The correct answer is A. I and III only.
Here's the reasoning for each statement:
I. True - In the early stages of solar system formation, a fragment of an interstellar cloud of dust and gas collapsed due to gravity and started to rotate, which is consistent with current models of solar system formation.
II. False - The planets did not orbit another nearby star before becoming part of our solar system. The solar system formed from a solar nebula, and the planets formed from the material within that nebula.
III. True - Gravity played a crucial role in the aggregation of small particles in the solar nebula, allowing them to collide and stick together to form larger bodies, ultimately leading to the formation of planets.
IV. False - The Sun did not get pulled away from a nearby star cluster due to the combined gravities of the planets. The Sun formed in isolation from a solar nebula.
Therefore, only statements I and III are accurate in describing the role of gravity in the formation of our solar system.