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Physics problem about Earths rotation after 45 centuries

  1. May 24, 2012 #1
    1. The problem statement, all variables and given/known data

    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 45 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.)?


    I have tried and tried again and i keep getting 617 hours which is wrong, please help!
    2. Relevant equations



    3. The attempt at a solution
    45centuries*.001s/century=.045s
    (0s+.045s)/2=.0225 s longer than 1st
    (.0225second/day)(365day/yr)(4500yr)=36956.25 seconds
    (36956.25s)*(1hr/60sec)=615.94hours
     
  2. jcsd
  3. May 25, 2012 #2
    the few mistakes i can see are that you might want to use 365.25 days in a year instead of 365, and also you should do your time in seconds divided by 3600 not 60 (60 seconds in a minute, 60 minutes in an hour)

    so if your time in seconds was right, you would do:
    (36956.25s)*(1hr/60min)*(1min/(60sec) = (36956.25)*(1hr/3600sec) = 10.266 hours.
     
  4. May 25, 2012 #3
    Probably the easiest way is to draw a graph with x axis representing days and y axis representing time increase (you can start y at 0 since you only want time increase). after 36525 the y value is 0.001 (keeping values in day and seconds to make things easier) and at the end of 45 Centuries y value should be .045

    Find out how many days in 45 Centuries and time increase after 45 Centuries. Find the area underneath graph and that would represent time increase in ms over 45 Centuries.

    My calculations show it to be just a bit over 30 Seconds (0.01 Hours which sounds about right, I think :p
     
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