How to Scientifically Measure How Many Days Are in a Year | Physics Forums (2023)

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How many days are there in a year?

How to Scientifically Measure How Many Days Are in a Year | Physics Forums (1)
Ask pretty much anyone and they will tell you 365, except for leaps years which have 366. In addition, most people can tell you that a year is the amount of time that it takes for the Earth to go once around the Sun, and a day is the amount of time it takes for the Earth to rotate on its axis once. (I say “most”, because, in a survey done too long ago, only 74% of Americans surveyed even knew that the Earth went around the Sun.) Given the fact that leap years occur every four years (with exceptions), it turns out that the Earth rotates ~365.25 times for every trip it makes around the Sun, so you could say that there are ~365.25 days in a year.(The Julian calendar assumed that there were 365.25 days in the year and added a leap year every four years to account for that extra ¼ of a day. And while the Julian calendar has since been replaced with a more accurate one, astronomers still use Julian dates in many of their calculations. In fact, the light-year is the distance light travels in a Julian year.)

However, the above definitions of “day” and “year” are a little vague. One trip around the Sun and one rotation on the Earth’s axis, with respect to what? The reference often used by astronomers is that of the “fixed” stars. If we measure one rotation of the Earth with respect to the stars we call it a “stellar day”. And using the same reference, one trip of the Earth around the Sun with respect to the stars is called a “sidereal year”, from the Latin word “sidus” meaning star. (from this you would think that a rotation of the Earth with respect to the stars would be called a sidereal day, but oddly, a sidereal day is measured with respect to a different reference which we will deal with later on.)

If you measure the Earth’s rotation with respect to the stars you get 86164.098903691 seconds per rotation, and if you do the same for the Earth orbit around the Sun, you get 31558149.76… sec. This means that, with respect to the stars, the Earth rotates 366.25636623 times while it orbits the Sun once. This means that there are 366.25636623 stellar days to the sidereal year This is at least one whole “day” more than the 365.25 we came up with earlier. So where does this difference come from?

You may have noticed that the length of a stellar day differs from what we normally consider as a day of 24 hrs, with 60 min hrs and 60 sec minutes which works out to 86400 sec, and is almost 4 minutes longer than the stellar day. This is because our 24hr clock is based on the “Solar day”, or the time it takes for the Sun to go from noon on one day to noon of the next, and this time period is affected by the Earth’s orbit around the Sun.

In the time it takes the Earth to make one rotation with respect to the stars, the Earth travels a bit under 1 degree around the Sun. So a spot that starts directly under the Sun will not be so 1 stellar day later.

This means that the Earth must continue rotating a bit longer (~ 4 min) to finally return that spot directly under the Sun. So it turns out that 1 solar day equals 1.002737803 stellar days.
( The length of the solar day worked out above is for the “mean” solar day. The Earth does not orbit the Sun in a perfect circle but in an ellipse. Because of this, its orbital and angular speed around the Sun varies over the course of its orbit. It travels faster near perihelion and slower at aphelion. This makes the solar days when the Earth is near perihelion longer than those when we are near aphelion. At present, perihelion occurs in December, so this is when the longest solar days occur. So for those of you in the Northern hemisphere who feel that Winter days seem to drag on while Summer days fly by, you are not entirely incorrect. This will not always be the case, however, as we will learn later.)

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One of the side effects of this difference between the stellar and solar day is that the stars that we see in the night sky change over the course of a year. The Winter night sky will be different from the Summer night sky. In addition, if we could see the stars during the day, the constellation that we would see the Sun in also changes over the course of the year.(This is the basis of astrology. The Sun passes through twelve constellations which are the “signs” of the Zodiac in a year. The constellation in which the Sun is in on your birth date is your Sun sign.)

Sun’s position in Taurus on May 21, 2015

So now we can work out that there are 365.2563662 mean solar days to a sidereal year, which is slightly more than the 365.25 days per year we estimated earlier.

This means that if you wished to create a calendar that kept step with the sidereal year, you could start with the Julian calendar and then “fudge” it to make it more accurate

The Gregorian calendar, which is now used in most of the Western world is a result of such fudging.

