Final answer:
The sentence underscores the revolutionary nature of Newton's work, which proposed a single scientific principle of gravity influencing both Earth and the celestial realm, highlighting the unification of heaven and earth under one law.
Step-by-step explanation:
The sentence "With an audacious step in the service of scientific hegemony, Newton united the physics governing both heaven and earth and declared the force of gravity to be the invisible hand at work in each realm" serves to develop a central idea of the text by emphasizing how Sir Isaac Newton's theories on gravity were revolutionary. It highlights his bold approach in proposing a unified scientific principle that applied to both terrestrial objects and celestial bodies, thus bridging the gap between two realms that were previously considered separate under scientific laws. Newton's insight laid the groundwork for modern physics by suggesting that the laws governing motion on Earth also apply to the heavens, leading to the universal law of gravitation.