Final answer:
Two commas are added to the original text to properly separate the geographical location and appositive phrase, rendering the sentence grammatically correct and easier to read.
Step-by-step explanation:
The corrected text with the necessary commas is: "Astronomer Galileo Galilei, a key figure in the scientific revolution, died in Arcetri, Italy, on January 8, 1642, at age 77." The first comma after "Arcetri" separates the city from the country it is in, while the second comma after "Italy" is used to set off the appositive phrase that provides additional information about the date.
Galileo Galilei was an influential astronomer and a major contributor to the scientific revolution. He is well-known for his improvements to the telescope and his advocacy for the Copernican theory of a heliocentric solar system, which was controversial during his time. His works laid the groundwork for future scientists like Isaac Newton, and his findings in physics, mathematics, and astronomy established principles that have shaped modern science.