The Gregorian calendar is accurate to within 1 day in several thousand years when it comes to keeping the calendar in step with the seasons (The aim of most calendars). To accomplish this, leap days were eliminated on century years that were not evenly divisible by 400. (1900 was not a leap year, but 2000 was.) So every 400 years there are 97 leap days added for a total of 146097 days vs 100 leap days for a total of 146100 with the Julian calendar.

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But hold on. With 365.2563662 days to a sidereal year, in 400 sidereal years, you end up with 146102.5465 days or over 5 days more than accounted for by the Gregorian calendar and 2.5465 days more than accounted for by the Julian calendar. This means if we want to keep step with the sidereal year, then the Julian calendar is a better fit than the Gregorian calendar and in order to make it an even better fit, we would have to add more leaps years not fewer.

But the Gregorian year is a closer fit to the change of the seasons, why is it a worse fit to the sidereal year?

The reason is that the sidereal year and the seasons do not keep in step.

To understand why this is, we need to look into what causes the seasons, and this is the tilt of the Earth’s axis with respect to the Sun.

When the Northern hemisphere leans toward the Sun we have Summer, and when the Northern hemisphere leans away from it we have Winter. The moment the Northern hemisphere is inclined at its greatest to the Sun is called the Summer solstice and when it is inclined away by the greatest amount, it is called the Winter solstice. The Autumn and Spring (or Vernal) equinoxes are when the tilt is neither towards nor away.

The Northernmost line of latitude where the Sun can be directly overhead (during the Summer Solstice) is called the Tropic of Cancer.(so-called because astrologically speaking, the Sun sign at this time is Cancer.) The Southernmost line of latitude where the Sun can be directly overhead during the Winter solstice is the Tropic of Capricorn, so named for the same reason.)

The time period between Vernal equinoxes is called a tropical year. Because during this period the Sun goes from being directly overhead the equator at noon to overhead the Tropic of Cancer, to over the equator, to over the Tropic of Capricorn, and finally back to the equator again. This is also the seasonal year and so the Gregorian calendar is designed to fit the tropical year.

Now if this were all there was to it, and the Earth’s axis always pointed in the same direction with respect to the stars, the seasons would keep in step with the Earth’s trip around the Sun and the tropical year and sidereal year would be equal in length. But as we saw above, this isn’t the case.

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The truth is that the Earth’s axis doesn’t stay fixed with respect to the stars; It “wobbles” like a spinning top. This wobble is called precession.

A spinning top precesses because it is trying to fall over. Gravity pulls on it and applies torque to the axis of rotation. The top, in turn, tries to preserve angular momentum, and the torque is converted to a precession of the axis.

With the Earth, gravity is the culprit also, Both the Sun and Moon (and the other planets to a certain degree) exert a gravitational effect on the Earth, each pulling on the far side a little less than the near side. If the Earth was perfectly spherical, this would not matter, but the Earth is a slightly oblate spheroid. The effect of this gravitational difference across the Earth is that both the Moon and Sun exert a torque on the Earth which tries to align the equatorial bulge with the planes of the respective orbits. The combined torque exerted by both these bodies has the same effect as the gravity trying to topple over the spinning top and causes the spinning Earth to precess.

The resulting precession causes the Earth’s axis to trace out one complete circle with respect to the stars every 25770 years. This means if you started with the Northern hemisphere leaning towards the Sun, after the 12885 sidereal years, the Earth’s axis will also have precessed ~180 degrees with respect to the stars and you will have the Northern hemisphere leaning away from Sun after those 12885 sidereal years.

Thus with a calendar based on the sidereal year, the seasons would slowly drift with respect to the calendar, and you’d eventually have Summer weather occurring in December. The end result is that the tropical year is slightly shorter than the sidereal year, being 365.24219 mean solar days long vs. 365.2563662 mean solar days to a sidereal year. 365.2563662 times 400 equals 146096.876, which is very close to the 146097 days in the Gregorian calendar for the same period, which is why it is such a better fit.

