The correct answer is I and III only.
Here's a breakdown of each statement:
I. True - In the early stages of solar system formation, the interstellar cloud of dust and gas collapsed under its own gravity, leading to the formation of a rotating disk from which the solar system developed.
II. False - The eight planets were not originally orbiting a nearby star; rather, they formed from the same rotating disk of material surrounding the early Sun.
III. True - Gravity played a crucial role in helping small particles within the rotating solar nebula to stick together, eventually leading to the formation of larger bodies that became planets.
IV. False - The Sun did not get pulled away from a nearby star cluster into the center of the solar system due to the combined gravities of the planets. The Sun formed from the same cloud of material and is the center of the solar system.
Thus, the statements that accurately describe the role of gravity in the formation of our solar system are I and III only.