The correct accomplishments and obstacles faced by Galileo are:
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Tried by the Inquisition for his theory of the earth revolving around the sun: This is correct. Galileo faced significant opposition from the Church for his support of heliocentrism, which posited that the Earth revolves around the Sun.
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Discovered that the Milky Way contained innumerable stars clustered together: This is correct. Galileo used his telescope to observe the Milky Way and concluded that it was made up of a vast number of individual stars.
The other two options listed, about developing the theory of universal gravitation and inventing the mathematical field of calculus, are not correct accomplishments of Galileo:
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Developed the theory of universal gravitation: This theory is attributed to Sir Isaac Newton, not Galileo.
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Invented the mathematical field of calculus: Calculus was developed independently by both Isaac Newton and Gottfried Wilhelm Leibniz; Galileo did not invent calculus.
In summary, the correct answers regarding Galileo's accomplishments and obstacles are:
- Tried by the Inquisition for his theory of the earth revolving around the sun.
- Discovered that the Milky Way contained innumerable stars clustered together.