This difference of 0.0141762 days per year also leads to what is known as the precession of the equinoxes. If we compare the relative position of the Earth at the Vernal equinox with respect to the stars, we find that it changes over time.
(And this is why we have both a sidereal and stellar day as I mentioned earlier; the sidereal day is measured with respect to the Vernal equinox and the stellar with respect to the stars, making the sidereal day slightly shorter than the Stellar day)

Further, this means that not only does the night sky change day by day, it also changes over the years. On any given date, the night sky changes slightly from year to year. It isn’t much and isn’t really noticeable from one year to the next, but over the course of an average person’s lifetime it works out to be a shift of a bit over twice the width of the full Moon.

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This also means that the position of the Sun with respect to the stars on a given date as seen from the Earth also changes over the years. In the time since the dates for the astrological signs were established, the Sun has moved an entire Zodiac sign. Thus, during the Summer solstice this year, instead of just entering Cancer as the astrological dates suggest, the Sun is just leaving Taurus and entering Gemini.(So if the Tropic of Cancer had been named today, it would have likely been called the Tropic of Gemini and the Tropic of Capricorn would be the Tropic of Sagittarius).

So if you really wanted to keep the astrological signs in step with the constellation the that Sun is in on a particular day, you would need to shift the dates of the astrological sign by 1 day every 68 years or so.( Another indication of the silliness of astrology, as it does not even keep consistent with its original premise that the sign(constellation) the Sun is in on the day you were born determines your personality.)

So now we can finally answer the question: How many days are in a year?

Considering the 2 different “years”, sidereal and tropical, and 3 different “days”, stellar, solar, and sidereal a list comparing them all would look like this.

365.24219 solar days to a tropical year
365.256363009 solar days to a sidereal year
366.2421544183 stellar days to a tropical year
366.2421900073 sidereal days to a tropical year
366.2563662303 stellar days to a sidereal year
366.2564018207 sidereal days to a sidereal year.

Which pretty much wraps up the question. Except…

Remember earlier when I mentioned that perihelion of the Earth’s orbit occurred in December and that this made Winter days longer? I also said that this will not always be the case. Here’s why:

I already mentioned that the Earth does not orbit in a perfect circle but in an ellipse, with a perihelion and aphelion. The time it takes for the Earth to go from perihelion to perihelion is an “anomalistic year” (because the angular distance between a planet and its last perihelion is called the anomaly). Because the Earth’s orbit is subject to the gravitational tugs of other bodies in the Solar system, it undergoes a precession so that the perihelion shifts a bit over time with respect to the stars. Thus the time it takes for the Earth to go from perihelion to perihelion is just a bit longer than a sidereal year, which in turn is longer than a Tropical year, making the anomalistic year 365.259636 mean solar days long.

This also means that the perihelion date changes slightly from year to year, or by about 1 day every 57 years.
So for those of you lamenting those long Winter days in the Northern hemisphere, take heart, in 10,000 years or so they will be a bit shorter as the perihelion shifts to the Summer months.

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How did we figure out how many days are in a year? ›

Given the fact that leap years occur every four years (with exceptions), it turns out that the Earth rotates ~365.25 times for every trip it makes around the Sun, so you could say that there are ~365.25 days in a year.

How do we know there are 365 days in a year? ›

The Short Answer: It takes approximately 365.25 days for Earth to orbit the Sun — a solar year. We usually round the days in a calendar year to 365. To make up for the missing partial day, we add one day to our calendar approximately every four years.

How do we measure a year astronomically? ›

A year is the time it takes for the earth to revolve around the sun once. A calendar year is 365 days. A solar or tropical year is 365 days, 5 hours, 48 minutes, and 46 seconds. This year is used for most astronomical calculations.

Who accurately calculated the length of a day and a year *? ›

During his time at the Library of Alexandria, Eratosthenes devised a calendar using his predictions about the ecliptic of the Earth. He calculated that there are 365 days in a year and that every fourth year there would be 366 days.

How did ancient civilizations know how long a year was? ›

Celestial bodies — the Sun, Moon, planets, and stars — have provided us a reference for measuring the passage of time throughout our existence. Ancient civilizations relied upon the apparent motion of these bodies through the sky to determine seasons, months, and years.

