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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 \(1.0 \mathrm{~ms}\) longer than the day at the start of the century. In 20 centuries, what is the total of the daily increases in time?

Short Answer

Expert verified
The total increase over 20 centuries is 20 milliseconds per day cumulatively.

Step by step solution

01

Calculate the Increase in Each Day's Length

We know that at the end of 1 century, the length of the day increases by 1.0 milliseconds. Thus, the daily increase by the end of each century is 1.0 ms.
02

Determine the Number of Days in 20 Centuries

We need to calculate the number of days in 20 centuries. One century has 100 years. Therefore, 20 centuries have \( 20 \times 100 = 2000 \) years.
03

Calculate Total Number of Days

There are 365 days in a typical year. Assuming no leap years, the total number of days in 2000 years is \( 2000 \times 365 = 730,000 \) days. For leap years, every 4 years an extra day is added, disregarding leap century adjustments (as they don't apply within 2000 years). Calculation with leap years becomes \( 2000 \/ 4 = 500 \) extra days: \( 730,000 + 500 = 730,500 \) days.
04

Calculate Total Increase in Day Length Over 20 Centuries

Since each day within a century increases by a fixed amount every century, we calculate 20 times the century end increase: \( 20 \times 0.001 = 0.020 \) seconds (or 20 ms) of increase for the last day following full centuries. We then add these individual increases for each day cumulatively.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Length of a day
Earth's days are not perfectly uniform in length. The day is defined by how long it takes for the Earth to complete one full rotation on its axis. Due to a variety of factors, including tidal forces exerted by the Moon, this rotation is gradually slowing. As a consequence, the length of a day is increasing over time. Each century, the length of the day increases by about 1 millisecond. This means that after a century, the time it takes for the Earth to complete one rotation is slightly longer, causing an average day that is 1 millisecond longer than it was at the start of the century. This incremental growth might seem small, but it accumulates significantly over extended periods.
Century
A century is a period of 100 years. It serves as a handy time unit in the historical timeline and has significant weight in long-term calculations, especially when we talk about changes in astronomical phenomena or Earth's rotation. In the context of Earth's slowing rotation, calculating the effect over centuries helps in understanding the cumulative nature of the changes. For example, over the span of one century, the increase in the length of a day is 1 millisecond. Over 20 centuries, or 2000 years, this gradual increase continues to build. These calculations provide insights into long-term planetary and timekeeping trends.
Milliseconds
A millisecond is a unit of time equal to one-thousandth of a second 鈴 like a blink, but even faster. Understanding milliseconds is crucial when discussing the changes in Earth's rotation. The 1 millisecond increase in the length of a day each century might seem negligible. However, it has significant implications when accumulated over multiple centuries. For example, over 20 centuries, this 1 millisecond increase adds up to a 20 milliseconds increase in the overall length of each day, emphasizing the tiny yet impactful changes in time over extensive periods.
Time measurement
Time measurement has transcended from sundials to atomic clocks, adapting as our technological advancements progressed. It plays a vital role in organizing human life and understanding natural phenomena. To measure very small changes, such as those observed in the Earth's rotation, accurate and precise time measurement is essential. Atomic clocks, for instance, can measure time in milliseconds and beyond. Each second is subdivided into milliseconds and smaller increments, allowing scientists to detect even the slight changes in day length. Proper time measurement helps in predicting future changes and preparing for their potential impact, which could affect everything from technology to how we plan our daily activities.

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Most popular questions from this chapter

The fastest growing plant on record is a Hesperoyucca whipplei that grew \(3.7 \mathrm{~m}\) in 14 days. What was its growth rate in micrometers per second?

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The micrometer \((1 \mu \mathrm{m})\) is often called the micron. (a) How many microns make up \(1.0 \mathrm{~km} ?\) (b) What fraction of a centimeter equals \(1.0 \mu \mathrm{m} ?\) (c) How many microns are in 1.0 yd?

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