Because Earth's rotation is gradually slowing, the length of each day increases: The day at the end of 1.0 century is 1.0 ms longer than the day at the start of the century. In 72 centuries, what is the total (in hours) of the daily increases in time (that is, the sum of the gain on the first day, the gain on the second day, etc.)?

total=.001ms/day(365days/yr)*72 years*1s/1000ms*1hr/3600s

check that.

Question, wouldn't it be 720 years? Because 10 years = 1 century.

So .001ms/day ( 365days/yr) * 720 years * 1s/1000ms * 1hr/3600s

Actually 100 years is a century

To calculate the total increase in time over the span of 72 centuries, we need to find the sum of the gains on each day from the start of the first day to the end of the 72nd century.

Given that the day at the end of 1.0 century is 1.0 ms longer than the day at the start of the century, we can calculate the increase in time for each day by multiplying the number of centuries by the increase per day.

1. Calculate the increase per day in milliseconds:
Increase per day = (1.0 ms / 100 years) = 0.01 ms

2. Convert the increase per day into hours:
Increase in hours per day = (0.01 ms * 1 s / 1000 ms * 1 min / 60 s * 1 hour / 60 min * 1 day) ≈ 2.7778e-9 h

3. Calculate the total increase in time over 72 centuries:
Total increase = (72 centuries * 100 years / century) * 365 days / year * Increase in hours per day

Now, let's calculate the total increase in time:

Total increase = (72 * 100 * 365) * 2.7778e-9

Total increase ≈ 2.5265 hours

Therefore, the total increase in time over 72 centuries is approximately 2.5265 hours.