Answer:
The word "protracted" means lasting longer than expected, or unusually long, so what protracted most clearly means based on the context of the excerpt is how the time period of celestial motion studies must have lasted unusually long.
Answer: The quality of being just; righteousness, equitableness, or moral rightness: to uphold the justice of a cause. rightfulness or lawfulness, as of a claim or title; justness of ground or reason: to complain with justice. the moral principle determining just conduct.
D- Disintegration because, “to minimize deterioration” is to minimize something from decaying or in the act of becoming worse or disintegrating