Answer to Question 1
According to Einstein's theory of general relativity, compact objects in a binary system will radiate energy in the form of gravitational waves. This energy will cause the orbital radius to decrease, and the orbiting objects to get closer together.
Answer to Question 2
It is assumed that Galileo faced the Inquisition because his book, Dialogo, which confronts the Aristotle/Ptolemaic model of a geocentric universe with the Copernican model of a heliocentric universe. The pope ordered Galileo to face Inquisition after he read a passage in Galileo's book disrespecting his own argument of God's omnipotence.
The Inquisition did not center on his belief in Copernican model, but rather, the trial centered on the instructions given Galileo in 1616 . From his file in the Vatican, his accusers produced a record of the meeting between Galileo and Cardinal Bellarmine that included the statement that Galileo was not to hold, teach, or defend in any way the principles of Copernicus. Therefore, The Inquisition condemned Galileo not for heresy but for disobeying the orders given him in 1616.
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General Mathematics