Find formula for how much longer each day is

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SUMMARY

The gradual slowing of Earth's rotation results in an increase in the length of each day, specifically by 1.0 millisecond per century. Over a span of 53 centuries, the cumulative increase in daily time can be calculated using the formula for the sum of an arithmetic progression. The initial increase is 1.0 ms, and the total increase over 53 centuries amounts to a significant duration that can be expressed in hours.

PREREQUISITES
  • Understanding of arithmetic progression
  • Basic knowledge of time measurement
  • Familiarity with mathematical summation techniques
  • Concept of Earth's rotational dynamics
NEXT STEPS
  • Study the formula for the sum of an arithmetic series
  • Calculate the total increase in time over 53 centuries using the derived formula
  • Explore the implications of Earth's rotational slowdown on timekeeping
  • Research historical data on Earth's rotation and its changes over centuries
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Students in physics or astronomy, mathematicians interested in time measurement, and anyone studying the effects of Earth's rotational dynamics on daily timekeeping.

jja6782
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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 53 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.)?

Dont have a clue where to start...

_James
 
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Try to find formula for how much longer each day is, then try to calculate sum.
 

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