How did the Romans know how long a year was? ›

Originally, it was based on the moon, not the sun. Lunar calendars take their dates from observed lunar phases -- new moon to full moon and back again. The priests of Rome juggled a shifting 12-month calendar that ran at least ten days behind the solar year.

How is a day determined? ›

The Earth orbits the sun once every 365 days and rotates about its axis once every 24 hours. Day and night are due to the Earth rotating on its axis, not its orbiting around the sun. The term 'one day' is determined by the time the Earth takes to rotate once on its axis and includes both day time and night time.

What determines the length of a day on Earth? ›

How fast Earth spins determines the number of hours in a given day. As Earth orbits the sun it spins about its axis approximately once every 24 hours.

What is the draconic year? ›

A draconic year is 346.620075883 days (346 days, 14 hours, 53 minutes, 54 seconds). The Sothic year is the interval between heliacal risings of the star Sirius (ancient name Sothis).

How do scientists know how many light years away something is? ›

In a vacuum, light travels at 670,616,629 mph (1,079,252,849 km/h). To find the distance of a light-year, you multiply this speed by the number of hours in a year (8,766). The result: One light-year equals 5,878,625,370,000 miles (9.5 trillion km).

How do you measure sidereal days? ›

A measurement of the sidereal day is made by noting the time at which a particular star passes the celestial meridian (i.e. directly overhead) on two sucessive nights. On Earth, a sidereal day lasts for 23 hours 56 minutes 4.091 seconds, which is slightly shorter than the solar day measured from noon to noon.

What is 1 light-year in human years? ›

For most space objects, we use light-years to describe their distance. A light-year is the distance light travels in one Earth year. One light-year is about 6 trillion miles (9 trillion km). That is a 6 with 12 zeros behind it!

What is the scientific meaning of day length? ›

A day is the time period of a full rotation of the Earth with respect to the Sun. On average, this is 24 hours, 1440 minutes, or 86,400 seconds. In everyday life, the word "day" often refers to a solar day, which is the length between two solar noons or times the Sun reaches the highest point.

What is the real duration of a day? ›

On Earth, a sidereal day is almost exactly 23 hours and 56 minutes.

How time was measured in ancient times? ›

Time was measured by sundials and the day split into 12 hours, the length of which varied by the seasons. The calendar was based on lunar months - and a “leap” month had to be added every second year to keep the seasons at the right time. Q.

How did the Egyptians know how long a year was? ›

To solve this problem the Egyptians invented a schematized civil year of 365 days divided into three seasons, each of which consisted of four months of 30 days each. To complete the year, five intercalary days were added at its end, so that the 12 months were equal to 360 days plus five extra days.

How did people know the time 200 years ago? ›

Sundials consisted of a tall vertical or diagonal-standing object used to measure the time, called a gnomon. Sundials were able to measure time (with relative accuracy) by the shadow caused by the gnomon.

What did human civilization look like 10,000 years ago? ›

In the Paleolithic period (roughly 2.5 million years ago to 10,000 B.C.), early humans lived in caves or simple huts or tepees and were hunters and gatherers. They used basic stone and bone tools, as well as crude stone axes, for hunting birds and wild animals.

Who added an extra day to January giving it 31 days instead of 30? ›

In order to fully sync the calendar with the lunar year, the Roman king Numa Pompilius added January and February to the original 10 months. The previous calendar had had 6 months of 30 days and 4 months of 31, for a total of 304 days.

Why did they add January and February? ›

The ancestor of the Gregorian calendar was the first Roman calendar which had some differences: it consisted of 10 months rather than 12. In order to synchronise the calendar with the lunar year, the Roman king Numa Pompilius added 2 more months, January and February.

Did the Romans have an 8 day week? ›

For centuries the Romans used a period of eight days in civil practice, but in 321 CE Emperor Constantine established the seven-day week in the Roman calendar and designated Sunday as the first day of the week.

