On September 30, 2016, Jupiter was covered by the Moon. Determine the duration of coverage and the day of the week the event occurred. Confirm your answer with calculations.
Let’s start by defining the day of the week. Since the tour runs on Monday, November 28th, the last day of October (October 31st) was also Monday (28 is evenly divisible by 7). Therefore, October 3 (31−28 = 3) is also Monday, and then you can simply count the days, finding out that September 30 is Friday.
During coverage, Jupiter almost does not move against the background of the stars (because it is far from the Earth), and the duration of coverage is determined by the Moon, which moves along Jupiter. The covering can be, as they say, “central” (when Jupiter passes behind the Moon along its diameter) and in this case, it will obviously be the longest. Let us estimate the duration of the central coverage.
The moon makes one complete revolution across the sky against the background of stars in 27.3 days (this value is called a sidereal month). However, such accuracy is not needed to solve the problem; it is quite enough to assume that it takes a calendar month (i.e., about 30 days). Consequently, in one day it moves by 360◦ / 27.3 = 13◦ (or 12 if the estimate of the sidereal period was more rough). In this case, the angular diameter of the Moon’s disk is about 0.5, and it takes 1/26 (or 1/24) of a day to travel this distance across the sky. Accordingly, the duration of the central coverage is approximately 1 hour, but if the coverage is not central, then it may be less.