Chapter 13.1, Problem 36PPSE

Solution

a.

Difference between the days of calendar year and the solar year after 100 years.

The difference between the days of calendar year and the solar year after 100 years is 24.22 days.

Given:

A day is a basic measure of time. A solar year has 365.2422 days.

Calculation:

If every calendar has 365days,

In 100 years the calendar will have,

  $100\times 365=36500$ days.

In Solar calendar there are 365.2422 days, then in 100 years the solar calendar will have,

  $100\times 365.2422=36524.22$ days.

So, the difference between the days of calendar year and the solar year is $36524.22-36500=24.22$ days.

Thus, the difference between the days of calendar year and the solar year after 100 years is 24.22 days.

Conclusion:

The difference between the days of calendar year and the solar year after 100 years is 24.22 days.

b.

Difference between the days of calendar year and the solar year after 100 years if every fourth year has an extra “leap” day added.

Difference between the days of calendar year and the solar year after 100 years if every fourth year has an extra “leap” day added is 0.78 days.

Given:

A day is a basic measure of time. A solar year has 365.2422 days.

Calculation:

If every calendar has 365days and every fourth year has an extra leap day added, then out of 100 years, 25 years will have 366 days and 75 years will have 365 days.

In 75 years the calendar will have,

  $75\times 365=27375$ days.

In 25 years the calendar will have,

  $25\times 366=9150$ days.

In 100 years the calendar will have,

  $27375+9150=36525$ days.

In Solar calendar there are 365.2422 days, then in 100 years the solar calendar will have,

  $100\times 365.2422=36524.22$ days.

So, the difference between the days of calendar year and the solar year is $36525-36524.22=0.78$ days.

Thus, the difference between the days of calendar year and the solar year after 100 years if every fourth year has an extra “leap” day added is 0.78 days.

Conclusion:

Difference between the days of calendar year and the solar year after 100 years if every fourth year has an extra “leap” day added.

c.

Difference between the days of calendar year and the solar year after 100 years if every hundred years the “leap” day is omitted.

Difference between the days of calendar year and the solar year after 100 years is 0.22 days, if every hundred years the “leap” day is omitted.

Given:

A day is a basic measure of time. A solar year has 365.2422 days.

Calculation:

If every calendar has 365days and every fourth year has an extra leap day added but the hundredth year will not be counted as a leap year, then out of 100 years, 24 years will have 366 days and 76 years will have 365 days.

In 76 years the calendar will have,

  $76\times 365=27740$ days.

In 24 years the calendar will have,

  $24\times 366=8784$ days.

In 100 years the calendar will have,

  $27740+8784=36524$ days.

In Solar calendar there are 365.2422 days, then in 100 years the solar calendar will have,

  $100\times 365.2422=36524.22$ days.

So, the difference between the days of calendar year and the solar year is $36524.22-36524=0.22$ days.

Thus, the difference between the days of calendar year and the solar year after 100 years is 0.22 days, if every hundred years the “leap” day is omitted.

Conclusion:

Difference between the days of calendar year and the solar year after 100 years is 0.22 days, if every hundred years the “leap” day is omitted.

d.

The difference between the calendar year and the solar year should be zero.

It is important that the difference between the calendar year and the solar year should be zero.

Given information:

A day is a basic measure of time. A solar year has 365.2422 days.

Explanation:

Every calendar has 365days and the solar calendar has365.2422 days. The difference between the days of calendar year and the solar year is $365.2422-365=0.2422$ days. That means a solar year has 0.2422 more days than a calendar year. If there will be loss of 0.2422 days every year that means every hundred years 24.22 days will be less and every thousand years 242.2 days will be less. If the difference between the calendar year and the solar year will not be zero then there will be the year where the weather will be summer but according to the calendar it will be winter and the calendar will show summer but the weather will be winter. So, the calendar and weather will not match. Therefore, it is important that the difference between the calendar year and the solar year should be zero.