Who invented the 24-hour day? ›

The ancient Egyptians are seen as the originators of the 24-hour day. The New Kingdom, which lasted from 1550 to 1070 bce, saw the introduction of a time system using 24 stars, 12 of which were used to mark the passage of the night.

Who invented 60 minutes in an hour? ›

Who decided on these time divisions? THE DIVISION of the hour into 60 minutes and of the minute into 60 seconds comes from the Babylonians who used a sexagesimal (counting in 60s) system for mathematics and astronomy. They derived their number system from the Sumerians who were using it as early as 3500 BC.

What happens to the extra 4 minutes in a day? ›

The reason for the nearly 4-minute difference between a sidereal day and a solar day is that in one day, the Earth travels about 1.5 million miles along its orbit. So it takes an extra 4 minutes of rotation to bring us back in line with the sun as compared with the day before.

What is the shortest day on Earth? ›

Take June 29, 2022, which was nearly 1.6 milliseconds under 24 hours, making it the shortest day ever recorded. To those in the know, it came as no surprise, however. For more than half a century, Earth's average rotation has been gradually speeding up, slowly skimming fractions of a millisecond off our days.

What affects the length of the day? ›

As the Earth moves around the Sun, the length of the day changes. The length of day at a particular location on Earth is a periodic function of time. This is all caused by the 23.5-degree tilt of the Earth's axis as it travels around the sun.

Is 1 hour in space 7 years on Earth? ›

No, it is not true that one hour in space is 7 years on Earth. This claim is a popular myth that has been circulating for many years, but it has no scientific basis.

What language do dragons speak? ›

Draconic was the language of dragons. Dragons called their language Glav (meaning "speech/converse"), and it used its own distinct alphabet, called Iokharic.

What language do Dragonborn speak? ›

What language do Dragonborn speak? Dragonborn speak Draconic, an ancient language that is only spoken by those with a connection to the dragons.

Is draconic a real language? ›

Draconic is a language of hard consonants and sibilants that usually sounded like hissing when spoken, like sj, ss, and sv.

Are we alone in our solar system? ›

Observations from the ground and from space have confirmed thousands of planets beyond our solar system. Our galaxy likely holds trillions. But so far, we have no evidence of life beyond Earth.

How can we see 46 billion light years away? ›

The light that travels the longest gets stretched by the greatest amount, and the object that emitted that light is now at a greater distance because the universe is expanding. We can see objects up to 46.1 billion light-years away precisely because of the expanding universe.

How can we see light from 13 billion years ago? ›

We know that light takes time to travel, so that if we observe an object that is 13 billion light years away, then that light has been traveling towards us for 13 billion years. Essentially, we are seeing that object as it appeared 13 billion years ago.

What is celestial time? ›

Astronomers are more interested in the stars and wish to know what stars are above the horizon. As a result they use celestial time or Siderial Time. Definition of Siderial Time: Siderial Time equals the Hour Angle of the Vernal Equinox.

How long is a celestial year? ›

An astronomical year is defined to be exactly 365.25 days (31,557,600 seconds), where days are exactly 24 hours (86,400 seconds) long.

Why is there a 4 minute difference between the solar day and sidereal day? ›

To complete a solar day, Earth must rotate an additional amount, equal to 1/365 of a full turn. The time required for this extra rotation is 1/365 of a day, or about 4 minutes. So the solar day is about 4 minutes longer than the sidereal day. Figure 1: Difference Between a Sidereal Day and a Solar Day.

Do you age in light-years? ›

Five years on a ship traveling at 99 percent the speed of light (2.5 years out and 2.5 years back) corresponds to roughly 36 years on Earth. When the spaceship returned to Earth, the people onboard would come back 31 years in their future--but they would be only five years older than when they left.

How fast is the actual speed of light? ›

Constant Speed

So what does this sentence really mean? Surprisingly, the answer has nothing to do with the actual speed of light, which is 300,000 kilometers per second (186,000 miles per second) through the "vacuum" of empty space.

How far is 31 light-years away? ›

It's only 31 light-years, or roughly 186 trillion miles, away. By human standards, this hardly seems like a short distance. In fact, if a jet could fly that far, it would be a 40 million-year journey.

