Final answer:
Galileo Galilei is the astronomer who wrote Dialogue on the Two Greatest Systems in the World.
Step-by-step explanation:
The astronomer who wrote Dialogue on the Two Greatest Systems in the World is Galileo Galilei. He is known for his contributions to the field of astronomy, including his support for the heliocentric theory proposed by Nicolaus Copernicus. Galileo's observations and writings played a significant role in convincing his scientific contemporaries of the reality of the Copernican theory.