Tell you what you didn't know about leap years

Usually, we all know that there are 366 days in leap years and 365 days in ordinary years.

And the year of a leap year is a multiple of 4, not a multiple of 100, but it can be a multiple of 400; but do you know why?

I first popularized a secondary school geography problem back to the year with the year of the stars

The regression year refers to the interval between two consecutive direct rays of the Sun on the Tropic of Cancer

A stellar year is the actual time interval required for the Earth to orbit the Sun

It should be noted here that the stellar year is to choose a fixed point in space, this fixed point can be the sun, can be a star such as the North Star, the earth orbits the sun for a week, and back to this position that we originally chose, relative to the North Star, this time difference is a star year. Simply put, the time it takes for the Earth to rotate 360 degrees around the Sun is a stellar year.

At the moment you are reading this article, the time at this time corresponds to the position of the earth at this time, then the next time the earth reaches this position, this time difference is a regression year, and the Tropic of Cancer is selected in the scientific measurement.

Why are there stellar years and regression years?

This is because the Earth is still spinning as it orbits the Sun, because of the gravitational pull from the Moon (the main) and other planets, and because the Earth itself is not a perfect sphere, so its rotation is not regular, but variable, in Earth science, which is called a "solid tide". Because of the presence of solid tides, the angular velocity of the Earth's crust is about 50 arcs per second slower than the angular velocity of the mantle, which is also the phenomenon of "precession".

Therefore, in the calendar we use the regression year as 1 year of the Earth, and in astrophysics we use the stellar year as 1 year.

1 year of return≈ 365.2422 days

In the usual timing, 1 year = 365 days, ignoring the 0.2422 days in this real regression year, in order to make up for this difference, in the 4th year, by adding a day, that is, adding leap years to balance the difference. In this way, in 4 years, our time is almost equal.

The multiple of 100 must be a multiple of 4, so why is there a "multiple of 100 is not a leap year, but it can be a multiple of 400"?

In order to explain this problem, let's first do a simple math problem:

How many leap years are there between 1 AD and 10,000 AD?

We use the set in middle school mathematics to calculate this problem.

Set A, B, C three sets, respectively

A: Multiples of all 4 in 1 to 10,000

B: Multiples of all 100 in 1 to 10,000

C: Multiples of all 400 in 1 to 10,000 miles

It is easy to know A = 2500, B = 100, C = 25

The painting is ugly

In this set relationship, A contains B and B contains C, then the number of leap years is all the white parts of the picture, that is

The number of leap years

X=A-B+C=2500-100+25=2425

That is, if we stipulate that a leap year is "a leap year is a multiple of 4, not a multiple of 100, but a multiple of 400", then from 1000 to 10000 AD, there will be 2425 leap years in these 10000 years.

That is to say, 2425 days more than the original 365 * 10000 days, on the other hand, because a return time is 365.2422 days, 10000 years will have 365 * 10000 + 2422 days, so that our provision makes the error of 10000 years only 3 days, compared to 10000 years, the error of three days is still very acceptable, and it can be said to be quite accurate.

Here you may have to ask, if there is no such provision, the number of leap years we set before X is equal

X=A=2500 is only 78 days worse than the actual one, so why are there so many regulations?

In fact, no, if you calculate the error, the error of 3 days is only:

Error w=3/3652422=8.214e^(-7)

The error of 78 days is:

w=78/3652422=2.136e^(-5)

The difference between the million level and the million level is obviously a bit too big, which is like the difference between a business loss of 21,360 and a loss of 8.214 million, which is lost in a thousand miles.

This issue brings you leap year knowledge, everyone has to know what kind of knowledge, you can leave a message in the comment area Oh, I hope you pay more attention to Oh