What is the science behind longer and shorter days? ›

As the Earth circles the Sun during the year, half of the Earth get more or less sunlight than the other half of the Earth. In the summer months, the northern half of the Earth, where we live, tilts towards the Sun. This means we get more sunlight, making the days longer.

What determines how long a year is? ›

A year on Earth is approximately 365 days. Why is that considered a year? Well, 365 days is about how long it takes for Earth to orbit all the way around the Sun one time.

What is it called when the length of day and night are the same? ›

There are days around the time of the equinox, where day and night are equal length. These are called equilux, and when they happens depends on latitude.

How long was a day 1 billion years ago? ›

1.7 billion years ago the day was 21 hours long and the eukaryotic cells emerged. The multicellular life began when the day lasted 23 hours, 1.2 billion years ago. The first human ancestors arose 4 million years ago, when the day was already very close to 24 hours long.

How long was a day 5 billion years ago? ›

After all, how long did a day last when the Earth and the Moon came to be? "At first, the Moon was at a distance of three times the Earth's radius, immediately after the Roche limit. With this distance and the estimated angular momentum, it can be said that the day lasted only 4 hours.

Were days longer in the past? ›

If there just aren't enough hours in the day for you, think of this: Earth's day is longer now than it used to be. A recent study found that 70 million years ago, it was a half-hour shorter than it is now. And as you go even farther into the past, the day gets even shorter.

When did humans start telling time? ›

ACCORDING TO archaeological evidence, the Babylonians and Egyptians began to measure time at least 5,000 years ago, introducing calendars to organize and coordinate communal activities and public events, to schedule the shipment of goods and, in particular, to regulate cycles of planting and harvesting.

How did Egyptians measure time? ›

1500 B.C.), there is evidence that sundials, shadow clocks (12.181. 307), and water clocks (17.194. 2341) were used to measure the passing of the hours. There is no evidence that the Egyptians tracked minutes or seconds, although there are general terms for time segments shorter than an hour.

What are the 3 ancient methods of measuring time? ›

Sundials and water clocks were first used in ancient Egypt from 1500 BC and later by the Babylonians, the Greeks and the Chinese. Incense clocks were being used in China by the 6th century. In the medieval period, Islamic water clocks were unrivalled in their sophistication until the mid-14th century.

When did the year change from 360 days to 365? ›

In 46 B.C., Julius Caesar reformed the calendar by ordering the year to be 365 days in length and to contain 12 months.

Why are there 355 days in a year? ›

According to tradition, the Roman ruler Numa Pompilius added January and February to the calendar. This made the Roman year 355 days long. To make the calendar correspond approximately to the solar year, Numa also ordered the addition every other year of a month called Mercedinus.

Why is there only 28 or 29 days in February? ›

Because Romans believed even numbers to be unlucky, each month had an odd number of days, which alternated between 29 and 31. But, in order to reach 355 days, one month had to be an even number. February was chosen to be the unlucky month with 28 days.

Why was the 13th month removed? ›

Why aren't there 13 months, each with 28 days? There are 13 lunations, each with 28 days, that is the moon's phases around the earth but it doesn't fit exactly in the rotation of the earth around the sun which is 365 days, not 364, so calendars have never matched.

Why do accountants use 360 days in a year? ›

Before calculators and computers, accountants had to perform financial calculations with pencil and paper. A calendar year with 365 or 366 days doesn't divide evenly across the 12 months, so it became standard practice to record interest on accounts payable using a 360-day year, treating each month as 30 days.

What was the 13th month called? ›

The thirteenth month, placed between February and March, would be called Vern, due to its proximity to the vernal equinox and the beginning of spring. (Later versions of the bill dropped the name Vern and replaced it with the month of “Liberty.”)

How did Egyptians track years? ›

The ancient Egyptians used a lunar calendar exclusively until they adopted their solar calendar. The lunar calendar was then used for their religious festivals and rituals, but for their daily lives, the ancient Egyptians used a solar calendar which contained 365 days per year.


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