the planets, including Mercury and Venus, orbiting the Sun. The Copernican model also predicted Venus would exhibit a full range of phases similar to the Moon, which could not be accounted for in the geocentric model. This was later confirmed with the invention of the telescope.
The Big Bang theory suggests that the universe began from a single point and has been expanding ever since. The evidence to support this includes the observation that galaxies are moving away from each other, which is key to understanding why scientists believe in the Big Bang theory (Option B). Finally, Earth is capable of supporting life primarily because Earth's hydrosphere and atmosphere help maintain the necessary conditions for life (Option A).